Scheduling Short-Run Changes in Production to Minimize Long-Run Expected Costs

This paper investigates the problem of scheduling production from one period to the next to minimize long-run expected costs where the only relevant considerations are the expense of revising production and the charges related to inventory. We first consider the case of constant sales known over time in order to compare exact and approximate solutions. The approach to these solutions is based on minimizing the costs of deviating from long-run equilibrium values of production and inventory. The same approach is then used to handle the more realistic possibility of uncertain future demands. Solutions are obtained for both linear and quadratic inventory and production cost functions. Because future demand is assumed to be specified by some probability distribution, inventory costs must be approximated in order to obtain a closed-form solution; however, the result should differ insignificantly from an exact optimal solution.