Design of optimal control strategies for a supply chain with competing manufacturers under consignment contract

In this paper, we discuss the effects of competition among the manufacturers on both the equilibrium strategies and the performance of supply chain under consignment contract based an optimal control theory. The retailer is responsible for the improvement of store-assistance to reduce consumer returns, and two manufacturers sell their products to end customers through the retailer and control the retail price. The aim of this paper is to derive and compare the equilibrium strategies under the different game environments. Accordingly, it is illustrated that the cooperation between retailer and manufactures can lead to a higher retail prices and the store-assistance service investment, moreover, a higher competition also could result in a higher store-assistance service investment. Furthermore, the supply chain in the non-cooperative environment can be coordinated by designing a modified cost-sharing contract, where all members can benefit from this coordination. Finally, numerical simulations are presented to illustrate the impact from the competition among the manufacturers on the profit and contract of supply chain.