Optimal Allocations in the Construction of k-Out-of-n Reliability SystemsDerman, C.; Lieberman, G. J.; Ross, S. M.
doi: 10.1287/mnsc.21.3.241pmid: N/A
We want to build n components so as to form an n component system which will function if at least k of the components function. If x dollars are invested in building a component, then this component will function with probability P(x). Given a total income of A dollars, the problem of interest is to determine how much money we should invest in each component so as to maximize the probability of attaining a functioning system. This problem is considered both in the sequential and in the nonsequential cases. Conditions under which it is optimal to allocate A/n units at each stage, when A is your initial fortune, are presented. The special case P(x) min(x, 1) is also considered in detail.
Optimum Checking Schedules for Systems Subject to Random FailureKeller, Joseph B.
doi: 10.1287/mnsc.21.3.256pmid: N/A
An optimum checking schedule is one that minimizes the expected cost, which is the sum of the cost of checking and the expected loss due to an undetected failure. The problem is made tractable by supposing that checking is so frequent that it can be described by a continuous density n(t) of checks per unit time. The optimum n(t) is found by the methods of the calculus of variations. An explicit result is given when the loss is proportional to the duration of an undetected failure. A minimax solution is also given for the case in which the probability of failure is not known.
Inspection Procedures for Markov ChainsSackrowitz, Harold; Samuel-Cahn, Ester
doi: 10.1287/mnsc.21.3.261pmid: N/A
Consider a production process where the categories of successive units form a Markov chain with known transition matrix. Whenever a unit is produced, we may, at a fixed cost, inspect it. If its value is less than maximal, we may replace it with a perfect (maximal value) unit. We obtain optimal inspection procedures (procedures for which the value of the outgoing units is high and which keep the cost of inspection down).
A Linear Program for Economic Lot Sizes using Labor PrioritiesMay, J. Gaylord
doi: 10.1287/mnsc.21.3.277pmid: N/A
This paper presents the development of a mathematical model to generate economic lot sizes, on a weekly basis, for an assembly-type shop. The model appears as a linear program which optimizes assigned labor priorities. Included is a description of the results achieved from a successful implementation of the model into the assembly operations.The paper also identifies this shop's problem within the general context of multi-product, multi-period scheduling. In particular, a certain class of scheduling problems is formulated using described techniques.
The Assortment Problem with Probabilistic DemandsPentico, David W.
doi: 10.1287/mnsc.21.3.286pmid: N/A
The early work done on the assortment problem assumed known demands and additive and proportional substitution cost functions for single period problems. The extension of this problem (to consider probabilistic demands and multiple periods) complicates the problem considerably. By making some assumptions about the pattern of demands and the form of a reasonable solution, the problem can be approached by using dynamic programming thus finding the shortest route through a network.
Expected Objective Value of a Stochastic Linear Program and the Degree of Uncertainty of ParametersItami, Hiroyuki
doi: 10.1287/mnsc.21.3.291pmid: N/A
In this paper, we characterize the relationship between the expected optimal value of a stochastic linear program and a stochastic program with recourse and the degree of uncertainty in the objective function coefficients c and the stipulation vector b. It is shown that under certain conditions the expected objective value is nondecreasing as the degree of uncertainty in c increases and the opposite is true for the case of b. The degree of uncertainty of a random vector is defined in terms of a covariance matrix. Some managerial interpretations are also given.
Marketing Strategy and the Optimal Production ScheduleLeitch, Robert Alan
doi: 10.1287/mnsc.21.3.302pmid: N/A
Incorporation of marketing strategy in production planning can reduce overall costs and significantly increase profits.In this paper a solution procedure similar to the traditional Holt, Modigliani, Muth, and Simon production smoothing model is used to find a combined marketing and production plan in which advertising promotion is utilised to avoid peak-load production costs by shifting seasonal demand for a product. The solution procedure is applicable to a wide variety of market characterizations, and the technique may also be readily adapted to analyse impacts of various aspects of market behavior on the optimal production schedule.