A Quality Decision Model Considering the Delay Effects in a Dual-Channel Supply Chain

Quality is not only the basis for business survival and development but also a key issue that cannot be ignored in supply chain management decisions. In practice, the impact of quality on goodwill does not show an immediate effect, and there is a dynamic delayed effect. Therefore, we developed a dynamic model that considers the delayed effect of quality on goodwill. Firstly, we constructed a delayed differential equation for the effect of quality on goodwill based on the Nerlove-Arrow model for a two-channel supply chain in a competitive environment and studied the dynamic quality decision problem of manufacturers and retailers under the delay effect. Secondly, we constructed the manufacturer and retailer Hamilton functions based on the principles of being of great value, solving and comparing the optimal product quality level, having an optimal service quality level, product goodwill, and overall profit of the supply chain under both decentralized and centralized decision modes, and investigated the effect of delay time on the profit and quality decisions of supply chain members. The conclusions show that: (i) delay time is an important reference for supply chain members when choosing the decision mode, and the overall profit size of the supply chain has different relationships with the different values of delay time taken into account with the two decision scenarios. (ii) Adopting a centralized decision mode can motivate manufacturers and retailers to improve the quality level, which in turn promotes the sales of products and the accumulation of brand goodwill.