A Multi-period Stochastic Production Planning and Sourcing Problem with Discrete Demand Distribution

This paper studies a new class of multi-period stochastic production planning and sourcing problem with minimum risk criteria, in which a manufacturer has a number of plants or subcontractors and has to meet the product demands according to the service levels set by its customers. In the proposed problem, demands are characterized by stochastic variables with known probability distributions. The objective of the problem is to minimize the probability that the total cost exceeds a predetermined maximum allowable cost, where the total cost includes the sum of the inventory holding, setup and production costs in the planning horizon. For general demand distributions, the proposed problem is very complex, so we cannot solve it by conventional optimization methods. To avoid this difficulty, we assume the demands have finite discrete distributions, and derive the crisp equivalent forms of both probability objective function and the probability level constraints. As a consequence, we turn the original stochastic production planning problem into its equivalent integer programming one so that the branch-and-bound method can be used to solve it. Finally, to demonstrate the developed modeling idea, we perform some numerical experiments via one 3-product source, 8-period production planning problem.