New Optimal-Control-Based Advertising Strategies and Coordination of a Supply Chain With Differentiated Products Under Consignment Contract

With the aid of optimal control theory, the cooperative advertising problem is discussed for a supply chain under consignment contract in a competitive environment. Consider the case that the market demand of products is affected by advertising effort and goodwill, both the optimal advertising strategies and advertising participation rate in the centralized and decentralized settings are given. The state-dependent contract with the slotting fees is introduced to coordinate the considered supply chain. Our results demonstrate that the participation rate is closely related to the marginal profits of channel members and the competition intensity between products. Besides, the state-dependent contract with the slotting fees can effectively coordinate the supply chain when the contract parameters satisfy certain conditions. Finally, the sensitivity analysis of the competition intensity between products is conducted by using some simulations.