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.