Optimal production-inventory policy for an integrated multi-stage supply chain with time-varying demand

•A new model for an integrated multi-stage supply chain with time-varying demand is considered.•This paper generalizes the time-varying demand to multiple phases up to an arbitrary integer.•The global minimum total operational cost is computed by the developed algorithm.•A sensitivity analysis is done to assist supply chain decision makers.

An integrated multi-stage supply chain with time-varying demand over a finite planning horizon is considered in this paper. The objective is to devise the optimal production-inventory policy to minimize the total operational cost. The model is formulated as a mixed integer nonlinear programming problem. The problem is represented as a weighted directed acyclic graph. The global minimum total operational cost is computed in polynomial time by the developed algorithm. Two numerical examples of a seasonal product and a product over its life cycle are studied to illustrate the results. A sensitivity analysis of the system parameters is conducted to assist the supply chain decision makers.