Optimal dynamic promotion strategies in the multiple competing supply chains

Abstract

In this paper, the optimal decision problem is investigated for a class of dynamic promotions in the multiple competing supply chains. Here, the dynamic advertising model is allowed to be influenced by horizontal joint promotions (HJP) and vertical joint promotions (VJP). We extend the classical Nerlove–Arrow model by considering the effect of competitive manufacturer’s VJP effort on brand goodwill. Also, the continuous-time demand is constructed with the effect of competitive retailer’s VJP and HJP efforts. Based on the Hamilton–Jacobi–Bellman equation, the optimal HJP and VJP strategies of supply chain members and the optimal promotion cost sharing rate of each manufacturer are obtained under the Decentralized–Decentralized and Decentralized–Centralized structures, respectively. Subsequently, the comparison between the two structures shows that the optimal VJP and HJP efforts of supply chain members increase with their marginal profits and each manufacturer is willing to pay for the retailer’s VJP effort level when the marginal profit of manufacturer exceeds the half of retailer’s marginal profit. Numerical examples are provided to show the change of profit difference with parameters α and β under the different structures.