In recent years, the environment surrounding companies has become more challenging. It has become more difficult for many companies in the manufacturing industry to possess all the skills they need, such as production, warehousing, and retailing, so they need to outsource certain skills. In supply chains with several companies, each has an optimal strategy. Specifically, supply chains where the solution is decided through negotiations with their partners are defined as “decentralized supply chains.” In such situations, collaborative relationships are important. One possible approach is replenishment contracts between vendors and buyers under the condition that demand for each buyer is constant. In a buyer-dominated supply chain, because the vendor cannot choose solutions that lower the satisfaction of buyers, it is difficult to change the replenishment intervals. The common replenishment epochs (CRE) strategy is one of the methods used to address this issue. The vendor integrates the buyers’ replenishment timings using CRE and provides a price discount on the products to compensate for the increase in the cost to the buyers. The price discount rate is calculated based on the worst reduction rate in the costs incurred by the buyers based on the economic order quantity (EOQ) model. The optimal CRE and discount rate are decided such that the cost incurred by vendor is minimized. The increased emphasis on the worst reduction rates can potentially lead to biases in buyer satisfaction, and the price discount rate is overestimated. Then, the cost of the vendor increases. Hence, through the negotiations with less satisfied buyers, the vendor changes the CRE so that their satisfaction is improved and the price discount is lower. As a result, the vendor can reduce its cost. This study develops a model to find an improved solution after the negotiations. If satisfaction of multiple players is regarded as multi-objective, a solution of multi-player decision-making is obtained using multi-objective optimization. Linear physical programming (LPP) has been applied as a form of multi-objective optimization, and it is possible to determine the weight coefficients using the preference ranges of the objective functions. In addition, by considering the buyers’ preference levels, the constraints of the discount rates are relaxed and the vendor’s cost can be reduced. Therefore, this study develops a model based on the CRE strategy using LPP.
Physical programming for preference driven evolutionary multi-objective optimization