Optimal and Heuristic Profit Sharing Using Sales Rebate Contract in a Multi-level Supply Chain

Abstract

A supply chain (SC) is an interdependent network of many SC members who add value to the product successively until it gets to the final stage and attains utility. One of the most important problems in any supply chain (SC) consisting of organizations is the sub-optimization due to the fact that the SC decision making is distributed over various players. An interesting solution to the issue, which leaves the decision power and supply chain structure intact, is the use of contract mechanisms. Ideally, contract mechanisms ensure that the whole SC is optimized as if it were a single unit (coordination) and is designed such that all the players benefit from working together through the coordination mechanism (win-win). Once coordination is in place, the next challenge is to devise some mechanism to share the profits gained due to coordination. To enable coordination among the SC members, sales rebate contracts in a multi-level SC using fair share mechanism have been devised. In the sales rebate contract, the supplier charges the buyer wholesale price per unit purchased but then gives rebate to the buyer per unit sold above some threshold. The objective of this paper is to determine the optimal rebates given to downstream SC members and threshold value of sales, which maximizes the SC profit as well as fairly shares the profits among the SC members. This objective can be achieved by minimizing the deviation between proportion of each member’s value addition and proportion of each member’s respective share in the total profit by coordinating through sales rebate contract. An analytical model is developed to formulate the supply chain coordination problem and simultaneously formulate the optimization problem to achieve fair distribution of profit among the SC members. Three heuristic search techniques based on genetic algorithm and simulated annealing have been proposed to solve the problem.