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.