Capacity requirements planning by stochastic linear programming

In this paper we formulate the problem of capacity requirements planning under uncertainty as a stochastic linear program (SLP). The objective is to minimize the total cost of underutilization, overtime production, and carrying inventory. Although it is desirable to achieve a stable inventory level in a production system, the stochastic nature of the demand causes inventory fluctuation over the planning horizon. As a result, we incorporate in our model the deviation of the actual inventory level from the ideal inventory level as a set of chance constraints, which may be violated with a specified probability. In this way the SLP problem is transformed into an ordinary deterministic LP problem, which can be solved efficiently and cheaply on computers to obtain the optimal planning strategy.