TY - JOUR
AU - Plà, L. M.
AB - ABSTRACT This paper presents a multiperiod planning tool for multisite pig production systems based on Linear Programming (LP). The aim of the model is to help pig managers of multisite systems in making short-term decisions (mainly related to pig transfers between farms and batch management in fattening units) and mid-term or long-term decisions (according to company targets and expansion strategy). The model skeleton follows the structure of a three-site system that can be adapted to any multisite system present in the modern pig industry. There are three basic phases, namely, piglet production, rearing pigs, and fattening. Each phase involves a different set of farms; therefore, transportation between farms and delivering of pigs to the abattoir are under consideration. The model maximizes the total gross margin calculated from the income of sales to the abattoir and the production costs over the time horizon considered. Production cost depends on each type of farm involved in the process. Parameters like number of farms per phase and distance, farm capacity, reproduction management policies, feeding and veterinary expenses, and transportation costs are taken into account. The model also provides a schedule of transfers between farms in terms of animals to be transported and number of trucks involved. The use of the model is illustrated with a case study based on a real instance of a company located in Catalonia (Spain). INTRODUCTION During the last decades, a transformation from the traditional single-site system of pig production based on small family farrowing-to-finish farms to larger, more industrialized, controlled, and efficient farms has been observed (Taylor, 2006; Nijhoff-Savvaki et al., 2012). Nowadays, multisite systems concerned with housing production phases like breeding, rearing, or fattening at different sites are more common. For each of these phases, a set of specialized farms have their own characteristics, facilities, and location, and therefore transportation is necessary. Private companies and cooperatives tend to integrate and coordinate their operations into pork supply chains by using tighter vertical coordination linkages (Rodríguez et al., 2012). Supply chains have competitive advantages and are becoming important for the sector (Perez et al., 2009) because they help reduce risk and uncertainty and creates value (Taylor, 2006). In this context, aggregate planning provides a unified production plan to chain and production managers at the lowest cost (Mezghani et al., 2012). Aggregation allows pig chain managers to make decisions at strategic, operational, and tactical levels (Tsolakis et al., 2014). That is, to coordinate and control the stock of animals and their flow along the chain, scheduling transfers among farms over a time horizon. A survey of literature on pig production reveals most papers are devoted to operations on individual farms like the replacement of sows (Rodríguez et al., 2009), sow herd models management (Plà, 2007), or deliveries to the abattoir (Ohlmann and Jones, 2011; Morel et al., 2012). So far, only a few models had been proposed (e.g., Plà and Romero, 2008). Thus, this paper presents a multiperiod planning tool for multisite pig production systems based on linear programming (LP). The aim of the model is to help pig managers of multisite systems in the decisions cited above. MATERIAL AND METHODS The procedures involving animals and animal care conditions were approved by the Ethical Committee of Animal and Human Experimentation of the Universitat de Lleida, Spain. Modeling the Pig Production System The research is motivated by a case study of a Spanish pig production company located in the northeastern region of Spain (specifically in Catalonia). The company's support is essential for the development of the model and during the validation of the preliminary results presented here. The model has two purposes, each with a different scope. The first one aims to support and help to produce the week-by-week schedule of transports. This schedule is related to the decision making process regarding where, when, and how many piglets or pigs will be transported weekly and the number of trips needed. The second purpose is strategic, emphasizing the analysis of the production capacity by farm, phase, and whole system in the mid-term or long-term. Decisions involved include buying or selling farms to balance production and capacity, enlarging or shrinking the size of the company, and establishing a reward policy for employees in charge of specific individual farms or phases. For instance, at present, the company's management team conducts a growth strategy based on the acquisition of new sow farms to increase production without taking into account the farm's location. The model should permit the exploration of the impact of the addition or removal of farms from the system, adjusting their supplies for future demand. Therefore, the company can also consider grant subsidies and penalties for farmers depending on their contribution to the total revenue of the system. The production process considered in this paper involves different kinds of farms: 9 sow farms, 22 rearing farms, and 131 fattening farms plus 1 abattoir. Figure 1 shows the production process and the relationship between the different farms involved. For all the farms, parameters such as farm capacity, initial inventory, and transfers between farms and to the abattoir are considered. In https://cv.udl.cat/x/3YD0x3, the complete list of parameters are given in detail. Figure 1. View largeDownload slide Pig production system: phases (sow, rearing, fattening, and abattoir) and transfers between farms. See online version for figure in color. Figure 1. View largeDownload slide Pig production system: phases (sow, rearing, fattening, and abattoir) and transfers between farms. See online version for figure in color. According to the phases in the pig production process, the first phase takes place in sow farms. The aim of sow farms is to wean the maximum number of piglets to be transferred to rearing farms. Each sow is inseminated and is expected to become pregnant. If not, there are possible additional attempts until a successful conception happens, leading to a farrowing and subsequent lactation period. For simplicity, the herd size of sow farms is taken as a constant representing the steady state of the herd structure and, accordingly, the associated piglet production. That is, each sow can produce 0.518 piglets per week (i.e., 26.95 piglets per sow per year on average). After giving birth 9 times, the sow is sent to the abattoir for infertility reasons. Piglets stay in the sow farms for 4 wk before being sent to rearing farms. The cost per piglet and sow each week is 1.874€ and 4.85€, respectively. The second phase involves piglets that are sent to rearing farms to be fed for a 6 wk period. Here, the cost per piglet and week is 2.66€. Finally, in the third phase, piglets are transferred to the fattening farms with the aim of selling them to the abattoir once they have reached a marketable weight. Pigs are sent to the abattoir after 18 wk and cost 4.382€ per week. The costs presented include all the associated costs corresponding to each phase of the production process (feeding, doses of insemination, labor, transportation, and veterinary expenses). Transportation is outsourced to a single and specialized subcontractor. Thus, the company reduces fixed costs, such as the management of a truck fleet, additional facilities, and associated personnel. Hence, the number of trucks is not taken into consideration explicitly; instead, the number of trips required for transportation is needed. The company sends the trip schedule, and the subcontractor creates a transportation plan according to their constraints. Transportation cost depends on the distance between farms or to the abattoir, having a price per kilometer, from the source farm to its destination. The distance between the truck's origin to the source farm is not taken into consideration as that cost is assumed by the subcontractor. Transportation cost is set to 1€ per km and truck. Capacity of trucks, weight, and cost are taken into account depending on the type of animals transported. One truck can transport up to 700 piglets from sow farms to rearing farms and from rearing farms to fattening farms but only 240 pigs from fattening farms to the abattoir. The capacity of trucks for the sow farms that are culled is also 240 per truck. The model also takes into account the selling price based on the average of recent historical market series and remains constant through the time horizon defined. Two different values are considered based on the quality of the animal sold, namely, whether they come from the fattening farms or from sow farms, that is, commercial pigs or culled sows. The experiment takes 126€ in both cases, representing a lower value per kilogram of meat in sows with respect to fattened pigs. A time horizon of 156 wk (3 yr) has been considered realistic for the experiment. In Table 1, a list of all the activities and constraints, which were taken into consideration by the model, is shown. The constraints are discussed in detail in the next section. Table 1. Activities and constraints in the multi-period linear programming model Activity  Constraints  Sow farms  Initial inventory  Sows management  Capacity of facilities  Capacity control  Sow herd dynamics  Reproduction  Abattoir  Transfers to the abattoir  Growth of animals  Piglet's  Transfers between farms  Sow herd control  Transportation capacity  Piglet's weaning  Piglets' birth  Transfers to rearing farms  Demand  Rearing farms    Capacity control    Growth control    Transfers to fattening farms    Fattening farms    Capacity control    Growth control    Transfers to the abattoir    Activity  Constraints  Sow farms  Initial inventory  Sows management  Capacity of facilities  Capacity control  Sow herd dynamics  Reproduction  Abattoir  Transfers to the abattoir  Growth of animals  Piglet's  Transfers between farms  Sow herd control  Transportation capacity  Piglet's weaning  Piglets' birth  Transfers to rearing farms  Demand  Rearing farms    Capacity control    Growth control    Transfers to fattening farms    Fattening farms    Capacity control    Growth control    Transfers to the abattoir    View Large Table 1. Activities and constraints in the multi-period linear programming model Activity  Constraints  Sow farms  Initial inventory  Sows management  Capacity of facilities  Capacity control  Sow herd dynamics  Reproduction  Abattoir  Transfers to the abattoir  Growth of animals  Piglet's  Transfers between farms  Sow herd control  Transportation capacity  Piglet's weaning  Piglets' birth  Transfers to rearing farms  Demand  Rearing farms    Capacity control    Growth control    Transfers to fattening farms    Fattening farms    Capacity control    Growth control    Transfers to the abattoir    Activity  Constraints  Sow farms  Initial inventory  Sows management  Capacity of facilities  Capacity control  Sow herd dynamics  Reproduction  Abattoir  Transfers to the abattoir  Growth of animals  Piglet's  Transfers between farms  Sow herd control  Transportation capacity  Piglet's weaning  Piglets' birth  Transfers to rearing farms  Demand  Rearing farms    Capacity control    Growth control    Transfers to fattening farms    Fattening farms    Capacity control    Growth control    Transfers to the abattoir    View Large Formulation of the Model The objective of this model is to get the maximum gross margin achieved by optimizing the production from sow farms to the abattoir (for a complete definition of the model, see Nadal-Roig and Plà, 2014). This benefit is represented by the gross margin calculated by the addition of incomes from pigs sold to the abattoir minus the total amount of pigs' expenses and the transportation cost incurred for each farm. The model is formulated on a weekly basis given most of the activities on the farm and transportation between phases and to the abattoir occur regularly at this time frame. Therefore, the objective function is the total gross margin. It is calculated as the summation of weekly income minus cost over the time horizon for all farms. The general specification of the objective function is as follows:  where vt,h corresponds to the total weekly income of farm h in the t week, in particular, sales to the abattoir of culled and fattened pigs. The incomes only include sow farms and fattening farms, whereas ct,h, corresponding to the total weekly cost of farm h in the t week, includes all the farms in the production process. Different groups of constraints representing scarcity in some resources or limiting capacities have to be added to the model to achieve the objectives. Capacity of facilities. All facilities have a limited capacity. The capacity in sow farms depends on the number of sows that can be housed, whereas in rearing and fattening farms it depends on the maximum number of pigs that can be fed at a time. The capacity of each farm must be considered each week. Initial inventory. All farms which are part of the production process must have an initial inventory at the beginning of the planning horizon. This initial inventory affects the flow of animals along the chain in the succeeding weeks and over the time horizon period that is being considered. Sow herd dynamics. It is assumed that sow farms are operating under a steady state derived from the herd structure at equilibrium. This is because sow herd dynamics are modelled as a Markov decision process (Plà et al., 2009). For this reason, the steady state in each sow farm has to be considered. Abattoir. The abattoir is big enough to accept all pigs produced weekly, so there is no need to consider abattoir capacity or limit production, although it would be also possible to do it depending on the case study or if the company enlarged its own production much more. Growth of animals. Pigs that are fed on farms grow from one stage to the next. We assume that all pigs are fed under the same regime and grow in proportion to their age. Therefore, the inventory has to be updated over the time horizon considered. For simplicity, casualties of growing pigs are taken into account at the moment the animals are transferred to the following phase in the chain. This way the system tends to overestimate costs, but not the income, as casualties are not sent to the abattoir. Transfers between farms. Piglets that are transferred to the rearing or fattening farms are assumed to be done at the beginning of a week. Later on, after completing the number of weeks expected to grow for the current phase, all of them exit at the end of the last week. For this reason, the weekly flow of piglets sent to rearing farms cannot exceed the total number of piglets weaned the same week. The number of pigs starting the fattening phase cannot exceed the number of pigs finishing in the rearing phase in the same week. Transportation capacity. Constraints affecting transportation are related to the capacity of each truck. Animals sent to the abattoir are heavier than those transferred between farms, so different capacities or trucks may apply depending on what is to be transported. Hence, the number of trucks used to transport culled sows to the abattoir will depend on the replacement rate in each sow farm and the trucks capacity. Accordingly, the capacity of the trucks to transport piglets will vary depending the phase. Litter size. The number of piglets born alive will depend on the parity number and the number of sows per parity, and it is stated by an average litter size (Plà et al., 2009). Abattoir's quota. The company requires the farmers to meet a minimum production quota. The aggregate of this quota must satisfy a minimum quantity of animals sent to the abattoir. This is a strategic decision of the company to ensure a minimum production based on the overall production capacity. To develop the model, the modeling language ILOG OPL has been used. The solver CPLEX v12.2 solved the model in a laptop computer (Pentium Dual-Core CPU at 2.1 GHz and 4 GB RAM). The database has been developed with Microsoft Excel. It contains different sheets where users are allowed to register and maintain all input parameters for the model. The enterprise resource planning (ERP) of the company generates a Microsoft Excel file with an updated inventory of animals for each farm as well as the rest of parameters as prices and unitary costs considered by the model. After the model is executed, model outputs are retrieved, and reports and statistics are generated. The automation of this process is enough to allow an easy adoption of the model by the company. RESULTS The model, according to the parameters, has 948,792 constraints and 1,397,374 variables. The execution time is 4.5 h, having a GAP of 0.47% (because of the complexity of the model, a tolerance between the approximated solution given and the upper bound solution is defined). The optimization model shows a profit of 0.35€ per kilo of meat sent to the abattoir and a profit of 992.25€ per sow per year. As some of the direct cost incurred in the whole supply chain are taken approximately (such as labor, farms maintenance, electricity, water, etc.), this amount can be used as a reference but not as an exact value. In addition, the production capacity of each farm, phase, and the entire production process over time can be evaluated. In this sense, the outcome indicates that the capacity of all facilities involved in the production process are enough to host all produced pigs. In particular, rearing and fattening farms are capable of rearing and fattening all piglets produced in the sow farms. The steady state inventory of sows is of 12,705 animals. They are weaning a steady production of 6,585 piglets per week. Moreover, all the culled sows are sent to the abattoir and replaced by new ones. The global capacity of rearing farms is never overflowed. This means that the set of farms can accommodate all the piglets produced by the sow's farms. Although all rearing farms are used, their average occupancy varies depending on the week. Rearing farms tend to be occupied between 65% and 85% of their maximum capacity. At this phase, transfers between sows and rearing farms tend to locate near the piglets to the slaughterhouse or where the fattening farm's population is higher. This is because a truck can transport more pigs at this stage than when the pigs become heavier. Figure 2 shows the abattoir in coordinates (0,0), the location of sow farms and the preferred rearing farms used. Figure 2. View largeDownload slide Location of the sow farms (circles) and rearing farms (squares) from the abattoir (coordinates (0,0)), where most occupied rearing farms are the ones nearest to the abattoir. See online version for figure in color. Figure 2. View largeDownload slide Location of the sow farms (circles) and rearing farms (squares) from the abattoir (coordinates (0,0)), where most occupied rearing farms are the ones nearest to the abattoir. See online version for figure in color. The fattening farm's capacity is higher than the rest of the farms because the pigs stay in this phase longer (18 wk). The location of farms used at this stage do not have a pattern, as shown in Fig. 3. The occupancy varies from one to another. For instance, Fig. 4 shows a farm with a high occupancy that has been only emptied twice in the entire time horizon. On the contrary, Fig. 5 shows a farm occupancy used only in certain weeks when the other farms are full. Figure 3. View largeDownload slide Location of the fattening farms from the abattoir (coordinates (0,0)), where the most used farms are near rearing farms. See online version for figure in color. Figure 3. View largeDownload slide Location of the fattening farms from the abattoir (coordinates (0,0)), where the most used farms are near rearing farms. See online version for figure in color. Figure 4. View largeDownload slide Example of Farm #270, with a capacity of 1,040 piglets and located 27 km from the abattoir where the occupancy is high. See online version for figure in color. Figure 4. View largeDownload slide Example of Farm #270, with a capacity of 1,040 piglets and located 27 km from the abattoir where the occupancy is high. See online version for figure in color. Figure 5. View largeDownload slide Example of Farm #154, with a capacity of 660 piglets and located 49 km from the abattoir where the occupancy is not high. See online version for figure in color. Figure 5. View largeDownload slide Example of Farm #154, with a capacity of 660 piglets and located 49 km from the abattoir where the occupancy is not high. See online version for figure in color. To help with the operational decisions, the model can provide a weekly transportation schedule of the transfers to be done between farms and between farms and the abattoir. Tables 2 and 3 show examples of the transfers from sow farms to rearing farms and from rearing farms to fattening farms during the third week. These examples show the source and the destination farms as well as the quantity of piglets and the number or trips needed to transport them. Table 2. Weekly example of piglets' transfers from sow farms to rearing farms From sow farm  Piglets' quantity  Number of trucks  To rearing farm  4  300  1  1  4  244  1  128  5  232  1  15  8  624  1  15  9  1,039  2  128  14  126  1  140  14  421  1  294  15  105  1  15  15  562  1  23  15  556  1  199  17  686  1  15  17  540  1  137  18  575  1  290  132  504  1  176  132  71  1  128  Totals  6,585  16    From sow farm  Piglets' quantity  Number of trucks  To rearing farm  4  300  1  1  4  244  1  128  5  232  1  15  8  624  1  15  9  1,039  2  128  14  126  1  140  14  421  1  294  15  105  1  15  15  562  1  23  15  556  1  199  17  686  1  15  17  540  1  137  18  575  1  290  132  504  1  176  132  71  1  128  Totals  6,585  16    View Large Table 2. Weekly example of piglets' transfers from sow farms to rearing farms From sow farm  Piglets' quantity  Number of trucks  To rearing farm  4  300  1  1  4  244  1  128  5  232  1  15  8  624  1  15  9  1,039  2  128  14  126  1  140  14  421  1  294  15  105  1  15  15  562  1  23  15  556  1  199  17  686  1  15  17  540  1  137  18  575  1  290  132  504  1  176  132  71  1  128  Totals  6,585  16    From sow farm  Piglets' quantity  Number of trucks  To rearing farm  4  300  1  1  4  244  1  128  5  232  1  15  8  624  1  15  9  1,039  2  128  14  126  1  140  14  421  1  294  15  105  1  15  15  562  1  23  15  556  1  199  17  686  1  15  17  540  1  137  18  575  1  290  132  504  1  176  132  71  1  128  Totals  6,585  16    View Large Table 3. Weekly example of piglets' transfers from rearing farms to fattening farms From rearing farm  Piglets' quantity  Number of trucks  To fattening farm  15  664  1  281  15  699  1  306  15  406  1  145  20  789  2  289  20  684  1  291  20  240  1  204  137  406  1  221  176  518  1  145  190  1,199  2  103  199  99  1  112  199  203  1  267  256  678  1  203  15  664  1  281  15  699  1  306  Totals  6,585  14    From rearing farm  Piglets' quantity  Number of trucks  To fattening farm  15  664  1  281  15  699  1  306  15  406  1  145  20  789  2  289  20  684  1  291  20  240  1  204  137  406  1  221  176  518  1  145  190  1,199  2  103  199  99  1  112  199  203  1  267  256  678  1  203  15  664  1  281  15  699  1  306  Totals  6,585  14    View Large Table 3. Weekly example of piglets' transfers from rearing farms to fattening farms From rearing farm  Piglets' quantity  Number of trucks  To fattening farm  15  664  1  281  15  699  1  306  15  406  1  145  20  789  2  289  20  684  1  291  20  240  1  204  137  406  1  221  176  518  1  145  190  1,199  2  103  199  99  1  112  199  203  1  267  256  678  1  203  15  664  1  281  15  699  1  306  Totals  6,585  14    From rearing farm  Piglets' quantity  Number of trucks  To fattening farm  15  664  1  281  15  699  1  306  15  406  1  145  20  789  2  289  20  684  1  291  20  240  1  204  137  406  1  221  176  518  1  145  190  1,199  2  103  199  99  1  112  199  203  1  267  256  678  1  203  15  664  1  281  15  699  1  306  Totals  6,585  14    View Large Sensitivity to Parameter Changes As the model aims to be a useful tool for the company and other companies or researchers, some others experiments have been done to study the model's behavior. A lot of experiments can be done this way, but to simplify and give a clear example of model behavior, Table 4 only shows the most relevant behaviors and the variance between them: increasing the sales price, decreasing transportation cost, and increasing or decreasing the litter size. The experiments show that increasing the sales prices at the proposed range does not affect the production, having a minimal effect on transfers between farms as the cost of transportation does not change. Therefore, the sales price affects the final benefit but not at the operations level in the production process. On the other hand, the transportation cost affects both the cost of transport and the number of trips needed. According to Table 4, in case this cost is eliminated or reduced drastically, the model would not take into consideration the distance between farms when scheduling transports. Finally, the decrease in the number of litter per sow affects the entire production process only in terms of quantity to be produced, and consequently, the benefit decreases. On the other hand, an increase of the litter size per sow can generate an overproduction, making the farms overloaded. In this case, the model could not transfer all the piglets produced in the sow farms to the rearing farms due to the capacity restrictions, and the model would not have solution. Table 4. Percent of variance of farm occupancy and trips per experiment   Farm occupancy1  Number of trips2  Experiment  Sow  Rearing  Fattening  SA  SR  RF  FA  Base3  26,342  39,513  118,540  1,705  2,278  2,036  4,432  Sales price +20%  0%  0%  0%  0%  0.1%  0.01%  0%  Sales price + 30%  0%  0%  0%  0%  0%  0.01%  0%  Transport cost = 0€  0%  0%  0%  0%  60%  117%  40%  Litter size = -20%  –20%  –20%  –20%  0%  –8.77%  –10%  –16.69%  Litter size = +20%4  –  –  –  –  –  –  –    Farm occupancy1  Number of trips2  Experiment  Sow  Rearing  Fattening  SA  SR  RF  FA  Base3  26,342  39,513  118,540  1,705  2,278  2,036  4,432  Sales price +20%  0%  0%  0%  0%  0.1%  0.01%  0%  Sales price + 30%  0%  0%  0%  0%  0%  0.01%  0%  Transport cost = 0€  0%  0%  0%  0%  60%  117%  40%  Litter size = -20%  –20%  –20%  –20%  0%  –8.77%  –10%  –16.69%  Litter size = +20%4  –  –  –  –  –  –  –  1Farm occupancy in number of piglets in sow farms, rearing farms and fattening farms. 2Number of trips: SA = From sow farms to the abattoir; SR = From sow farms to rearing farms; RF = From rearing farms to fattening farms; FA = From fattening farms to the abattoir. 3The experiment described in this paper. 4Shows no result due the fattening farms exceeds the occupancy. View Large Table 4. Percent of variance of farm occupancy and trips per experiment   Farm occupancy1  Number of trips2  Experiment  Sow  Rearing  Fattening  SA  SR  RF  FA  Base3  26,342  39,513  118,540  1,705  2,278  2,036  4,432  Sales price +20%  0%  0%  0%  0%  0.1%  0.01%  0%  Sales price + 30%  0%  0%  0%  0%  0%  0.01%  0%  Transport cost = 0€  0%  0%  0%  0%  60%  117%  40%  Litter size = -20%  –20%  –20%  –20%  0%  –8.77%  –10%  –16.69%  Litter size = +20%4  –  –  –  –  –  –  –    Farm occupancy1  Number of trips2  Experiment  Sow  Rearing  Fattening  SA  SR  RF  FA  Base3  26,342  39,513  118,540  1,705  2,278  2,036  4,432  Sales price +20%  0%  0%  0%  0%  0.1%  0.01%  0%  Sales price + 30%  0%  0%  0%  0%  0%  0.01%  0%  Transport cost = 0€  0%  0%  0%  0%  60%  117%  40%  Litter size = -20%  –20%  –20%  –20%  0%  –8.77%  –10%  –16.69%  Litter size = +20%4  –  –  –  –  –  –  –  1Farm occupancy in number of piglets in sow farms, rearing farms and fattening farms. 2Number of trips: SA = From sow farms to the abattoir; SR = From sow farms to rearing farms; RF = From rearing farms to fattening farms; FA = From fattening farms to the abattoir. 3The experiment described in this paper. 4Shows no result due the fattening farms exceeds the occupancy. View Large DISCUSSION The model has been considered useful by the company at this stage. Benefits come mainly through the week-by-week schedule to support and help make decisions regarding where, when, and how many piglets will be transported for a certain period of time; evaluation of the production capacity of each farm, phase, and the entire supply chain over time; and in the planning and scheduling of the trucks needed weekly, which means saving oil and time. Moreover, the execution of the model can be useful for the company in making midterm or long-term decisions. It is also worth mentioning that before the project started, the company's department of production was assisted only by an Excel spreadsheet as well as by conducting weekly meetings that decided the flow of animals to be transported, that is, origin and destination, but without considering the transportation costs or the need for buying new fattening farms to allocate for unforeseen number of piglets. After the delivery of the preliminary results, meetings at the company have become more relaxed and productive. They can now allocate more time to discuss other strategic topics for which they did not have time before. Relationships between the department of production, technicians, and pig specialist working on the farm have improved because the planning is clearer and decisions are explained. The model can be adapted to different multifarm production systems as a result of its flexibility when setting up their parameters. The structure of the model described is focused on a three-site system, but a two-site system or a mixture of both can be also modeled this way. Despite the advantages shown in the previous section, the results of the model itself indicate opportunities for improvements. First, the current model can be extended in a stochastic optimization model to deal with the uncertainty of some parameters such as sale prices and demand. Second, the explicit inclusion of batches of animals in fattening farms may extend the model's functionality for those companies which work with it. That is, the so-called all-in-all-out management system that has been demonstrated as useful for disease prevention and control of the animals. Third, adding flexibility in the duration of phases to create a marketing window for deliveries to the abattoir and therefore to account for uncertainties in the growth of animals allow to better the capture of opportunity costs from the market. Finally, the huge number of farms involved and the relationship between them demand a large amount of computational time. The extension of the model having more functionalities as requested by the company will make the model more complex. Hence, the parallelization of the model with the aim to improve the execution time is an interesting approach that we are exploring. At present, other Spanish companies, as well as consultancies, have already shown interest in the proposed model. Conclusions Our contribution emphasizes the importance and complexity of decision making tasks in the modern organization of the pork sector. Therefore, models and tools that help in this decision making context are needed. Although the model presented open areas for improvement, such as schedule transports, planning the flow of animals, and analysis capacities as described previously, it can be used as it is, and it makes it possible to envision and explore new business opportunities for a single pork supply chain. Finally, the capability of the model of being integrated into the ERP of pig companies allows the model to be easily adopted by them. LITERATURE CITED Mezghani M. Loukil T. Aouni B. 2012. Aggregate planning through the imprecise goal programming model: Integration of the manager's preferences. Int. Trans. Oper. Res.  19( Suppl. 4): 581 – 597. Google Scholar CrossRef Search ADS   Morel P. C. H. Sirisatien D. Wood G. R. 2012. Effect of pig type, cost and prices, and dietary restraints on dietary nutrient specification for maximum profitability in grower-finisher pig herds: A theoretical approach. Livest. Sci.  148: 255– 267. Google Scholar CrossRef Search ADS   Nadal-Roig E. Plà L. M. 2014. Optimal planning of pig transfers along a pig supply chain under uncertainty. In: Plà-Aragonés L. M. editor, Handbook of operations research in agriculture and the agri-food industry.  Springer, Berlin, in press. Nijhoff-Savvaki R. Trienekens J. H. Omta S. W. F. 2012. Drivers for innovation in niche pork netchains: A study of UK, Greece and Spain. Br. Food J.  114: 1106– 1127. Google Scholar CrossRef Search ADS   Ohlmann J. Jones P. 2011. An integer programming model for optimal pork marketing. Ann. Oper. Res.  190: 271– 287. Google Scholar CrossRef Search ADS   Perez C. de Castro R. Font i Furnols M. 2009. The pork industry: A supply chain perspective. Br. Food J.  111( Suppl. 3): 257– 274. Google Scholar CrossRef Search ADS   Plà L. M 2007. Review of mathematical models for sow herd management. Livest. Sci.  106: 107– 119. Google Scholar CrossRef Search ADS   Plà L.M. Faulín J. Rodríguez S.V. 2009. A linear programming formulation of a semi-Markov model to design pig facilities. J. Oper. Res. Soc.  60( Suppl 5): 619– 625 Google Scholar CrossRef Search ADS   Plà L. M. Romero D. 2008. Planning modern intensive livestock production: The case of the Spanish pig sector. In: Int. Workshop in Oper. Res., La Havana, Cuba. Rodríguez S. V. Albornoz V. M. Plà L. M. 2009. A two-stage stochastic programming model for scheduling replacements in sow farms. Top (Madr.)  17: 171– 189. Rodríguez S. V. Faulin J. Plà L. M. 2012. New opportunities of operations research to improve pork supply chain efficiency. Ann. Oper. Res.  in press. Taylor D. H 2006. Strategic consideration in the development of lean agri-food supply chains: A case study of the UK pork sector. Supply Chain Manage. Int. J.  11( Suppl. 3): 271– 280. Google Scholar CrossRef Search ADS   Tsolakis N. K. Keramydas C. A. Toka A. K. Aidonis D. A. Lakovou E. T. 2014. Agrifood supply chain management: A comprehensive hierarchical decision-making framework and a critical taxonomy. Biosystems Eng.  120: 47– 64. Google Scholar CrossRef Search ADS   American Society of Animal Science
TI - Multiperiod planning tool for multisite pig production systems
JF - Journal of Animal Science
DO - 10.2527/jas.2014-7784
DA - 2014-09-01
UR - https://www.deepdyve.com/lp/oxford-university-press/multiperiod-planning-tool-for-multisite-pig-production-systems-DCaf96sU3d
SP - 4154
EP - 4160
VL - 92
IS - 9
DP - DeepDyve
ER -