Stochastic production planning models with capacity constraints

Abstract

This thesis considers production planning procedures for the following four cases. first, a single-product production planning problem with stochastic demand and a finite number of planning periods is investigated where cumulative nds up to each period are independent random variables with continuous probability distributions. sin the problem backlogging is allowed and production is restricted by its capacity limit. Dynamic linear costs of inventory holding and backlogging, and of production with setup charge are considered. Second, the single-product production planning problem is extended to a multi-product problem with joint setup costs. Third, the first problem is considered in a rolling horizon environment. Finally, the single-product production planning problem is considered again where demands are deterministic but capacity constraints are imposed on production, inventory holding, and inventory backlogging, respectively. In the first and second cases, the stochastic production planning problem is transformed to equivalent deterministic problems of which cost functions are mixture of concave and convex functions. As solution procedures, a branch and bound algorithm is developed for the first case to find an optimal plan within finite searching steps by approximating the objective function to a convex function at each searching step. The generalized Benders decomposition procedure is considered in a specific context for the second case, since the multi-product factor with the joint setup cost makes the branch and bound algorithm not easy to apply for the multi-product problem. The generalized Benders decomposition procedure is also adapted in the specific context for the deterministic problem in the last case, where a characterization of solution space is found to resolve some difficulties incurred otherwise by the capacity constraints of inventory holding and inventory backlogging. The computational performance of the solution procedure for each of ...