Optimal integer-ratio inventory coordination policy for an integrated multi-stage supply chain

• The mathematical model integrates four stages into one chain.
• The optimal integer-ratio inventory coordination policy is obtained.
• The optimal integer ratio is dependent on the system and transportation costs.
• The optimal integer ratio is dependent on the ratio of demand rate to production rate.
• The optimal total operational cost is proven to reach its global minimum after relaxation.

An integrated production-inventory-distribution planning problem faced by a multinational corporation managing a multi-stage supply chain over an infinite time horizon is considered in this paper. Based on the supply chain management practice of this company, we devise an optimal integer-ratio coordination policy for inventory replenishment across its supply chain. Under the proposed optimal integer-ratio inventory coordination policy, the total operational cost of the supply chain is proven to reach its global minimum after the integrality constraints are relaxed. Numerical examples are presented with a sensitivity analysis. Computational results show that the difference in the optimal total operational costs between integer and real number solutions is not significant.