Mathematical model for dynamic cell formation in fast fashion apparel manufacturing stage

Mathematical model for dynamic cell formation in fast fashion apparel manufacturing stage This paper presents a mathematical programming model for dynamic cell formation to minimize changeover-related costs (i.e., machine relocation costs and machine setup cost) and inter-cell material handling cost to cope with the volatile production environments in apparel manufacturing industry. The model is formulated through findings of a comprehensive literature review. Developed model is validated based on data collected from three different factories in apparel industry, manufacturing fast fashion products. A program code is developed using Lingo 16.0 software package to generate optimal cells for developed model and to determine the possible cost-saving percentage when the existing layouts used in three factories are replaced by generated optimal cells. The optimal cells generated by developed mathematical model result in significant cost saving when compared with existing product layouts used in production/assembly department of selected factories in apparel industry. The developed model can be considered as effective in minimizing the considered cost terms in dynamic production environment of fast fashion apparel manufacturing industry. Findings of this paper can be used for further researches on minimizing the changeover-related costs in fast fashion apparel production stage. Keywords Dynamic cell  Labor-intensive  Apparel  Product layout  Changeover  Cost saving Introduction (Mo 2015; Jovanovic et al. 2014; Moretta Tartaglione and Antonucci 2013; Aus 2011). More importantly, Caro and Fast fashion apparels are highly fashionable products with Martı´nez-de-Albe´niz (2015) stated it as a high growth affordable prices in the mid-to-low range, which demands potential area of international apparel business. for quick response and frequent assortment changes In order to remain competitive in dynamic market (Vecchi and Buckley 2016; Elavia 2014; Caro and Martı- conditions of fast fashion apparel industry, the apparel nez-de-Albe´niz 2015; Cachon and Swinney 2011). As manufacturers are under immense pressure to achieve high mentioned by Bhardwaj and Fairhurst (2009), Jovanovic degree of manufacturing flexibility (Caro and Martınez-de- et al. (2014), Memic and Minhas (2011) and Cachon and Albe´niz 2015; Jovanovic et al. 2014). Low manufacturing Swinney (2011), frequent fluctuation of customer demand cost is another important aspect that determines the com- with smaller batch quantities and, short production and petitiveness of manufacturing industries (Bayram and distribution lead-times, are the key characteristics of fast Sahin 2016; Khannan et al. 2016). Hence, it is essential to fashion apparels. Because of the increasing consumer focus on improving manufacturing flexibility while ensur- demand, fast fashion segment in apparel industry has ing low manufacturing cost to survive under volatile mar- shown a rapid growth internationally during past few years ket conditions. Several authors have emphasized the need of improving layout flexibility in order to increase the manufacturing & Gayathri Perera flexibility (Neumann and Fogliatto 2013; Raman et al. upamali28@gmail.com 2009). Incorporating flexible layouts that can accommodate Vijitha Ratnayake dynamic production environments while ensuring mini- vijithar@uom.lk mum manufacturing cost is vital to be competitive in Department of Textile and Clothing Technology, University of Moratuwa, Moratuwa, Sri Lanka 123 Journal of Industrial Engineering International volatile market conditions (De Carlo et al. 2013; Hamedi three apparel manufacturing factories that are currently et al. 2012). manufacturing fast fashion products. These factories use Niakan et al. (2016) and Nouri (2016) suggested product layout in their production environments. Numeri- Dynamic Cellular Manufacturing System (DCMS) as the cal results of developed model show that dynamic cellular most suitable approach in achieving high degree of flexi- layouts lead to significant cost saving when it is applied to bility and agility to manage changes in product mix. volatile production environments that are currently using High degree of manufacturing flexibility can be product layout. achieved by minimizing changeover time between different products (De Carlo et al. 2013; Neumann and Fogliatto 2013; Egilmez et al. 2012). Several authors have stated that Literature review dynamic cellular layouts show promising results in mini- mizing changeover times of industries with volatile CMS design approaches demand conditions (Bayram and Sahin 2016; Dalfard 2013; Asgharpour and Javadian; 2004). Hence, minimization of Group Technology (GT) is one of the most widely used changeover-related cost has become one of the primary approaches in handling shorter product life cycles and high objectives of dynamic cellular layout designs. Furthermore, variety of products with minimum manufacturing costs as stated by Shafigh et al. (2017) about 20–50% of the (Nunkaew and Phruksaphanrat 2013; Rafiei and Ghodsi manufacturing cost is related to material handling. Mini- 2013). GT is a manufacturing philosophy that exploits the mization of material handling cost is the most prominent similarities within a manufacturing system. Under GT, cost function used in available studies on mathematical products with similar design and manufacturing charac- programming of DCMS designs (Sakhaii et al. 2016; teristics are grouped into product families (Rajput 2007) Moradgholi et al. 2016). A well-designed layout can min- and relevant machines that are required to process the imize manufacturing cost through effective minimization product families are grouped into GT cells (Giri and of the material handling costs (Shafigh et al. 2017; Chang Moulick 2016). et al. 2013) CMS is the corresponding feature of GT to the layout of According to Bayram and Sahin (2016), and Kia et al. manufacturing industries. Reduced setup time and cost (2013) cell formation, group layout, group scheduling and required to perform setups, simplified material flows and resource allocation are four basic stages of designing reduced material handling, reduced work-in-progress Cellular Manufacturing System (CMS). As the first step of inventory, reduced throughput time and improved CMS design, Cell Formation (CF) seeks to assign parts to sequencing and scheduling on the shop floor are some of their respective families and grouping the corresponding the most outstanding benefits of CMS (Nunkaew and machines to relevant machine cells. A part family com- Phruksaphanrat 2013; Modra´k 2011; Hachicha et al. 2006). prises of part types having similar manufacturing charac- The main purpose of CMS is to retain benefits of high teristics, product design features, product demand, productivity in product layout and flexibility of process- processing requirements, etc. (Mahdavi et al. 2013; Dalfard oriented layouts (Rajput 2007; Case and Newman 2004). 2013). Construction of part families and machine cells, and As mentioned by Bayram and Sahin (2016), Kia et al. assignment of part families to respective machine cells is (2013) and Mahdavi et al. (2013), designing of a CMS done by optimizing a selected set of performance measures comprise of four stages as CF, group layout, group such as material handling cost, machine setup cost, scheduling and resource allocation. grouping efficacy and exceptional elements (Deep and Cell Formation Problem (CFP) involves grouping Singh 2015; Bagheri and Bashiri 2014; Rafiei and Ghodsi machines and products into families based on their simi- 2013). larities (Rajput 2007). Routing similarities and/or pro- This paper addresses the first stage of CMS design under cessing similarities are used to generate product families. dynamic environment (i.e., CF). This paper presents a These two types of similarities are likely to occur more or mathematical programming model developed for the less independent to each other. In other words, products Dynamic Cell Formation (DCF) that aims to generate that require same operation do not necessarily share similar optimal cells that can minimize the costs of machine routings. Best approach to address the CFP is combining relocation, machine setup and inter-cell material handling both routing and processing similarities such that resultant of production environment with machine reliability issues product family has a set of products with similar operations in a labor-intensive apparel manufacturing industry under and similar routes (Kumar and Moulick 2016). volatile demand conditions of fast fashion apparels. Per- Three main approaches are used to address the CFP formance of the developed model is validated based on (Kahraman 2012; Modra´k 2011; Curry and Feldman 2010). data collected from actual production environments of They are: 123 Journal of Industrial Engineering International 1. Product family identification (PFI), (Balakrishnan and Hung Cheng 2005; Chowdary et al. 2. Machine group identification (MGI), 2005). Furthermore, Marsh et al. (1997) argued that static 3. Product families/machine grouping (PF/MG). cells are associated with low routing flexibility. It will directly deteriorate the layout flexibility (Neumann and In the first approach, initially the product families are Fogliatto 2013). identified by using an appropriate technique. Thereafter, DCMS is introduced to overcome the drawbacks of the machines are allocated to the respective product fam- CMS. As mentioned by Niakan et al. (2016), Deep and ilies. Machine group identification (MGI) approach groups Singh (2016) and Mahdavi et al. (2010), DCF is done by the machines into cells based on routing similarities fol- dividing considered planning horizon into multiple plan- lowed by assignment of product families to the formed ning periods. Instead of using stable product mix and cells. In the third approach, product family formation and demand for entire planning horizon, the dynamic cellular machine grouping are done simultaneously. Out of these, layouts are formed by considering possible variations in the third approach is highlighted as optimum CF method multiple periods (Niakan 2015). These variations require (Kahraman 2012; Mungwattana 2000). reconfiguration of the dynamic cells (Niakan 2015; According to Kia et al. (2013), group layout of CMS Houshyar et al. 2014). Cell reconfigurations are minimized design deals with two aspects as inter-cell layout and intra- by considering all the possible demands in corresponding cell layout. Inter-cell layout determines the location of cells planning horizon and optimizing the selected performance with respect to each other whereas intra-cell layout con- measures for considered planning horizon and defined siders machine arrangement with each cell (Mahdhavi et al. planning periods (Niakan et al. 2016;Su¨er et al. 2010). As 2013). Scheduling of part families is done in third stage of stated by Niakan (2015) and Houshyar et al. (2014), layout CMS design (Kia et al. 2013). Resource allocation stage reconfiguration of dynamic cells is done by switching of consists of assignment of required resources to the cells existing machines between cells, adding new machines to (i.e., man, material and other required tools.). the cells and removing existing machines from cells. Based on the production requirements and desired As stated by Mungwattana (2000), four basic types of design attributes, CMS can be broadly categorized into two production requirement are considered in GT-based cellu- segments as Static Cellular Manufacturing System (SCMS) lar layout designs. They are static, dynamic, stochastic and and Dynamic Cellular Manufacturing System (DCMS) deterministic. Production requirement in any industry can (Niakan et al. 2016; Khannan et al. 2016). be represented by using one or more of these types. Static Designing of a SCMS is done by assuming deterministic production requirement assumes a constant product mix product demand and product mix for the considered plan- and demand for entire planning horizon. There can be ning horizon (Hachicha et al. 2006). In other words, it is either static-deterministic production requirement or static- assumed that the product demand and product mix are stochastic production requirement. In first case, the product known with certainty for the periods in considered plan- mix and demand for entire period is exactly known at the ning horizon. In SCMS, cells that optimize the selected cell formation stage. For the second one, possible product performance measures for all the product demand and mix and demand for the period is known with certain product mix are used for the entire planning horizon con- probabilities. Similarly, dynamic cells incorporate the sidered in SCMS design (Hachicha et al. 2006). possible production requirements in either stochastic or As stated by Houshyar et al. (2014), presently the low deterministic nature (Balakrishnan and Hung Cheng 2005; volume-high variety products with volatile demand and Mungwattana 2000). In both types of product demand, shorter lead-times are popular in most of the industries. dynamic cells form physical grouping of cells based on GT Optimal cells of a particular period may not be optimal for principles while rearranging the cells when necessary. This other periods due to possible variations of production allows the dynamic cellular layouts to retain the flexibility requirements of different product mixes (Niakan et al. through cell reconfiguration on a planned basis and to gain 2016; Deep and Singh 2016). According to Niakan et al. advantages of static cells. Excessive rearrangement of cells (2016), static cells are beneficial if the same product mix is may significantly increase cost of machine movement and manufactured for entire planning horizon or the new lost of production time (Kia et al. 2013). Conversely, products are perfectly matched with existing product increasing robustness for multiple demand scenarios dete- families being manufactured in static cells. Pillai et al. riorates the cell performance due to increased material (2011), Modra´k(2011) and, Marsh et al. (1997) argued that handling. Furthermore, using an inappropriate cell layout the static cells are inflexible for introduction of completely for a particular period may lead to increased reconfigura- new product mix. Introduction of new products to the static tion costs in subsequent periods (Niakan 2015). Designing cells result in deteriorate of the cell performance and process of DCMS aims to obtain optimal cells by balancing eventually cause a major rearrangement of machines these two conflicting scenarios. 123 Journal of Industrial Engineering International Machine-intensive and labor-intensive a biobjective mathematical model for dynamic cell for- mation by considering both machine and operator skill manufacturing cells levels. Niakan et al. (2016) formulated and validated their model by using theoretical data sets. Sakhaii et al. (2016) As mentioned by Egilmez et al. (2012), manufacturing cells can be either machine-intensive or labor-intensive. developed a robust optimization approach for a mixed-in- teger linear programming model to obtain solutions for a Limited operator involvement in operations is the key characteristic of machine-intensive cells. Operators load DCMS with unreliable machines and a production planning the raw material or half-assembled product to the machine, problem in a simultaneous manner. Main considerations of control quality and unload the output from machine. their study are DCFP, inter-cell layout, operator assign- In labor-intensive cells, complete operator involvement ment problem, unreliable machines, alternative process routes and production planning decisions. Objective func- in operations is essential and the output and performance of operation significantly fluctuate based on operator-related tion of the mathematical model developed by Sakhaii et al. (2016) sought to minimize the costs of inter- and intra-cell factors (Zhao and Yang 2011). As mentioned by Su¨er and Dagli (2005), labor-intensive cells consist of lightweight material handling, operator training and hiring, machine relocation, machine breakdowns, inventory holding and small machines and equipments that are easy to relocate. Utilization of the existing machines is encouraged in labor- backorder. The biobjective stochastic model developed by ¨ Zohrevand et al. (2016) addresses human-related problems intensive manufacturing cells (Suer and Dagli 2005). Production/assembly department of apparel industry is in DCFP by considering labor utilization, worker overtime known as highly labor-intensive (Islam et al. 2015; Guo cost, worker hiring/laying-off, and worker cell assignment. Their model seeks to minimize the total costs of machine et al. 2015). According to Zhao and Yang (2011) and Mittlehauser (1997), machines used in production depart- procurement, machine relocation, inter-cell moves, over- time utilization, worker hiring/laying-off, and worker ment of apparel manufacturing factories can be categorized into two types based on the level of operator intervention to moves between cells while maximizing the labor utiliza- tion. The model proposed by Tavakkoli-Moghaddam et al. complete an operation. Fully automatic machines Operators load the raw (2011) is one of the noticeable studies on incorporating human-related factors in cell formation. Their model con- material or half-assembled product to the machine, monitor the quality and unload output from machine. Machines can sists of cell formation problem with two conflicting objectives as; optimizing the labor allocation while maxi- be pre-programmed to operate automatically with little intervention of the operator. Examples for such machines mizing the cell utilization. The developed model is solved are button-hole, bar-tack and pocket sewer machines. using multiobjective particle swarm optimization. Semi-automatic machines Operator should continually attend to control the machine to process a particular Impact of machine breakdowns on DCMS design operation. Machine breakdowns in the system play a major role in determining the available capacity for production. There DCMS design with labor-related issues are two main categories of machine breakdown as; Chronic breakdowns and Sporadic breakdowns. As stated by Ireland Nonlinear integer programming model for dynamic cell formation is developed by Mahdavi et al. (2010) to address and Dale (2001) and Cheng and Podolsky (1996), five common causes of chronic breakdowns are: the problem of operator assignment to cells. Improving operator assignment flexibility concurrently with dynamic 1. Failure to maintain machines, i.e., cleaning and minor cell formation is the main feature of the developed model. repairs, Multiple attributes are considered in their model as; multi- 2. Failure to maintain operating conditions such as period production planning, machine duplication, dynamic temperature, speed, system reconfiguration, machine capacity, available time of 3. Insufficient operator skills such as improper and operators and operator assignment. The objective function erroneous machine handling, seeks to minimize eight cost functions namely; holding 4. Deterioration of machine parts, cost, backorder cost, inter-cell material handling cost, 5. Poor design of machine parts due to wrong materials maintenance and overhead cost of machines, machine and sizes. relocation cost, salary cost, hiring cost and firing cost. In the presence of chronic breakdowns, operators are Mahdavi et al. (2010) emphasized the need of considering able to perform required operations but with reduced speed. operator-related factors in cell design to achieve expected benefits of cellular layouts. Niakan et al. (2016) introduced These breakdowns are continual and may result in minor stoppages that can be repaired within a short time (Ireland 123 Journal of Industrial Engineering International and Dale 2001; Leflar 2001). Neglecting the chronic Two possible machine setup scenarios considered in the breakdowns leads to sporadic breakdowns, which are developed model are: suddenly exposed and unexpected. Badiger and Laxman (i) Machines required for particular operations in (2013) discussed that sporadic breakdowns can cease entire current period are available in dynamic cells of operation and it typically requires major troubleshooting to previous period and it is needed to perform restore the machine to working condition or to replace with different machine settings to use them in current new machine. period. Machine breakdowns restrain the machine availability (ii) Machines required for particular operations in when designing a DCMS (Esmailnezhad et al. 2015; current period are not available in dynamic cells Houshyar et al. 2014). Majority of the previous CMS of previous period and required machine setup design considered 100% machine reliability, which is activities are performed in setup area. practically hard to achieve (Nouri et al. 2014; Saxena and Jain 2011; Chung et al. 2011). As stated by Kannan (2011), Inter-cell material handling cost occurs when a partic- the severity of machine reliability issues is high in CMS. ular part requires a machine that is located outside of the Reason for that is failure of any machine/tools assigned for cell assigned for that part type. a particular cell will halt entire production of the manu- It is assumed that the material handling between oper- facturing cell (Kannan 2011). According to Houshyar et al. ations is done manually without using an automated sys- tem. Labor-intensive cells consist of lightweight small (2014), machine breakdowns have direct influence on due dates and optimal cost of the system. Seifoddini and machines and equipments that are easy to relocate (Su¨er Djassemi (2001) stated that machine breakdowns have and Dagli 2005). Hence, an assumption is made as the greater effect on productivity of entire manufacturing machine movements between two locations are done by operations. Machine breakdowns are a crucial factor that using manual trolleys. According to Heizer (2016) and must be incorporated in designing of CMS (Houshyar et al. Chary (1988) Method Time Measurement (MTM) system 2014; Chung et al. 2011). One of the studies that incor- provides standard times for elements of fixed standard porate variable failure rates of the machines is the model categories of work motions such as reach, move, turn, proposed by Yadollahi et al. (2014). The objective func- grasp. MTM data are widely used when determining the tions of their model are minimizing the purchase cost of standard times of manual operations (Aft 2000). MTM machines, intra-cellular movements and the inter-cellular values are used when calculating the time taken for respective material and machine movements of developed movement costs of materials while minimizing the total repair time for failed machines. model. Development of mathematical programming Model formulation model Mathematical model is formulated to generate optimal Assumptions dynamic cells that can ensure minimum costs of machine relocation, machine setup and inter-cell material handling 1. Each part type has a set of operations that must be in labor-intensive production environments subjected to processed based on the given operation sequence. machine breakdowns. 2. Product mix and respective demand for each part type are known in advance. It is assumed that a specific area is used to perform machine setup activities (if needed). It is referred as setup 3. Each machine has a limited capacity in each period area. In the developed model, excessive machines in par- and it is expressed in minutes. ticular period are stored in setup area. Machines with 4. Each machine is capable of processing more than completed setup activities required for a particular period one operation. are moved from this area to the corresponding cell. Pos- 5. Standard processing times for each operation and sible scenarios of machine relocations in the developed setup times for each machine setup activity are model can be listed as follows: known. 6. All the operators and mechanics are multi-skilled. i) Moving machines between different cells, Hence, no additional training is required during ii) Moving machines between cells and setup area. product changeovers. In the mathematical model development, summation of 7. Multi-skilled operator pool is available to mitigate costs for above two relocations is referred as total machine the effects of absenteeism. relocation cost. 123 Journal of Industrial Engineering International 8. There are no delays due to raw material supply, D : Demand quantity for part type t during period h t;h management failures or power failures. g : Standard processing time for operation n of O ;m t;n i;j 9. Production requirement is dynamic-deterministic. part type t on machine m i;j 10. Cell reconfiguration (if any) involves machine setup U : Time taken to load and unload machine m to/ m i;j i;j activities and machine relocations between and/or from the trolley within the cells. c : Cost per minute value during period h 11. Physical partitioning of the cells is prohibited. u : Time to perform machine setting l on l;m i;j Furthermore, cell reconfiguration does not require machine; m i;j modifications to the buildings. Therefore, other than # : Total number of machines in plant floor during h;m i;j the machine relocation costs, any physical reconfig- period h uration costs (i.e., changes in lighting and ventilation k : Number of turning motions when moving materials systems) are not allowed. between cells 12. Adequate lighting and environmental conditions s : Non - negative random number for corrective i;j required for the operations are provided. repair time of machine m ij 13. Multiple duplicate machines of each type are dF ðÞ h : Breakdown rate of machine m when t;m i;j i;j available. Existing machines at the beginning of processing part type t during period h each period are utilized when developing dynamic X : Capacity of machine m during period h ðgiven h;m i;j cells. Therefore, machine procurement is excluded. i;j in minutesÞ 14. Machine availability is limited due to machine 1 if operation n of part type t requires breakdowns. < x ¼ machine m with setting l 15. Preventive maintenance activities are done outside m ;l;O i;j i;j t;n 0 otherwise the plant floor and it do not affect the numbers of machines available within the floor. 16. Inter-cell material handling cost does not depend on Decision variables the product type. 17. Handling of materials in cells and machine move- Integer variables f : Number of times that an t;m ;m i;j 0 ; 0 i j ments are done manually. operation at machine m immediately follows an operation i;j 18. Cost per unit time for each period is known. at machine m 0 or vice versa i ;j Indices Binary variables h : Index for period; h ¼ 1; 2; ...; H t : Index for part type; t ¼ 1; 2; ...; T 1 if machine m is at machine setup area during period h i;j n : Index for number of operations; n ¼ 1; 2; ...; N d ¼ h;m i;j 0 otherwise O : Index for operation n of part type t t;n i : Index for machine types; i; i ¼ 1; 2; ...; I 1 if machine m is in cell k during period h i;j b ¼ k;h;m i;j j : Index for machine number in each machine type; 0 otherwise j; j ¼ 1; 2; ...; J m : Index for jth machine of machine type i i;j 1 if machine m is with setting l during period h i;j e ¼ l;h;m i;j l : Index for machine setting; l ¼ 1; 2; ...; L 0 otherwise k : Index for cells; k; k ¼ 1; 2; ......; K 1 if machine m is required for operation n of part type t i;j l ¼ m ;O i;j t;n 0 otherwise Input parameters 1 if part type t is assigned to cell k during period h h ¼ t;k;h 0 otherwise T : Number of part types in planning horizon N : Number of operations in each part type I : Number of available machine types J : Number of machines available from each machine Objective function seeks to minimize the summation of total machine relocation cost, machine setup cost and inter- type H : Number of periods in planning horizon cell material handling cost. Formulation of objective L : Number of available machine settings function and constraints of developed mathematical pro- gramming model are discussed hereafter. 123 Journal of Industrial Engineering International O m Mathematical model H K T;N I;J XXXX g :D :l :b t;h k;h;m O ;m m ;O i;j t;n i;j i;j t;n h¼1 k¼1 t¼1 i¼1 MinðÞ EMRC þ MSC þ EMHC ð1Þ n¼1 j¼1 0 1 h;m i;j EMRC ¼ MRC þ MRC ð1:1Þ A B m I;J B C b : X  s :dF ðÞ h ð5Þ m @ A H K K I;J  k;h;m h;m m t;m i;j i;j i;j i;j XXXX i¼1 MRC ¼ 1  b 0 1  b : A k ;h;m k;ðÞ hþ1 ;m 0 i;j i;j j¼1 h¼1 k¼1 k ¼1 i¼1 0 L I;J j¼1 k6¼k XX u ; 8k l;m i;j b :b 0 : U þ 0:0102dis 0 :c k;h;m k ;ðÞ hþ1 ;m m k;k i;j i;j i;j ðÞ hþ1 l¼1 i¼1 j¼1 ð1:2Þ H K K I;J XXXX h ¼ 1; 8k; h ð6Þ t;k;h MRC ¼ 1  b 1  b 0 :d : B k;h;m k ;h;m h;m i;j i;j i;j t¼1 h¼1 k¼1 k ¼1 i¼1 j¼1 k6¼k H; R; K; f  0 and integer; 8h; k; t; m ð7Þ t;m m 0 0 i;j i;j i ;j b : U þ 0:0102dis :c k;ðÞ hþ1 ;m m k;D i;j i;j ðÞ hþ1 d ; x ; b ; e ; l ; h 2fg 0; 1 ð8Þ h;m m ;l;O k;h;m l;h;m t;k;h i;j i;j t;n i;j i;j m ;O i;j t;n ð1:3Þ The objective function is shown in Eq. (1). Detailed m O H K I;J L L T;N XXXXXX description of each cost term and constraint is presented MSC ¼ b :l : k;ðÞ hþ1 ;m i;j m ;O i;j t;n h¼1 k¼1 i¼1 l¼1 l ¼1 t¼1 hereafter. ð1:4Þ j¼1 ¼1n l6¼l EMRC is the total cost for following activities during 0 0 x :e :e :u 0 :c m ;l ;O l ;ðÞ hþ1 ;m l;h;m i;j t;n i;j l ;m ðÞ hþ1 layout reconfigurations. i;j i;j P ij C C O h k k tn T XXXXXX • Loading machine to the manually operated trolley EMHC ¼ D :b :l : t;h k;h;m i;j m ;O i;j t;n • Transporting machine to required locations 0 0 t;n t h i6¼i k k6¼k • Unloading machine from manually operated trolley j6¼j 0 0 b :l :f : 0:0102dis þ 0:02232k : Mital et al. (2017) and Karger and Bayha (1987) stated k ;h;m t;m ;m k;k 0 0 m ;O 0 i ;j 0 0 i;j ; 0 i ;j t;ðÞ nþ1 i j that walking time per foot value when transporting 0 0 c 8i 6¼ i ; j 6¼ j ð1:5Þ machines using manually operated trolleys in obstructed paths is 17 TMU (Time Measurement Unit) or 0.0102 min Subject to: as per MTM systems. Total machine relocation cost for TNðÞ 1 considered planning periods is calculated by Eq. (1.1). f ¼ l :l þ l :l ; t;m m 0 0 i;j m ;O m 0 0 ;O m 0 0 ;O m ;O i ;j i;j t;n i ;j t;ðÞ nþ1 i ;j t;n i;j t;ðÞ nþ1 Equation (1.2) calculates the machine relocation cost n¼1 between cells, whereas machine relocation cost between 0 0 8t; m [ m i ;j i;j cells and setup area is calculated by Eq. (1.3). ð2Þ Specific setup activities must be performed when two m m K I;J I;J XX X operations can be processed at same machine but with #  b þ d ; 8m ; k; h ð3Þ h;m k;h;m h;m i;j i;j i;j i;j different machine settings in consecutive periods. Total i¼1 i¼1 k¼1 machine setup time when converting from one machine j¼1 j¼1 0 1 setting to another is used to calculate machine setup cost m O m O I;J T;N K I;J T;N for each machine. If the machine requires same setting for XX XXX B C B C D :g ¼ D :g ; t;h t;h two consecutive periods, no setup activity for such O ;m O ;m t;n i;j @ t;n i;jA ð4Þ i¼1 t¼1 k¼1 i¼1 i¼1 machines is performed. Machine setup cost for considered j¼1 n¼1 j¼1 j¼1 planning periods is calculated as given in Eq. (1.4). 8m ; k; h ij 123 Journal of Industrial Engineering International Operators’ walking between cells will possibly restrict optimal number of cells with maximum machine due to movement of other operators and machines. As stated utilization. by Mital et al. (2017) and Karger and Bayha (1987), walking The part processing on machines is limited by available time per foot is 17.0 TMU (0.0102 min) for obstructed paths machine capacity for a particular period. In ideal situation, the and 37.2 TMU (0.02232 min) per turn. Inter-cell material total machine capacity, i.e., shift operating time can be utilized handling cost is calculated as given in Eq. (1.5). for part processing. Practically, machine capacities are limited Equation (2) determines the number of times that an due to possible machine breakdowns and setup activities. operation at machine m immediately follows an operation Using shift time as the available machine capacity is erroneous i,j 0 0 at machine m . in this situation. Constraint given in Eq. (5) limits the part i ;j Equation (3) guarantees that the total number of processing capability of all machine types based on total machine capacity available for individual machine types. machines in plant floor should be greater than or equal to summation of number of machines in cells and setup area In case of labor-intensive manufacturing industries, simultaneous processing of multiple different part types for a particular period. It prevents additional machine procurement when generating dynamic cells. within a single cell will lead to forgetting effect, compli- cated supervision and increased machine stoppages due to In a dynamic production environment, it is possible to have fluctuations of product demand during different variable machine settings. Hence, the maximum number of part types assigned to a single cell is limited to one at a periods. Workload for the production environment must be balanced among the cells to prevent possible complications time by using Eq. (6). arise due to unbalanced workload. One of the possible Equations (7) and (8) are used to define integer and binary variables. issues due to unbalanced workload is operators assigned to different cells may get different workloads and thereby Linearization of the proposed model have different incentive ceilings. It may result in operator frustration due to feel of unfairness. Developed model The developed model is nonlinear due to the terms (1.2), considers three main approaches of cell workload balanc- ing based on possible demand fluctuations. If the product (1.3), (1.4) and (1.5) of the objective function, the con- straints Eq. (2), and Eq. (5). demand for particular period is significantly lower than other periods of considered planning horizon, two 0 For the term (1.2), the nonlinear term 1  b : k ;h;m i;j approaches are considered to balance the cell workload. 1  b :b :b 0 can be linearized by k;h;m k;ðÞ hþ1 ;m k ;ðÞ hþ1 ;m i;j i;j i;j First approach is reducing number of operating cells by Eqs. (9)–(14) and is replaced by the variable w 0 . m ;k;k ;h;ðÞ hþ1 disintegrating the existing cells from previous period and i;j forming minimum number of cells in current period. Since 0 0 0 w ¼ 1  b : 1  b :b :b m ;k;k ;h;ðÞ hþ1 k ;h;m k;ðÞ hþ1 ;m k;h;m k ;ðÞ hþ1 ;m i;j i;j i;j i;j i;j the developed model assumes existing machines are used ð9Þ to generate dynamic cells, first approach will lead to machine idling in the particular period. Second approach is w 0  1  b 0 ð10Þ m ;k;k ;h;ðÞ hþ1 k ;h;m i;j i;j to operate with reduced workload that is equally distributed among available machines of the period. This will lead to w 0  1  b ð11Þ m ;k;k ;h;ðÞ hþ1 k;ðÞ hþ1 ;m i;j i;j underutilization of cells. If the workload for particular w  b ð12Þ period is not less than other periods, third approach is used m ;k;k ;h;ðÞ hþ1 k;h;m i;j i;j to balance the workload among optimum the number of 0 0 w  b ð13Þ m ;k;k ;h;ðÞ hþ1 k ;ðÞ hþ1 ;m i;j i;j cells, while ensuring maximum resource utilization. Workload balancing constraint, Eq. (4) is formulated to w 0  1  b 0 þ 1  b þ b m ;k;k ;h;ðÞ hþ1 k ;h;m k;ðÞ hþ1 ;m k;h;m i;j i;j i;j i;j address those three approaches. By using Eq. (4), it is þ b 0  4:5 ð14Þ k ;ðÞ hþ1 ;m possible to customize the workload balancing among cells i;j as per the desired approach. The factor q 2 [0, 1] where, The nonlinear term of the term (1.3), {q =0 B q B 1} is used to determine the extent of 1  b 1  b :d :b was linearized k;h;m k ;h;m h;m i;j i;j i;j k;ðÞ hþ1 ;m i;j workload balance between the dynamic cells. Setting by replacing it from the variable x as given by k;h;m i;j q & 0 while simultaneously reducing the number of Eqs. (15)–(20). operating cells (K), corresponds to the first approach used when total workload leads to underutilized resources. x ¼ 1  b 1  b 0 :d :b ð15Þ k;h;m k;h;m k ;h;m h;m k;ðÞ hþ1 ;m i;j i;j i;j i;j i;j Second approach can be satisfied by setting q & 0 with x  1  b ð16Þ k;h;m k;h;m i;j i;j unchanged number of cells. Third approach considers q & 1 with equally distributed workload while operating 123 Journal of Industrial Engineering International a  l þ l  1 ð38Þ x  1  b 0 ð17Þ k;h;m m ;O m ;O k;h;m k ;h;m i;j 0 0 i;j i;j i;j t;n i ;j t;ðÞ nþ1 x  d ð18Þ v ¼ l :l ð39Þ k;h;m h;m i;j i;j k;h;m i;j m 0 0 ;O m ;O i ;j t;n i;j t;ðÞ nþ1 x  b ð19Þ k;h;m k;ðÞ hþ1 ;m i;j i;j v  l ð40Þ k;h;m i;j m 0 0 ;O t;n i ;j x  1  b þ 1  b 0 þ d k;h;m k;h;m k ;h;m h;m i;j i;j i;j i;j v  l ð41Þ k;h;m i;j m ;O i;j t;ðÞ nþ1 þ b  4:5 ð20Þ k;ðÞ hþ1 ;m i;j v  l þ l  1 ð42Þ k;h;m i;j m 0 0 ;O m ;O t;n i;j i ;j t;ðÞ nþ1 0 0 b :l :x :e :e is the non- k;ðÞ hþ1 ;m m ;l ;O l ;ðÞ hþ1 ;m l;h;m i;j m ;O i;j t;n i;j i;j i;j t;n l :b the nonlinear term in Eq. (5) can be replaced linear term in (1.4) of the objective function. It was k;h;m m ;O i;j i;j t;n replaced by y as given in Eqs. (21)–(27). by as given in Eqs. (43)–(46). k;h;m i;j y ¼ b :l :x :e 0 :e k;h;m m ;l ;O l;h;m b ¼ l :b ð43Þ i;j k;ðÞ hþ1 ;m m ;O i;j t;n l ;ðÞ hþ1 ;m i;j k;h;m i;j i;j t;n i;j k;h;m m ;O i;j i;j i;j t;n ð21Þ b  l ð44Þ k;h;m m ;O i;j i;j t;n y  b ð22Þ k;h;m k;ðÞ hþ1 ;m i;j i;j b  b ð45Þ k;h;m k;h;m i;j i;j y  l ð23Þ k;h;m i;j m ;O i;j t;n b  l þ b  1 ð46Þ k;h;m k;h;m m ;O i;j i;j i;j t;n y  x ð24Þ k;h;m m ;l ;O i;j i;j t;n Equation (47) determines the values of defined variables y  e 0 ð25Þ k;h;m l ;ðÞ hþ1 ;m for linearization. i;j i;j y  e ð26Þ w ; x ; y ; z ; a ; b 2fg 0; 1 k;h;m l;h;m k;h;m k;h;m k;h;m k;h;m k;h;m i;j i;j i;j i;j i;j i;j i;j k;h;m i;j ð47Þ y  b þ l þ x þ e 0 k;h;m m ;l ;O i;j k;ðÞ hþ1 ;m m ;O i;j t;n l ;ðÞ hþ1 ;m i;j i;j t;n i;j þ e  5:5 l;h;m i;j ð27Þ Solution approach Nonlinear term The cell formation problem is considered as NP-hard b :l :b 0 :l :f of the term k;h;m m ;O k ;h;m 0 0 m ;O t;m ;m 0 i;j i;j t;n i ;j 0 0 i;j ; 0 i ;j t;ðÞ nþ1 i j (nondeterministic polynomial hard) combinatorial opti- (1.5) is linearized by replacing it by z as given in k;h;m i;j mization problem due to solution complexity (Bayram and Eqs. (28)–(34). Sahin 2016; Rodriguez Leon et al. 2013). Due to solution complexity, manual computation to obtain solutions may z ¼ b :l :b :l :f ð28Þ k;h;m k;h;m k ;h;m 0 0 t;m ;m 0 i;j i;j m ;O m 0 0 ;O i;j i;j t;n i ;j t;ðÞ nþ1 ; 0 i ;j i j produce erroneous results. z  b ð29Þ k;h;m k;h;m LINGO, CPLEX and GAMS are the most commonly i;j i;j used software packages to obtain optimal solutions for z  l ð30Þ k;h;m m ;O i;j i;j t;n mathematical programming models (Agrawal et al. 2015; z  b ð31Þ k;h;m k ;h;m 0 0 Esmailnezhad et al. 2015; Anbumalar and Raja Chandra i;j i ;j Sekar 2015; Pinheiro et al. 2016; Azadeh et al. 2015; z  l ð32Þ k;h;m i;j m ;O 0 0 i ;j t;ðÞ nþ1 Kasimbeyli et al. 2010). The developed model is solved by generating a program z  f ð33Þ k;h;m t;m ;m 0 i;j i;j ; i j code using Lingo 16.0 software package. z  b þ l þ b 0 þ l k;h;m k;h;m m ;O k ;h;m 0 0 m ;O i;j i;j i;j t;n i ;j 0 0 i ;j t;ðÞ nþ1 ð34Þ þ f  5:5 t;m ;m 0 i;j ; 0 i j Model evaluation and validation The nonlinear terms l :l and m ;O m 0 0 ;O i;j t;n t;ðÞ nþ1 i ;j l :l are replaced by a and v , Detailed description of the factories selected k;h;m k;h;m m 0 0 ;O m ;O i;j i;j i ;j t;n i;j t;ðÞ nþ1 for the evaluation and validation respectively. Linearization is given in Eqs. (35)–(42). of the developed model a ¼ l :l ð35Þ k;h;m i;j m ;O m 0 0 ;O i;j t;n t;ðÞ nþ1 i ;j Case studies on three different apparel manufacturing a  l ð36Þ k;h;m i;j m ;O i;j t;n factories were selected for the evaluation and validation of a  l ð37Þ k;h;m i;j m 0 0 ;O the developed model. The program code generated on i ;j t;ðÞ nþ1 Lingo 16.0 software package is used to identify the optimal dynamic cells for the collected data from factories. These 123 Journal of Industrial Engineering International factories are referred as Factory 1, 2 and 3. Data collection types used for model validation in factory 1, 2 and 3 are was done in production/assembly department. given in Table 1. Semi-automatic sewing machines are used in majority of Initially, the developed model was evaluated by using the apparel manufacturing plants for past few decades data collected from Factory 1. According to the initial (Zhao and Yang 2011). Therefore, operator should be evaluation based on Factory 1, the developed model continually attended to control the machine to process a resulted in 31.12% of total costs saving for the considered particular operation. According to the analysis done by three cost terms. After the initial evaluation the model was Zhao and Yang (2011) and Moll et al. (2009), over 90% of validated by using data collected from Factory 2 and 3. the operations in production department of apparel industry is done by using semi-automatic machines. Similar situa- Numerical example tion is observed in the selected factories for case studies. Percentage of semi-automatic machines used in production Outputs of the developed system are presented by using a department of factory 1, 2 and 3 are 95.7, 92.0 and 98.1, numerical example by considering data collected from respectively. All the selected factories are currently using factory 2 for 11 part types with 15 machine types. Input product layouts with machine sharing in their production data used for the numerical example are given in ‘‘Ap- environments. pendix A’’. Part families and respective part types of optimal solu- Model validation procedure tions for the numerical example are given in Table 2. Table 3 shows part types and their respective dynamic cells with The values of cost terms used in objective function number of machines of each machine type during two peri- (Sect. 3.1.5) are calculated from the collected data on ods. Assigned machine numbers of each machine type to the current layouts. Thereafter, these total cost values of cur- respective dynamic cell are given in Table 4. Corresponding rent layouts are used to calculate the cost-saving percent- cost saving is 34.60% for the given numerical example. age when applying the obtained optimal dynamic cells for same data sets. Cost-saving percentage is calculated by formula given in Eq. (48). Results and discussion T  T L D Cost saving percentage ¼  100% ð48Þ Resultant cost-saving percentages for individual cost terms and total cost of the objective function for factory 1, 2 and where T summation of considered cost terms of current 3 are given in Table 5. layout system, T optimal cost value for objective function Table 2 Resultant part families of developed model. Part family Part type (t) and corresponding part types Criteria used for evaluating and determining the validity 1 2,5,4 of developed model is as follows. 2 6, 10, 1, 3 T  T L D 3 8,7,9 if  100% [ 0 model is validated. Otherwise, model is invalid in mini- Table 3 Part types and their respective dynamic cells with number of machines of each machine type mizing cost terms. Developed model was evaluated and validated by tk h Number of machines of type i incorporating the total cost of machine relocations, 123 45678910111213 machine setups and material handling calculated for the currently used product layouts in selected factories. Sum- 2 11131 411200 0000 mary of the number of part types and number of machine 5 22131 420200 0000 4 31131 033200 0000 6 41210 321232 0000 Table 1 Number of part types and machine types used for model 10 51120 211222 0001 validation 1 62111 231222 0000 Factory Number of part types Number of machine types 3 72231 302311 0000 8 81101 121201 1221 121 13 7 92010 034211 0111 211 15 9 102211 012100 1120 318 12 123 Journal of Industrial Engineering International Table 4 Assigned machines of each machine type to the respective dynamic cell k Assigned machines of each machine type (m ) i,j 1 2 3 4 56 78 9 1011 12 13 1 1 9 11 1,5,6,11 1 15 3, 4 0 0 0 0 0 0 2 12 26, 10, 16 12 2, 17, 28, 14 16, 14 0 2, 5 0 0 0 0 0 0 3 18, 13 13, 8, 6 7 0 10, 11, 13 2, 3, 5 1, 8 0 0 0 0 0 0 4 2 1 0 12, 15, 18 2, 3 6 16, 6 13, 10, 1 2, 6 0 0 0 0 5 10 21, 22 0 16, 20 9 8 12, 7 18, 21 16, 10 0 0 0 4 6 11, 20 11 5 25, 19 7, 8, 12 7 14, 18 11, 8 4, 9 0 0 0 0 7 23 14, 12, 23 18 3, 7, 10 0 12, 16 11, 15, 16 2 1 0 0 0 0 8 16 0 2 9 26, 4 9 13, 22 0 10 2 12, 5 2, 5 1 9 0 2 0 0 5, 6 10, 15, 17, 18 20, 10 14 8 0 1 3 2 10 21, 17 4 13 0 18 2 17 0 0 18 14 22, 1 0 volume and low product variety. Kumar and Suresh (2006) Table 5 Cost-saving percentages of selected factories and, Nunkaew and Phruksaphanrat (2013) mentioned that Factory 1 2 3 two of the key problems of product layout are high cost of layout reconfiguration and lack of flexibility. According to Total machine relocation (%) 30.29 39.87 56.05 the results given in Table 5, the optimal dynamic cells Machine setup (%) 34.10 23.49 29.61 generated from developed model can surpass the product Inter-cell material handling (%) 28.41 47.66 37.48 layouts in minimizing the considered cost terms. Therefore, Total cost of the objective function (%) 31.12 34.60 47.14 it is encouraged to use the developed model to mitigate the drawbacks of product layout in dynamic production Minimized costs of manufacturing including change- environment. overs and shorter manufacturing lead-times are essential to remain competitive in fast fashion apparel industry. Several researchers have addressed the issues related with supply Future research directions chain management and retailing decisions of fast fashion apparel products in order to achieve the demanded shorter According to Bayram and Sahin (2016), Kia et al. (2013) lead-times (Sabet et al. 2017; Orcao and Perez 2014; Shen and Mahdavi et al. (2013), cell formation, group layout, 2014; Zhelyazkov 2011; Zhenxiang and Lijie 2011; Mihm group scheduling and resource allocation are four basic 2010). As the fast fashion apparel segment is introduced stages of designing CMS. This paper is focused on first recently, there exists a significant gap in the available lit- stage of CMS design and the developed model can be erature on production layout systems applicable for fast extended to remaining three stages. fashion orders (Kentli et al. 2013). The developed model is tested for three selected facto- Lago et al. (2013) and Johnson (2003) stated that manu- ries in apparel industry. It is expected to validate the facturing lead-time can be drastically reduced by decreasing developed model for other labor-intensive manufacturing changeover time between different products. Positive values industries in future. of cost-saving percentage (Table 5) imply that the dynamic In the developed model, it is assumed that all the operators cells generated from developed model are capable of and mechanics in production environment are multi-skilled improving the current layout system with respect to the and processing time of each operation is a predefined stan- considered cost terms. It is possible to conclude the validity dard value. As stated by Badiru (2013) and, Mir and Reza- of developed model in minimizing the considered cost terms eian (2016), the distribution of skill levels, degree of for fast fashion apparel products manufactured in dynamic workforce cross-training, impact of individual operators’ production environment of labor-intensive apparel industry. learning and forgetting characteristics, motivational issues Hence, the developed model can be used to address the and attitudes, absenteeism rates, operator turnover rates, prevailing gap of literature on a layout system appropriate for frequency of product revisions, and workforce assignment fast fashion products. patterns are some of the important factors that determine the As stated by Malakooti (2014), product layout or performance of the system. The present research can be assembly line layout is suitable for products with high extended by considering such operator-related issues. 123 Journal of Industrial Engineering International Open Access This article is distributed under the terms of the Creative Forghani et al. (2013) and Suresh and Kay (2012) Commons Attribution 4.0 International License (http://creative emphasized that the maximum benefits of cell layout are commons.org/licenses/by/4.0/), which permits unrestricted use, dis- only achievable by incorporating production control, pro- tribution, and reproduction in any medium, provided you give cess planning, wage payment, accounting, purchasing, appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were material handling systems and determining staff level. As made. stated by Duncan (2011), significant reduction of change- over time can be achieved by scheduling of similar prod- ucts to cells that are processing same product families. As a Appendix A future research direction, it is possible to consider these factors when designing dynamic cells for volatile product See Tables 6, 7, 8, 9, 10 and 11. demand and product mix. Table 6 Required machine tO (i) t,n types for operations of part types 1 234567 8910 11 12 13 14 15 16 1145235 6 47858 9 9 7 2341522 7 44627 4 3236417 7 41274 8 9 6 2 4712576 3 52526 6 5173422 4 24755 4 6241596 1 48757 8 8 9 4 7258 13 57 9 126756 6116 8 4 7 11 5 12 3 9 7 12 11 5 10 1 6 13 96 11 135 12 7 1 5 12 106 10 482976 7 1 13 485 9 2 Table 7 Total number of machines of each machine type i 12345678910 11 12 13 J 15 21 12 20 23 20 20 11 14 2587 Table 8 Time for machine setting on each machine type l u l;m i;j 123 456 78910 11 12 13 1 13 12 4 3 9 4 20 2 17 15 12 17 14 2 112 39 16 583 12 6 148 8 317 14 1886 1138 1555 18 11 4 2 15 13 10 13 12 17 7 15 8 20 6 9 5 1016 7 11 16 715201214 1117 7 6 7 3 5 15 3 16 17 3 19 3 4 18 8 7 20 15 4 5 9 8 18 7 12 17 7 19 10 8 181312 9 813 5 41211 16 5 19 9 3 14 17 11 18 14 8 17 19 16 20 9 5 10 11 15 11 11 17 4 13 20 4 2 5 4 9 11 8 8 18 6 4 16 18 16 16 14 19 4 7 12 2 20 17 2 7 3 15 13 18 9 20 20 3 123 Journal of Industrial Engineering International Table 9 Demand data for hD t,h considered two periods in example 12 34 567 89 10 1 1906 1780 1257 2125 2191 1677 482 1730 2147 2245 1 1982 669 2421 553 578 481 2239 2110 1207 869 Table 10 Standard processing time of each operation of part types tO (g ) t,n O m t;n i;j 12 345 67 8910 11 12 13 14 15 16 1 0.62 0.67 3.01 1.30 0.89 0.63 1.02 1.23 0.48 2.21 1.45 1.53 2.34 1.20 1.26 2 1.12 2.31 0.23 3.01 0.55 0.28 1.41 2.01 1.15 1.11 1.03 2.11 0.36 3 2.0 1.08 2.10 1.22 2.03 0.41 0.89 2.03 0.39 1.05 2.31 2.61 1.55 2.46 1.25 3.06 4 2.11 2.53 1.53 1.33 1.25 2.15 2.45 1.64 1.36 1.36 1.68 3.02 1.55 5 3.33 1.35 2.01 0.23 0.89 0.92 0.59 2.82 1.22 0.66 1.32 1.40 1.28 6 0.69 2.13 0.88 2.03 2.30 1.35 2.01 2.22 2.36 2.89 2.65 2.36 3.01 1.23 1.99 2.69 7 2.98 3.66 3.48 4.33 1.32 3.11 2.89 2.36 1.32 1.65 3.21 2.35 3.33 3.21 3.01 8 1.02 2.31 2.31 1.35 3.02 2.37 2.33 3.12 3.02 2.03 2.03 3.14 1.02 3.08 1.56 9 1.23 3.33 2.09 2.19 1.20 3.02 3.12 0.23 1.25 0.59 3.0 2.99 10 1.32 1.56 3.06 2.31 2.03 1.09 2.85 1.10 1.11 2.22 1.21 0.97 1.55 1.35 Table 11 Breakdown rates of each machine for considered periods jdF ðÞ h t;m t i;j 123 456 789 10 11 12 13 1 1.60E-03 8.93E-05 4.58E-03 7.57E-04 1.02E-03 0.00E?00 1.23E-04 0.00E?00 2.59E-03 7.94E-05 9.24E-05 3.78E-04 5.36E-04 2 4.84E-03 1.94E-03 0.00E?00 4.75E-04 9.88E-04 7.74E-04 6.95E-05 2.34E-04 6.27E-04 7.82E-04 2.19E-03 9.48E-04 2.19E-03 3 1.42E-03 5.55E-04 6.45E-04 5.24E-04 3.91E-03 0.00E?00 2.38E-04 6.52E-04 7.21E-04 4.11E-04 5.49E-04 1.54E-03 4 8.71E-05 5.66E-04 1.00E-03 8.60E-04 0.00E?00 1.54E-03 8.19E-04 0.00E?00 2.86E-03 8.77E-04 7.37E-04 4.33E-04 5 3.55E-04 2.82E-04 4.67E-04 7.39E-04 9.12E-05 4.49E-04 8.78E-04 1.07E-03 1.58E-04 4.49E-04 1.77E-03 3.77E-04 6 7.74E-04 3.61E-04 6.84E-04 1.07E-03 8.60E-04 5.08E-04 4.22E-04 0.00E?00 2.89E-04 3.31E-04 6.41E-04 7 3.18E-03 1.81E-04 8.37E-04 9.89E-04 3.92E-04 6.57E-04 2.62E-03 8.32E-03 2.70E-04 7.60E-04 8 3.23E-03 8.22E-04 1.51E-03 5.86E-04 4.60E-04 3.02E-04 3.83E-04 0.00E?00 9.92E-04 4.92E-03 9 5.63E-04 1.15E-04 0.00E?00 1.36E-03 2.02E-04 0.00E?00 3.24E-04 2.23E-03 7.73E-04 10 1.45E-03 4.28E-04 6.16E-04 6.08E-04 9.67E-04 4.57E-04 1.46E-03 4.18E-03 4.26E-04 11 8.01E-05 1.49E-03 6.92E-04 1.21E-03 1.60E-03 3.95E-03 9.76E-04 0.00E?00 8.98E-04 12 7.04E-04 4.44E-03 6.15E-03 1.95E-03 2.26E-03 7.12E-04 6.08E-04 0.00E?00 13 1.42E-03 3.16E-03 6.53E-04 1.33E-03 1.90E-03 5.89E-04 7.65E-04 14 1.06E-03 8.76E-04 1.56E-04 1.25E-03 4.80E-04 1.11E-04 1.15E-03 15 5.75E-04 7.30E-03 5.41E-04 2.39E-03 3.36E-04 2.67E-04 16 1.19E-03 1.57E-03 0.00E?00 4.89E-04 9.98E-04 17 8.58E-04 0.00E?00 5.26E-04 9.12E-04 1.31E-03 18 7.94E-05 5.24E-04 0.00E?00 0.00E?00 6.81E-04 19 9.21E-04 1.18E-03 7.50E-05 5.56E-03 0.00E?00 20 8.50E-04 7.15E-04 4.17E-04 8.80E-04 1.77E-04 21 3.25E-04 6.57E-04 22 2.24E-03 23 1.85E-03 123 Journal of Industrial Engineering International Dalfard VM (2013) New mathematical model for problem of dynamic References cell formation based on number and average length of intra and intercellular movements. 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Mathematical model for dynamic cell formation in fast fashion apparel manufacturing stage

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Engineering; Industrial and Production Engineering; Quality Control, Reliability, Safety and Risk; Facility Management; Engineering Economics, Organization, Logistics, Marketing; Mathematical and Computational Engineering
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10.1007/s40092-018-0275-5
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Abstract

This paper presents a mathematical programming model for dynamic cell formation to minimize changeover-related costs (i.e., machine relocation costs and machine setup cost) and inter-cell material handling cost to cope with the volatile production environments in apparel manufacturing industry. The model is formulated through findings of a comprehensive literature review. Developed model is validated based on data collected from three different factories in apparel industry, manufacturing fast fashion products. A program code is developed using Lingo 16.0 software package to generate optimal cells for developed model and to determine the possible cost-saving percentage when the existing layouts used in three factories are replaced by generated optimal cells. The optimal cells generated by developed mathematical model result in significant cost saving when compared with existing product layouts used in production/assembly department of selected factories in apparel industry. The developed model can be considered as effective in minimizing the considered cost terms in dynamic production environment of fast fashion apparel manufacturing industry. Findings of this paper can be used for further researches on minimizing the changeover-related costs in fast fashion apparel production stage. Keywords Dynamic cell  Labor-intensive  Apparel  Product layout  Changeover  Cost saving Introduction (Mo 2015; Jovanovic et al. 2014; Moretta Tartaglione and Antonucci 2013; Aus 2011). More importantly, Caro and Fast fashion apparels are highly fashionable products with Martı´nez-de-Albe´niz (2015) stated it as a high growth affordable prices in the mid-to-low range, which demands potential area of international apparel business. for quick response and frequent assortment changes In order to remain competitive in dynamic market (Vecchi and Buckley 2016; Elavia 2014; Caro and Martı- conditions of fast fashion apparel industry, the apparel nez-de-Albe´niz 2015; Cachon and Swinney 2011). As manufacturers are under immense pressure to achieve high mentioned by Bhardwaj and Fairhurst (2009), Jovanovic degree of manufacturing flexibility (Caro and Martınez-de- et al. (2014), Memic and Minhas (2011) and Cachon and Albe´niz 2015; Jovanovic et al. 2014). Low manufacturing Swinney (2011), frequent fluctuation of customer demand cost is another important aspect that determines the com- with smaller batch quantities and, short production and petitiveness of manufacturing industries (Bayram and distribution lead-times, are the key characteristics of fast Sahin 2016; Khannan et al. 2016). Hence, it is essential to fashion apparels. Because of the increasing consumer focus on improving manufacturing flexibility while ensur- demand, fast fashion segment in apparel industry has ing low manufacturing cost to survive under volatile mar- shown a rapid growth internationally during past few years ket conditions. Several authors have emphasized the need of improving layout flexibility in order to increase the manufacturing & Gayathri Perera flexibility (Neumann and Fogliatto 2013; Raman et al. upamali28@gmail.com 2009). Incorporating flexible layouts that can accommodate Vijitha Ratnayake dynamic production environments while ensuring mini- vijithar@uom.lk mum manufacturing cost is vital to be competitive in Department of Textile and Clothing Technology, University of Moratuwa, Moratuwa, Sri Lanka 123 Journal of Industrial Engineering International volatile market conditions (De Carlo et al. 2013; Hamedi three apparel manufacturing factories that are currently et al. 2012). manufacturing fast fashion products. These factories use Niakan et al. (2016) and Nouri (2016) suggested product layout in their production environments. Numeri- Dynamic Cellular Manufacturing System (DCMS) as the cal results of developed model show that dynamic cellular most suitable approach in achieving high degree of flexi- layouts lead to significant cost saving when it is applied to bility and agility to manage changes in product mix. volatile production environments that are currently using High degree of manufacturing flexibility can be product layout. achieved by minimizing changeover time between different products (De Carlo et al. 2013; Neumann and Fogliatto 2013; Egilmez et al. 2012). Several authors have stated that Literature review dynamic cellular layouts show promising results in mini- mizing changeover times of industries with volatile CMS design approaches demand conditions (Bayram and Sahin 2016; Dalfard 2013; Asgharpour and Javadian; 2004). Hence, minimization of Group Technology (GT) is one of the most widely used changeover-related cost has become one of the primary approaches in handling shorter product life cycles and high objectives of dynamic cellular layout designs. Furthermore, variety of products with minimum manufacturing costs as stated by Shafigh et al. (2017) about 20–50% of the (Nunkaew and Phruksaphanrat 2013; Rafiei and Ghodsi manufacturing cost is related to material handling. Mini- 2013). GT is a manufacturing philosophy that exploits the mization of material handling cost is the most prominent similarities within a manufacturing system. Under GT, cost function used in available studies on mathematical products with similar design and manufacturing charac- programming of DCMS designs (Sakhaii et al. 2016; teristics are grouped into product families (Rajput 2007) Moradgholi et al. 2016). A well-designed layout can min- and relevant machines that are required to process the imize manufacturing cost through effective minimization product families are grouped into GT cells (Giri and of the material handling costs (Shafigh et al. 2017; Chang Moulick 2016). et al. 2013) CMS is the corresponding feature of GT to the layout of According to Bayram and Sahin (2016), and Kia et al. manufacturing industries. Reduced setup time and cost (2013) cell formation, group layout, group scheduling and required to perform setups, simplified material flows and resource allocation are four basic stages of designing reduced material handling, reduced work-in-progress Cellular Manufacturing System (CMS). As the first step of inventory, reduced throughput time and improved CMS design, Cell Formation (CF) seeks to assign parts to sequencing and scheduling on the shop floor are some of their respective families and grouping the corresponding the most outstanding benefits of CMS (Nunkaew and machines to relevant machine cells. A part family com- Phruksaphanrat 2013; Modra´k 2011; Hachicha et al. 2006). prises of part types having similar manufacturing charac- The main purpose of CMS is to retain benefits of high teristics, product design features, product demand, productivity in product layout and flexibility of process- processing requirements, etc. (Mahdavi et al. 2013; Dalfard oriented layouts (Rajput 2007; Case and Newman 2004). 2013). Construction of part families and machine cells, and As mentioned by Bayram and Sahin (2016), Kia et al. assignment of part families to respective machine cells is (2013) and Mahdavi et al. (2013), designing of a CMS done by optimizing a selected set of performance measures comprise of four stages as CF, group layout, group such as material handling cost, machine setup cost, scheduling and resource allocation. grouping efficacy and exceptional elements (Deep and Cell Formation Problem (CFP) involves grouping Singh 2015; Bagheri and Bashiri 2014; Rafiei and Ghodsi machines and products into families based on their simi- 2013). larities (Rajput 2007). Routing similarities and/or pro- This paper addresses the first stage of CMS design under cessing similarities are used to generate product families. dynamic environment (i.e., CF). This paper presents a These two types of similarities are likely to occur more or mathematical programming model developed for the less independent to each other. In other words, products Dynamic Cell Formation (DCF) that aims to generate that require same operation do not necessarily share similar optimal cells that can minimize the costs of machine routings. Best approach to address the CFP is combining relocation, machine setup and inter-cell material handling both routing and processing similarities such that resultant of production environment with machine reliability issues product family has a set of products with similar operations in a labor-intensive apparel manufacturing industry under and similar routes (Kumar and Moulick 2016). volatile demand conditions of fast fashion apparels. Per- Three main approaches are used to address the CFP formance of the developed model is validated based on (Kahraman 2012; Modra´k 2011; Curry and Feldman 2010). data collected from actual production environments of They are: 123 Journal of Industrial Engineering International 1. Product family identification (PFI), (Balakrishnan and Hung Cheng 2005; Chowdary et al. 2. Machine group identification (MGI), 2005). Furthermore, Marsh et al. (1997) argued that static 3. Product families/machine grouping (PF/MG). cells are associated with low routing flexibility. It will directly deteriorate the layout flexibility (Neumann and In the first approach, initially the product families are Fogliatto 2013). identified by using an appropriate technique. Thereafter, DCMS is introduced to overcome the drawbacks of the machines are allocated to the respective product fam- CMS. As mentioned by Niakan et al. (2016), Deep and ilies. Machine group identification (MGI) approach groups Singh (2016) and Mahdavi et al. (2010), DCF is done by the machines into cells based on routing similarities fol- dividing considered planning horizon into multiple plan- lowed by assignment of product families to the formed ning periods. Instead of using stable product mix and cells. In the third approach, product family formation and demand for entire planning horizon, the dynamic cellular machine grouping are done simultaneously. Out of these, layouts are formed by considering possible variations in the third approach is highlighted as optimum CF method multiple periods (Niakan 2015). These variations require (Kahraman 2012; Mungwattana 2000). reconfiguration of the dynamic cells (Niakan 2015; According to Kia et al. (2013), group layout of CMS Houshyar et al. 2014). Cell reconfigurations are minimized design deals with two aspects as inter-cell layout and intra- by considering all the possible demands in corresponding cell layout. Inter-cell layout determines the location of cells planning horizon and optimizing the selected performance with respect to each other whereas intra-cell layout con- measures for considered planning horizon and defined siders machine arrangement with each cell (Mahdhavi et al. planning periods (Niakan et al. 2016;Su¨er et al. 2010). As 2013). Scheduling of part families is done in third stage of stated by Niakan (2015) and Houshyar et al. (2014), layout CMS design (Kia et al. 2013). Resource allocation stage reconfiguration of dynamic cells is done by switching of consists of assignment of required resources to the cells existing machines between cells, adding new machines to (i.e., man, material and other required tools.). the cells and removing existing machines from cells. Based on the production requirements and desired As stated by Mungwattana (2000), four basic types of design attributes, CMS can be broadly categorized into two production requirement are considered in GT-based cellu- segments as Static Cellular Manufacturing System (SCMS) lar layout designs. They are static, dynamic, stochastic and and Dynamic Cellular Manufacturing System (DCMS) deterministic. Production requirement in any industry can (Niakan et al. 2016; Khannan et al. 2016). be represented by using one or more of these types. Static Designing of a SCMS is done by assuming deterministic production requirement assumes a constant product mix product demand and product mix for the considered plan- and demand for entire planning horizon. There can be ning horizon (Hachicha et al. 2006). In other words, it is either static-deterministic production requirement or static- assumed that the product demand and product mix are stochastic production requirement. In first case, the product known with certainty for the periods in considered plan- mix and demand for entire period is exactly known at the ning horizon. In SCMS, cells that optimize the selected cell formation stage. For the second one, possible product performance measures for all the product demand and mix and demand for the period is known with certain product mix are used for the entire planning horizon con- probabilities. Similarly, dynamic cells incorporate the sidered in SCMS design (Hachicha et al. 2006). possible production requirements in either stochastic or As stated by Houshyar et al. (2014), presently the low deterministic nature (Balakrishnan and Hung Cheng 2005; volume-high variety products with volatile demand and Mungwattana 2000). In both types of product demand, shorter lead-times are popular in most of the industries. dynamic cells form physical grouping of cells based on GT Optimal cells of a particular period may not be optimal for principles while rearranging the cells when necessary. This other periods due to possible variations of production allows the dynamic cellular layouts to retain the flexibility requirements of different product mixes (Niakan et al. through cell reconfiguration on a planned basis and to gain 2016; Deep and Singh 2016). According to Niakan et al. advantages of static cells. Excessive rearrangement of cells (2016), static cells are beneficial if the same product mix is may significantly increase cost of machine movement and manufactured for entire planning horizon or the new lost of production time (Kia et al. 2013). Conversely, products are perfectly matched with existing product increasing robustness for multiple demand scenarios dete- families being manufactured in static cells. Pillai et al. riorates the cell performance due to increased material (2011), Modra´k(2011) and, Marsh et al. (1997) argued that handling. Furthermore, using an inappropriate cell layout the static cells are inflexible for introduction of completely for a particular period may lead to increased reconfigura- new product mix. Introduction of new products to the static tion costs in subsequent periods (Niakan 2015). Designing cells result in deteriorate of the cell performance and process of DCMS aims to obtain optimal cells by balancing eventually cause a major rearrangement of machines these two conflicting scenarios. 123 Journal of Industrial Engineering International Machine-intensive and labor-intensive a biobjective mathematical model for dynamic cell for- mation by considering both machine and operator skill manufacturing cells levels. Niakan et al. (2016) formulated and validated their model by using theoretical data sets. Sakhaii et al. (2016) As mentioned by Egilmez et al. (2012), manufacturing cells can be either machine-intensive or labor-intensive. developed a robust optimization approach for a mixed-in- teger linear programming model to obtain solutions for a Limited operator involvement in operations is the key characteristic of machine-intensive cells. Operators load DCMS with unreliable machines and a production planning the raw material or half-assembled product to the machine, problem in a simultaneous manner. Main considerations of control quality and unload the output from machine. their study are DCFP, inter-cell layout, operator assign- In labor-intensive cells, complete operator involvement ment problem, unreliable machines, alternative process routes and production planning decisions. Objective func- in operations is essential and the output and performance of operation significantly fluctuate based on operator-related tion of the mathematical model developed by Sakhaii et al. (2016) sought to minimize the costs of inter- and intra-cell factors (Zhao and Yang 2011). As mentioned by Su¨er and Dagli (2005), labor-intensive cells consist of lightweight material handling, operator training and hiring, machine relocation, machine breakdowns, inventory holding and small machines and equipments that are easy to relocate. Utilization of the existing machines is encouraged in labor- backorder. The biobjective stochastic model developed by ¨ Zohrevand et al. (2016) addresses human-related problems intensive manufacturing cells (Suer and Dagli 2005). Production/assembly department of apparel industry is in DCFP by considering labor utilization, worker overtime known as highly labor-intensive (Islam et al. 2015; Guo cost, worker hiring/laying-off, and worker cell assignment. Their model seeks to minimize the total costs of machine et al. 2015). According to Zhao and Yang (2011) and Mittlehauser (1997), machines used in production depart- procurement, machine relocation, inter-cell moves, over- time utilization, worker hiring/laying-off, and worker ment of apparel manufacturing factories can be categorized into two types based on the level of operator intervention to moves between cells while maximizing the labor utiliza- tion. The model proposed by Tavakkoli-Moghaddam et al. complete an operation. Fully automatic machines Operators load the raw (2011) is one of the noticeable studies on incorporating human-related factors in cell formation. Their model con- material or half-assembled product to the machine, monitor the quality and unload output from machine. Machines can sists of cell formation problem with two conflicting objectives as; optimizing the labor allocation while maxi- be pre-programmed to operate automatically with little intervention of the operator. Examples for such machines mizing the cell utilization. The developed model is solved are button-hole, bar-tack and pocket sewer machines. using multiobjective particle swarm optimization. Semi-automatic machines Operator should continually attend to control the machine to process a particular Impact of machine breakdowns on DCMS design operation. Machine breakdowns in the system play a major role in determining the available capacity for production. There DCMS design with labor-related issues are two main categories of machine breakdown as; Chronic breakdowns and Sporadic breakdowns. As stated by Ireland Nonlinear integer programming model for dynamic cell formation is developed by Mahdavi et al. (2010) to address and Dale (2001) and Cheng and Podolsky (1996), five common causes of chronic breakdowns are: the problem of operator assignment to cells. Improving operator assignment flexibility concurrently with dynamic 1. Failure to maintain machines, i.e., cleaning and minor cell formation is the main feature of the developed model. repairs, Multiple attributes are considered in their model as; multi- 2. Failure to maintain operating conditions such as period production planning, machine duplication, dynamic temperature, speed, system reconfiguration, machine capacity, available time of 3. Insufficient operator skills such as improper and operators and operator assignment. The objective function erroneous machine handling, seeks to minimize eight cost functions namely; holding 4. Deterioration of machine parts, cost, backorder cost, inter-cell material handling cost, 5. Poor design of machine parts due to wrong materials maintenance and overhead cost of machines, machine and sizes. relocation cost, salary cost, hiring cost and firing cost. In the presence of chronic breakdowns, operators are Mahdavi et al. (2010) emphasized the need of considering able to perform required operations but with reduced speed. operator-related factors in cell design to achieve expected benefits of cellular layouts. Niakan et al. (2016) introduced These breakdowns are continual and may result in minor stoppages that can be repaired within a short time (Ireland 123 Journal of Industrial Engineering International and Dale 2001; Leflar 2001). Neglecting the chronic Two possible machine setup scenarios considered in the breakdowns leads to sporadic breakdowns, which are developed model are: suddenly exposed and unexpected. Badiger and Laxman (i) Machines required for particular operations in (2013) discussed that sporadic breakdowns can cease entire current period are available in dynamic cells of operation and it typically requires major troubleshooting to previous period and it is needed to perform restore the machine to working condition or to replace with different machine settings to use them in current new machine. period. Machine breakdowns restrain the machine availability (ii) Machines required for particular operations in when designing a DCMS (Esmailnezhad et al. 2015; current period are not available in dynamic cells Houshyar et al. 2014). Majority of the previous CMS of previous period and required machine setup design considered 100% machine reliability, which is activities are performed in setup area. practically hard to achieve (Nouri et al. 2014; Saxena and Jain 2011; Chung et al. 2011). As stated by Kannan (2011), Inter-cell material handling cost occurs when a partic- the severity of machine reliability issues is high in CMS. ular part requires a machine that is located outside of the Reason for that is failure of any machine/tools assigned for cell assigned for that part type. a particular cell will halt entire production of the manu- It is assumed that the material handling between oper- facturing cell (Kannan 2011). According to Houshyar et al. ations is done manually without using an automated sys- tem. Labor-intensive cells consist of lightweight small (2014), machine breakdowns have direct influence on due dates and optimal cost of the system. Seifoddini and machines and equipments that are easy to relocate (Su¨er Djassemi (2001) stated that machine breakdowns have and Dagli 2005). Hence, an assumption is made as the greater effect on productivity of entire manufacturing machine movements between two locations are done by operations. Machine breakdowns are a crucial factor that using manual trolleys. According to Heizer (2016) and must be incorporated in designing of CMS (Houshyar et al. Chary (1988) Method Time Measurement (MTM) system 2014; Chung et al. 2011). One of the studies that incor- provides standard times for elements of fixed standard porate variable failure rates of the machines is the model categories of work motions such as reach, move, turn, proposed by Yadollahi et al. (2014). The objective func- grasp. MTM data are widely used when determining the tions of their model are minimizing the purchase cost of standard times of manual operations (Aft 2000). MTM machines, intra-cellular movements and the inter-cellular values are used when calculating the time taken for respective material and machine movements of developed movement costs of materials while minimizing the total repair time for failed machines. model. Development of mathematical programming Model formulation model Mathematical model is formulated to generate optimal Assumptions dynamic cells that can ensure minimum costs of machine relocation, machine setup and inter-cell material handling 1. Each part type has a set of operations that must be in labor-intensive production environments subjected to processed based on the given operation sequence. machine breakdowns. 2. Product mix and respective demand for each part type are known in advance. It is assumed that a specific area is used to perform machine setup activities (if needed). It is referred as setup 3. Each machine has a limited capacity in each period area. In the developed model, excessive machines in par- and it is expressed in minutes. ticular period are stored in setup area. Machines with 4. Each machine is capable of processing more than completed setup activities required for a particular period one operation. are moved from this area to the corresponding cell. Pos- 5. Standard processing times for each operation and sible scenarios of machine relocations in the developed setup times for each machine setup activity are model can be listed as follows: known. 6. All the operators and mechanics are multi-skilled. i) Moving machines between different cells, Hence, no additional training is required during ii) Moving machines between cells and setup area. product changeovers. In the mathematical model development, summation of 7. Multi-skilled operator pool is available to mitigate costs for above two relocations is referred as total machine the effects of absenteeism. relocation cost. 123 Journal of Industrial Engineering International 8. There are no delays due to raw material supply, D : Demand quantity for part type t during period h t;h management failures or power failures. g : Standard processing time for operation n of O ;m t;n i;j 9. Production requirement is dynamic-deterministic. part type t on machine m i;j 10. Cell reconfiguration (if any) involves machine setup U : Time taken to load and unload machine m to/ m i;j i;j activities and machine relocations between and/or from the trolley within the cells. c : Cost per minute value during period h 11. Physical partitioning of the cells is prohibited. u : Time to perform machine setting l on l;m i;j Furthermore, cell reconfiguration does not require machine; m i;j modifications to the buildings. Therefore, other than # : Total number of machines in plant floor during h;m i;j the machine relocation costs, any physical reconfig- period h uration costs (i.e., changes in lighting and ventilation k : Number of turning motions when moving materials systems) are not allowed. between cells 12. Adequate lighting and environmental conditions s : Non - negative random number for corrective i;j required for the operations are provided. repair time of machine m ij 13. Multiple duplicate machines of each type are dF ðÞ h : Breakdown rate of machine m when t;m i;j i;j available. Existing machines at the beginning of processing part type t during period h each period are utilized when developing dynamic X : Capacity of machine m during period h ðgiven h;m i;j cells. Therefore, machine procurement is excluded. i;j in minutesÞ 14. Machine availability is limited due to machine 1 if operation n of part type t requires breakdowns. < x ¼ machine m with setting l 15. Preventive maintenance activities are done outside m ;l;O i;j i;j t;n 0 otherwise the plant floor and it do not affect the numbers of machines available within the floor. 16. Inter-cell material handling cost does not depend on Decision variables the product type. 17. Handling of materials in cells and machine move- Integer variables f : Number of times that an t;m ;m i;j 0 ; 0 i j ments are done manually. operation at machine m immediately follows an operation i;j 18. Cost per unit time for each period is known. at machine m 0 or vice versa i ;j Indices Binary variables h : Index for period; h ¼ 1; 2; ...; H t : Index for part type; t ¼ 1; 2; ...; T 1 if machine m is at machine setup area during period h i;j n : Index for number of operations; n ¼ 1; 2; ...; N d ¼ h;m i;j 0 otherwise O : Index for operation n of part type t t;n i : Index for machine types; i; i ¼ 1; 2; ...; I 1 if machine m is in cell k during period h i;j b ¼ k;h;m i;j j : Index for machine number in each machine type; 0 otherwise j; j ¼ 1; 2; ...; J m : Index for jth machine of machine type i i;j 1 if machine m is with setting l during period h i;j e ¼ l;h;m i;j l : Index for machine setting; l ¼ 1; 2; ...; L 0 otherwise k : Index for cells; k; k ¼ 1; 2; ......; K 1 if machine m is required for operation n of part type t i;j l ¼ m ;O i;j t;n 0 otherwise Input parameters 1 if part type t is assigned to cell k during period h h ¼ t;k;h 0 otherwise T : Number of part types in planning horizon N : Number of operations in each part type I : Number of available machine types J : Number of machines available from each machine Objective function seeks to minimize the summation of total machine relocation cost, machine setup cost and inter- type H : Number of periods in planning horizon cell material handling cost. Formulation of objective L : Number of available machine settings function and constraints of developed mathematical pro- gramming model are discussed hereafter. 123 Journal of Industrial Engineering International O m Mathematical model H K T;N I;J XXXX g :D :l :b t;h k;h;m O ;m m ;O i;j t;n i;j i;j t;n h¼1 k¼1 t¼1 i¼1 MinðÞ EMRC þ MSC þ EMHC ð1Þ n¼1 j¼1 0 1 h;m i;j EMRC ¼ MRC þ MRC ð1:1Þ A B m I;J B C b : X  s :dF ðÞ h ð5Þ m @ A H K K I;J  k;h;m h;m m t;m i;j i;j i;j i;j XXXX i¼1 MRC ¼ 1  b 0 1  b : A k ;h;m k;ðÞ hþ1 ;m 0 i;j i;j j¼1 h¼1 k¼1 k ¼1 i¼1 0 L I;J j¼1 k6¼k XX u ; 8k l;m i;j b :b 0 : U þ 0:0102dis 0 :c k;h;m k ;ðÞ hþ1 ;m m k;k i;j i;j i;j ðÞ hþ1 l¼1 i¼1 j¼1 ð1:2Þ H K K I;J XXXX h ¼ 1; 8k; h ð6Þ t;k;h MRC ¼ 1  b 1  b 0 :d : B k;h;m k ;h;m h;m i;j i;j i;j t¼1 h¼1 k¼1 k ¼1 i¼1 j¼1 k6¼k H; R; K; f  0 and integer; 8h; k; t; m ð7Þ t;m m 0 0 i;j i;j i ;j b : U þ 0:0102dis :c k;ðÞ hþ1 ;m m k;D i;j i;j ðÞ hþ1 d ; x ; b ; e ; l ; h 2fg 0; 1 ð8Þ h;m m ;l;O k;h;m l;h;m t;k;h i;j i;j t;n i;j i;j m ;O i;j t;n ð1:3Þ The objective function is shown in Eq. (1). Detailed m O H K I;J L L T;N XXXXXX description of each cost term and constraint is presented MSC ¼ b :l : k;ðÞ hþ1 ;m i;j m ;O i;j t;n h¼1 k¼1 i¼1 l¼1 l ¼1 t¼1 hereafter. ð1:4Þ j¼1 ¼1n l6¼l EMRC is the total cost for following activities during 0 0 x :e :e :u 0 :c m ;l ;O l ;ðÞ hþ1 ;m l;h;m i;j t;n i;j l ;m ðÞ hþ1 layout reconfigurations. i;j i;j P ij C C O h k k tn T XXXXXX • Loading machine to the manually operated trolley EMHC ¼ D :b :l : t;h k;h;m i;j m ;O i;j t;n • Transporting machine to required locations 0 0 t;n t h i6¼i k k6¼k • Unloading machine from manually operated trolley j6¼j 0 0 b :l :f : 0:0102dis þ 0:02232k : Mital et al. (2017) and Karger and Bayha (1987) stated k ;h;m t;m ;m k;k 0 0 m ;O 0 i ;j 0 0 i;j ; 0 i ;j t;ðÞ nþ1 i j that walking time per foot value when transporting 0 0 c 8i 6¼ i ; j 6¼ j ð1:5Þ machines using manually operated trolleys in obstructed paths is 17 TMU (Time Measurement Unit) or 0.0102 min Subject to: as per MTM systems. Total machine relocation cost for TNðÞ 1 considered planning periods is calculated by Eq. (1.1). f ¼ l :l þ l :l ; t;m m 0 0 i;j m ;O m 0 0 ;O m 0 0 ;O m ;O i ;j i;j t;n i ;j t;ðÞ nþ1 i ;j t;n i;j t;ðÞ nþ1 Equation (1.2) calculates the machine relocation cost n¼1 between cells, whereas machine relocation cost between 0 0 8t; m [ m i ;j i;j cells and setup area is calculated by Eq. (1.3). ð2Þ Specific setup activities must be performed when two m m K I;J I;J XX X operations can be processed at same machine but with #  b þ d ; 8m ; k; h ð3Þ h;m k;h;m h;m i;j i;j i;j i;j different machine settings in consecutive periods. Total i¼1 i¼1 k¼1 machine setup time when converting from one machine j¼1 j¼1 0 1 setting to another is used to calculate machine setup cost m O m O I;J T;N K I;J T;N for each machine. If the machine requires same setting for XX XXX B C B C D :g ¼ D :g ; t;h t;h two consecutive periods, no setup activity for such O ;m O ;m t;n i;j @ t;n i;jA ð4Þ i¼1 t¼1 k¼1 i¼1 i¼1 machines is performed. Machine setup cost for considered j¼1 n¼1 j¼1 j¼1 planning periods is calculated as given in Eq. (1.4). 8m ; k; h ij 123 Journal of Industrial Engineering International Operators’ walking between cells will possibly restrict optimal number of cells with maximum machine due to movement of other operators and machines. As stated utilization. by Mital et al. (2017) and Karger and Bayha (1987), walking The part processing on machines is limited by available time per foot is 17.0 TMU (0.0102 min) for obstructed paths machine capacity for a particular period. In ideal situation, the and 37.2 TMU (0.02232 min) per turn. Inter-cell material total machine capacity, i.e., shift operating time can be utilized handling cost is calculated as given in Eq. (1.5). for part processing. Practically, machine capacities are limited Equation (2) determines the number of times that an due to possible machine breakdowns and setup activities. operation at machine m immediately follows an operation Using shift time as the available machine capacity is erroneous i,j 0 0 at machine m . in this situation. Constraint given in Eq. (5) limits the part i ;j Equation (3) guarantees that the total number of processing capability of all machine types based on total machine capacity available for individual machine types. machines in plant floor should be greater than or equal to summation of number of machines in cells and setup area In case of labor-intensive manufacturing industries, simultaneous processing of multiple different part types for a particular period. It prevents additional machine procurement when generating dynamic cells. within a single cell will lead to forgetting effect, compli- cated supervision and increased machine stoppages due to In a dynamic production environment, it is possible to have fluctuations of product demand during different variable machine settings. Hence, the maximum number of part types assigned to a single cell is limited to one at a periods. Workload for the production environment must be balanced among the cells to prevent possible complications time by using Eq. (6). arise due to unbalanced workload. One of the possible Equations (7) and (8) are used to define integer and binary variables. issues due to unbalanced workload is operators assigned to different cells may get different workloads and thereby Linearization of the proposed model have different incentive ceilings. It may result in operator frustration due to feel of unfairness. Developed model The developed model is nonlinear due to the terms (1.2), considers three main approaches of cell workload balanc- ing based on possible demand fluctuations. If the product (1.3), (1.4) and (1.5) of the objective function, the con- straints Eq. (2), and Eq. (5). demand for particular period is significantly lower than other periods of considered planning horizon, two 0 For the term (1.2), the nonlinear term 1  b : k ;h;m i;j approaches are considered to balance the cell workload. 1  b :b :b 0 can be linearized by k;h;m k;ðÞ hþ1 ;m k ;ðÞ hþ1 ;m i;j i;j i;j First approach is reducing number of operating cells by Eqs. (9)–(14) and is replaced by the variable w 0 . m ;k;k ;h;ðÞ hþ1 disintegrating the existing cells from previous period and i;j forming minimum number of cells in current period. Since 0 0 0 w ¼ 1  b : 1  b :b :b m ;k;k ;h;ðÞ hþ1 k ;h;m k;ðÞ hþ1 ;m k;h;m k ;ðÞ hþ1 ;m i;j i;j i;j i;j i;j the developed model assumes existing machines are used ð9Þ to generate dynamic cells, first approach will lead to machine idling in the particular period. Second approach is w 0  1  b 0 ð10Þ m ;k;k ;h;ðÞ hþ1 k ;h;m i;j i;j to operate with reduced workload that is equally distributed among available machines of the period. This will lead to w 0  1  b ð11Þ m ;k;k ;h;ðÞ hþ1 k;ðÞ hþ1 ;m i;j i;j underutilization of cells. If the workload for particular w  b ð12Þ period is not less than other periods, third approach is used m ;k;k ;h;ðÞ hþ1 k;h;m i;j i;j to balance the workload among optimum the number of 0 0 w  b ð13Þ m ;k;k ;h;ðÞ hþ1 k ;ðÞ hþ1 ;m i;j i;j cells, while ensuring maximum resource utilization. Workload balancing constraint, Eq. (4) is formulated to w 0  1  b 0 þ 1  b þ b m ;k;k ;h;ðÞ hþ1 k ;h;m k;ðÞ hþ1 ;m k;h;m i;j i;j i;j i;j address those three approaches. By using Eq. (4), it is þ b 0  4:5 ð14Þ k ;ðÞ hþ1 ;m possible to customize the workload balancing among cells i;j as per the desired approach. The factor q 2 [0, 1] where, The nonlinear term of the term (1.3), {q =0 B q B 1} is used to determine the extent of 1  b 1  b :d :b was linearized k;h;m k ;h;m h;m i;j i;j i;j k;ðÞ hþ1 ;m i;j workload balance between the dynamic cells. Setting by replacing it from the variable x as given by k;h;m i;j q & 0 while simultaneously reducing the number of Eqs. (15)–(20). operating cells (K), corresponds to the first approach used when total workload leads to underutilized resources. x ¼ 1  b 1  b 0 :d :b ð15Þ k;h;m k;h;m k ;h;m h;m k;ðÞ hþ1 ;m i;j i;j i;j i;j i;j Second approach can be satisfied by setting q & 0 with x  1  b ð16Þ k;h;m k;h;m i;j i;j unchanged number of cells. Third approach considers q & 1 with equally distributed workload while operating 123 Journal of Industrial Engineering International a  l þ l  1 ð38Þ x  1  b 0 ð17Þ k;h;m m ;O m ;O k;h;m k ;h;m i;j 0 0 i;j i;j i;j t;n i ;j t;ðÞ nþ1 x  d ð18Þ v ¼ l :l ð39Þ k;h;m h;m i;j i;j k;h;m i;j m 0 0 ;O m ;O i ;j t;n i;j t;ðÞ nþ1 x  b ð19Þ k;h;m k;ðÞ hþ1 ;m i;j i;j v  l ð40Þ k;h;m i;j m 0 0 ;O t;n i ;j x  1  b þ 1  b 0 þ d k;h;m k;h;m k ;h;m h;m i;j i;j i;j i;j v  l ð41Þ k;h;m i;j m ;O i;j t;ðÞ nþ1 þ b  4:5 ð20Þ k;ðÞ hþ1 ;m i;j v  l þ l  1 ð42Þ k;h;m i;j m 0 0 ;O m ;O t;n i;j i ;j t;ðÞ nþ1 0 0 b :l :x :e :e is the non- k;ðÞ hþ1 ;m m ;l ;O l ;ðÞ hþ1 ;m l;h;m i;j m ;O i;j t;n i;j i;j i;j t;n l :b the nonlinear term in Eq. (5) can be replaced linear term in (1.4) of the objective function. It was k;h;m m ;O i;j i;j t;n replaced by y as given in Eqs. (21)–(27). by as given in Eqs. (43)–(46). k;h;m i;j y ¼ b :l :x :e 0 :e k;h;m m ;l ;O l;h;m b ¼ l :b ð43Þ i;j k;ðÞ hþ1 ;m m ;O i;j t;n l ;ðÞ hþ1 ;m i;j k;h;m i;j i;j t;n i;j k;h;m m ;O i;j i;j i;j t;n ð21Þ b  l ð44Þ k;h;m m ;O i;j i;j t;n y  b ð22Þ k;h;m k;ðÞ hþ1 ;m i;j i;j b  b ð45Þ k;h;m k;h;m i;j i;j y  l ð23Þ k;h;m i;j m ;O i;j t;n b  l þ b  1 ð46Þ k;h;m k;h;m m ;O i;j i;j i;j t;n y  x ð24Þ k;h;m m ;l ;O i;j i;j t;n Equation (47) determines the values of defined variables y  e 0 ð25Þ k;h;m l ;ðÞ hþ1 ;m for linearization. i;j i;j y  e ð26Þ w ; x ; y ; z ; a ; b 2fg 0; 1 k;h;m l;h;m k;h;m k;h;m k;h;m k;h;m k;h;m i;j i;j i;j i;j i;j i;j i;j k;h;m i;j ð47Þ y  b þ l þ x þ e 0 k;h;m m ;l ;O i;j k;ðÞ hþ1 ;m m ;O i;j t;n l ;ðÞ hþ1 ;m i;j i;j t;n i;j þ e  5:5 l;h;m i;j ð27Þ Solution approach Nonlinear term The cell formation problem is considered as NP-hard b :l :b 0 :l :f of the term k;h;m m ;O k ;h;m 0 0 m ;O t;m ;m 0 i;j i;j t;n i ;j 0 0 i;j ; 0 i ;j t;ðÞ nþ1 i j (nondeterministic polynomial hard) combinatorial opti- (1.5) is linearized by replacing it by z as given in k;h;m i;j mization problem due to solution complexity (Bayram and Eqs. (28)–(34). Sahin 2016; Rodriguez Leon et al. 2013). Due to solution complexity, manual computation to obtain solutions may z ¼ b :l :b :l :f ð28Þ k;h;m k;h;m k ;h;m 0 0 t;m ;m 0 i;j i;j m ;O m 0 0 ;O i;j i;j t;n i ;j t;ðÞ nþ1 ; 0 i ;j i j produce erroneous results. z  b ð29Þ k;h;m k;h;m LINGO, CPLEX and GAMS are the most commonly i;j i;j used software packages to obtain optimal solutions for z  l ð30Þ k;h;m m ;O i;j i;j t;n mathematical programming models (Agrawal et al. 2015; z  b ð31Þ k;h;m k ;h;m 0 0 Esmailnezhad et al. 2015; Anbumalar and Raja Chandra i;j i ;j Sekar 2015; Pinheiro et al. 2016; Azadeh et al. 2015; z  l ð32Þ k;h;m i;j m ;O 0 0 i ;j t;ðÞ nþ1 Kasimbeyli et al. 2010). The developed model is solved by generating a program z  f ð33Þ k;h;m t;m ;m 0 i;j i;j ; i j code using Lingo 16.0 software package. z  b þ l þ b 0 þ l k;h;m k;h;m m ;O k ;h;m 0 0 m ;O i;j i;j i;j t;n i ;j 0 0 i ;j t;ðÞ nþ1 ð34Þ þ f  5:5 t;m ;m 0 i;j ; 0 i j Model evaluation and validation The nonlinear terms l :l and m ;O m 0 0 ;O i;j t;n t;ðÞ nþ1 i ;j l :l are replaced by a and v , Detailed description of the factories selected k;h;m k;h;m m 0 0 ;O m ;O i;j i;j i ;j t;n i;j t;ðÞ nþ1 for the evaluation and validation respectively. Linearization is given in Eqs. (35)–(42). of the developed model a ¼ l :l ð35Þ k;h;m i;j m ;O m 0 0 ;O i;j t;n t;ðÞ nþ1 i ;j Case studies on three different apparel manufacturing a  l ð36Þ k;h;m i;j m ;O i;j t;n factories were selected for the evaluation and validation of a  l ð37Þ k;h;m i;j m 0 0 ;O the developed model. The program code generated on i ;j t;ðÞ nþ1 Lingo 16.0 software package is used to identify the optimal dynamic cells for the collected data from factories. These 123 Journal of Industrial Engineering International factories are referred as Factory 1, 2 and 3. Data collection types used for model validation in factory 1, 2 and 3 are was done in production/assembly department. given in Table 1. Semi-automatic sewing machines are used in majority of Initially, the developed model was evaluated by using the apparel manufacturing plants for past few decades data collected from Factory 1. According to the initial (Zhao and Yang 2011). Therefore, operator should be evaluation based on Factory 1, the developed model continually attended to control the machine to process a resulted in 31.12% of total costs saving for the considered particular operation. According to the analysis done by three cost terms. After the initial evaluation the model was Zhao and Yang (2011) and Moll et al. (2009), over 90% of validated by using data collected from Factory 2 and 3. the operations in production department of apparel industry is done by using semi-automatic machines. Similar situa- Numerical example tion is observed in the selected factories for case studies. Percentage of semi-automatic machines used in production Outputs of the developed system are presented by using a department of factory 1, 2 and 3 are 95.7, 92.0 and 98.1, numerical example by considering data collected from respectively. All the selected factories are currently using factory 2 for 11 part types with 15 machine types. Input product layouts with machine sharing in their production data used for the numerical example are given in ‘‘Ap- environments. pendix A’’. Part families and respective part types of optimal solu- Model validation procedure tions for the numerical example are given in Table 2. Table 3 shows part types and their respective dynamic cells with The values of cost terms used in objective function number of machines of each machine type during two peri- (Sect. 3.1.5) are calculated from the collected data on ods. Assigned machine numbers of each machine type to the current layouts. Thereafter, these total cost values of cur- respective dynamic cell are given in Table 4. Corresponding rent layouts are used to calculate the cost-saving percent- cost saving is 34.60% for the given numerical example. age when applying the obtained optimal dynamic cells for same data sets. Cost-saving percentage is calculated by formula given in Eq. (48). Results and discussion T  T L D Cost saving percentage ¼  100% ð48Þ Resultant cost-saving percentages for individual cost terms and total cost of the objective function for factory 1, 2 and where T summation of considered cost terms of current 3 are given in Table 5. layout system, T optimal cost value for objective function Table 2 Resultant part families of developed model. Part family Part type (t) and corresponding part types Criteria used for evaluating and determining the validity 1 2,5,4 of developed model is as follows. 2 6, 10, 1, 3 T  T L D 3 8,7,9 if  100% [ 0 model is validated. Otherwise, model is invalid in mini- Table 3 Part types and their respective dynamic cells with number of machines of each machine type mizing cost terms. Developed model was evaluated and validated by tk h Number of machines of type i incorporating the total cost of machine relocations, 123 45678910111213 machine setups and material handling calculated for the currently used product layouts in selected factories. Sum- 2 11131 411200 0000 mary of the number of part types and number of machine 5 22131 420200 0000 4 31131 033200 0000 6 41210 321232 0000 Table 1 Number of part types and machine types used for model 10 51120 211222 0001 validation 1 62111 231222 0000 Factory Number of part types Number of machine types 3 72231 302311 0000 8 81101 121201 1221 121 13 7 92010 034211 0111 211 15 9 102211 012100 1120 318 12 123 Journal of Industrial Engineering International Table 4 Assigned machines of each machine type to the respective dynamic cell k Assigned machines of each machine type (m ) i,j 1 2 3 4 56 78 9 1011 12 13 1 1 9 11 1,5,6,11 1 15 3, 4 0 0 0 0 0 0 2 12 26, 10, 16 12 2, 17, 28, 14 16, 14 0 2, 5 0 0 0 0 0 0 3 18, 13 13, 8, 6 7 0 10, 11, 13 2, 3, 5 1, 8 0 0 0 0 0 0 4 2 1 0 12, 15, 18 2, 3 6 16, 6 13, 10, 1 2, 6 0 0 0 0 5 10 21, 22 0 16, 20 9 8 12, 7 18, 21 16, 10 0 0 0 4 6 11, 20 11 5 25, 19 7, 8, 12 7 14, 18 11, 8 4, 9 0 0 0 0 7 23 14, 12, 23 18 3, 7, 10 0 12, 16 11, 15, 16 2 1 0 0 0 0 8 16 0 2 9 26, 4 9 13, 22 0 10 2 12, 5 2, 5 1 9 0 2 0 0 5, 6 10, 15, 17, 18 20, 10 14 8 0 1 3 2 10 21, 17 4 13 0 18 2 17 0 0 18 14 22, 1 0 volume and low product variety. Kumar and Suresh (2006) Table 5 Cost-saving percentages of selected factories and, Nunkaew and Phruksaphanrat (2013) mentioned that Factory 1 2 3 two of the key problems of product layout are high cost of layout reconfiguration and lack of flexibility. According to Total machine relocation (%) 30.29 39.87 56.05 the results given in Table 5, the optimal dynamic cells Machine setup (%) 34.10 23.49 29.61 generated from developed model can surpass the product Inter-cell material handling (%) 28.41 47.66 37.48 layouts in minimizing the considered cost terms. Therefore, Total cost of the objective function (%) 31.12 34.60 47.14 it is encouraged to use the developed model to mitigate the drawbacks of product layout in dynamic production Minimized costs of manufacturing including change- environment. overs and shorter manufacturing lead-times are essential to remain competitive in fast fashion apparel industry. Several researchers have addressed the issues related with supply Future research directions chain management and retailing decisions of fast fashion apparel products in order to achieve the demanded shorter According to Bayram and Sahin (2016), Kia et al. (2013) lead-times (Sabet et al. 2017; Orcao and Perez 2014; Shen and Mahdavi et al. (2013), cell formation, group layout, 2014; Zhelyazkov 2011; Zhenxiang and Lijie 2011; Mihm group scheduling and resource allocation are four basic 2010). As the fast fashion apparel segment is introduced stages of designing CMS. This paper is focused on first recently, there exists a significant gap in the available lit- stage of CMS design and the developed model can be erature on production layout systems applicable for fast extended to remaining three stages. fashion orders (Kentli et al. 2013). The developed model is tested for three selected facto- Lago et al. (2013) and Johnson (2003) stated that manu- ries in apparel industry. It is expected to validate the facturing lead-time can be drastically reduced by decreasing developed model for other labor-intensive manufacturing changeover time between different products. Positive values industries in future. of cost-saving percentage (Table 5) imply that the dynamic In the developed model, it is assumed that all the operators cells generated from developed model are capable of and mechanics in production environment are multi-skilled improving the current layout system with respect to the and processing time of each operation is a predefined stan- considered cost terms. It is possible to conclude the validity dard value. As stated by Badiru (2013) and, Mir and Reza- of developed model in minimizing the considered cost terms eian (2016), the distribution of skill levels, degree of for fast fashion apparel products manufactured in dynamic workforce cross-training, impact of individual operators’ production environment of labor-intensive apparel industry. learning and forgetting characteristics, motivational issues Hence, the developed model can be used to address the and attitudes, absenteeism rates, operator turnover rates, prevailing gap of literature on a layout system appropriate for frequency of product revisions, and workforce assignment fast fashion products. patterns are some of the important factors that determine the As stated by Malakooti (2014), product layout or performance of the system. The present research can be assembly line layout is suitable for products with high extended by considering such operator-related issues. 123 Journal of Industrial Engineering International Open Access This article is distributed under the terms of the Creative Forghani et al. (2013) and Suresh and Kay (2012) Commons Attribution 4.0 International License (http://creative emphasized that the maximum benefits of cell layout are commons.org/licenses/by/4.0/), which permits unrestricted use, dis- only achievable by incorporating production control, pro- tribution, and reproduction in any medium, provided you give cess planning, wage payment, accounting, purchasing, appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were material handling systems and determining staff level. As made. stated by Duncan (2011), significant reduction of change- over time can be achieved by scheduling of similar prod- ucts to cells that are processing same product families. As a Appendix A future research direction, it is possible to consider these factors when designing dynamic cells for volatile product See Tables 6, 7, 8, 9, 10 and 11. demand and product mix. Table 6 Required machine tO (i) t,n types for operations of part types 1 234567 8910 11 12 13 14 15 16 1145235 6 47858 9 9 7 2341522 7 44627 4 3236417 7 41274 8 9 6 2 4712576 3 52526 6 5173422 4 24755 4 6241596 1 48757 8 8 9 4 7258 13 57 9 126756 6116 8 4 7 11 5 12 3 9 7 12 11 5 10 1 6 13 96 11 135 12 7 1 5 12 106 10 482976 7 1 13 485 9 2 Table 7 Total number of machines of each machine type i 12345678910 11 12 13 J 15 21 12 20 23 20 20 11 14 2587 Table 8 Time for machine setting on each machine type l u l;m i;j 123 456 78910 11 12 13 1 13 12 4 3 9 4 20 2 17 15 12 17 14 2 112 39 16 583 12 6 148 8 317 14 1886 1138 1555 18 11 4 2 15 13 10 13 12 17 7 15 8 20 6 9 5 1016 7 11 16 715201214 1117 7 6 7 3 5 15 3 16 17 3 19 3 4 18 8 7 20 15 4 5 9 8 18 7 12 17 7 19 10 8 181312 9 813 5 41211 16 5 19 9 3 14 17 11 18 14 8 17 19 16 20 9 5 10 11 15 11 11 17 4 13 20 4 2 5 4 9 11 8 8 18 6 4 16 18 16 16 14 19 4 7 12 2 20 17 2 7 3 15 13 18 9 20 20 3 123 Journal of Industrial Engineering International Table 9 Demand data for hD t,h considered two periods in example 12 34 567 89 10 1 1906 1780 1257 2125 2191 1677 482 1730 2147 2245 1 1982 669 2421 553 578 481 2239 2110 1207 869 Table 10 Standard processing time of each operation of part types tO (g ) t,n O m t;n i;j 12 345 67 8910 11 12 13 14 15 16 1 0.62 0.67 3.01 1.30 0.89 0.63 1.02 1.23 0.48 2.21 1.45 1.53 2.34 1.20 1.26 2 1.12 2.31 0.23 3.01 0.55 0.28 1.41 2.01 1.15 1.11 1.03 2.11 0.36 3 2.0 1.08 2.10 1.22 2.03 0.41 0.89 2.03 0.39 1.05 2.31 2.61 1.55 2.46 1.25 3.06 4 2.11 2.53 1.53 1.33 1.25 2.15 2.45 1.64 1.36 1.36 1.68 3.02 1.55 5 3.33 1.35 2.01 0.23 0.89 0.92 0.59 2.82 1.22 0.66 1.32 1.40 1.28 6 0.69 2.13 0.88 2.03 2.30 1.35 2.01 2.22 2.36 2.89 2.65 2.36 3.01 1.23 1.99 2.69 7 2.98 3.66 3.48 4.33 1.32 3.11 2.89 2.36 1.32 1.65 3.21 2.35 3.33 3.21 3.01 8 1.02 2.31 2.31 1.35 3.02 2.37 2.33 3.12 3.02 2.03 2.03 3.14 1.02 3.08 1.56 9 1.23 3.33 2.09 2.19 1.20 3.02 3.12 0.23 1.25 0.59 3.0 2.99 10 1.32 1.56 3.06 2.31 2.03 1.09 2.85 1.10 1.11 2.22 1.21 0.97 1.55 1.35 Table 11 Breakdown rates of each machine for considered periods jdF ðÞ h t;m t i;j 123 456 789 10 11 12 13 1 1.60E-03 8.93E-05 4.58E-03 7.57E-04 1.02E-03 0.00E?00 1.23E-04 0.00E?00 2.59E-03 7.94E-05 9.24E-05 3.78E-04 5.36E-04 2 4.84E-03 1.94E-03 0.00E?00 4.75E-04 9.88E-04 7.74E-04 6.95E-05 2.34E-04 6.27E-04 7.82E-04 2.19E-03 9.48E-04 2.19E-03 3 1.42E-03 5.55E-04 6.45E-04 5.24E-04 3.91E-03 0.00E?00 2.38E-04 6.52E-04 7.21E-04 4.11E-04 5.49E-04 1.54E-03 4 8.71E-05 5.66E-04 1.00E-03 8.60E-04 0.00E?00 1.54E-03 8.19E-04 0.00E?00 2.86E-03 8.77E-04 7.37E-04 4.33E-04 5 3.55E-04 2.82E-04 4.67E-04 7.39E-04 9.12E-05 4.49E-04 8.78E-04 1.07E-03 1.58E-04 4.49E-04 1.77E-03 3.77E-04 6 7.74E-04 3.61E-04 6.84E-04 1.07E-03 8.60E-04 5.08E-04 4.22E-04 0.00E?00 2.89E-04 3.31E-04 6.41E-04 7 3.18E-03 1.81E-04 8.37E-04 9.89E-04 3.92E-04 6.57E-04 2.62E-03 8.32E-03 2.70E-04 7.60E-04 8 3.23E-03 8.22E-04 1.51E-03 5.86E-04 4.60E-04 3.02E-04 3.83E-04 0.00E?00 9.92E-04 4.92E-03 9 5.63E-04 1.15E-04 0.00E?00 1.36E-03 2.02E-04 0.00E?00 3.24E-04 2.23E-03 7.73E-04 10 1.45E-03 4.28E-04 6.16E-04 6.08E-04 9.67E-04 4.57E-04 1.46E-03 4.18E-03 4.26E-04 11 8.01E-05 1.49E-03 6.92E-04 1.21E-03 1.60E-03 3.95E-03 9.76E-04 0.00E?00 8.98E-04 12 7.04E-04 4.44E-03 6.15E-03 1.95E-03 2.26E-03 7.12E-04 6.08E-04 0.00E?00 13 1.42E-03 3.16E-03 6.53E-04 1.33E-03 1.90E-03 5.89E-04 7.65E-04 14 1.06E-03 8.76E-04 1.56E-04 1.25E-03 4.80E-04 1.11E-04 1.15E-03 15 5.75E-04 7.30E-03 5.41E-04 2.39E-03 3.36E-04 2.67E-04 16 1.19E-03 1.57E-03 0.00E?00 4.89E-04 9.98E-04 17 8.58E-04 0.00E?00 5.26E-04 9.12E-04 1.31E-03 18 7.94E-05 5.24E-04 0.00E?00 0.00E?00 6.81E-04 19 9.21E-04 1.18E-03 7.50E-05 5.56E-03 0.00E?00 20 8.50E-04 7.15E-04 4.17E-04 8.80E-04 1.77E-04 21 3.25E-04 6.57E-04 22 2.24E-03 23 1.85E-03 123 Journal of Industrial Engineering International Dalfard VM (2013) New mathematical model for problem of dynamic References cell formation based on number and average length of intra and intercellular movements. 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Journal of Industrial Engineering InternationalSpringer Journals

Published: May 29, 2018

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