Stochastic production planning and sourcing problems with service level constraints

Abstract

ABSTRACT We study stochastic multiperiod production planning problems of a manufacturer with single/multiple plant(s) and/or subcontractors. Each source, i.e. each plant and subcontractor, has a different production cost, capacity, and lead time. The manufacturer has to meet the demand for single/multiple product(s) according to the service level requirements set by a retailer. The demand for each product in each period is random. We present a methodology that a manufacturer can utilize to make its production and sourcing decisions, i.e., to decide how much to produce, when to produce, where to produce, how much inventory to carry, etc. This methodology is based on a mathematical programming approach. Stochasticity in the problem that comes from random demand and service level constraints is integrated in a deterministic mathematical program by adding a number of additional linear constraints. Solving this deterministic equivalent problem yields the an approximation to the solution of the stochastic problem. We justify the equivalencies between the base stock model and the deterministic equivalent model with modified service level constraints solved on a rolling horizon basis in the single product single production facility setting. For the multiple plants setting without lead time, we show that the deterministic equivalent model gives good enough solutions to the threshold subcontracting model. Finally, motivated by a production planning and sourcing problem in the textile- apparel-retail channel, we use the proposed methodology to perform some numerical experiments to get insights regarding the interaction among the cost, lead time, and variability of demand and how they affect the sourcing decisions. Keywords: stochastic production planning, service level constraints, subcontracting m