A two-echelon supply chain coordination for deteriorating item with a multi-variable continuous demand function

This paper considers a two-echelon supply chain system consisting of one manufacturer and one retailer for deteriorating items. Shortages are not allowed and the market demand is simultaneously influenced by multiple factors including promotional effort, selling price, on-hand inventory level and time. Demand information is symmetrically known to both the manufacturer and the retailer, hence, the promotional effort is assumed to be provided by both members. For the system where the manufacturer and the retailer share the investment cost of promotional effort equally, it is shown that revenue sharing contract and revenue and cost sharing contract can both lead to perfect coordination. Comparing these two contracts, it is also found that the latter contract is easier to be accepted by the system. Hence, revenue and cost sharing contract is applied to coordinate the general system, and the range of revenue sharing fraction leading to a win-win outcome is obtained. Two numerical examples are presented to illustrate the development of the model with sensitivity analysis.