A Piecewise-objective Fuzzy-probabilistic Programming Approach for Supplier Selection Problems Involving Discounted Prices/Costs and Uncertain Parameters

The problems of supplier selection involve two parties, namely manufacturers/retailers and suppliers. This paper aims to propose a piecewise-objective fuzzy-probabilistic optimization model that can be used to solve such problems which involve discounted prices/costs and uncertain parameters. The costs of raw materials/products rejected from suppliers and the costs of late deliveries/shortages of raw materials/products are considered as probabilistic parameters on the assumption that data are available to build the probability density functions. Meanwhile, the raw material/product demand is considered as a fuzzy parameter on the assumption that data are not available, and thus the decision-maker makes use of their intuition and experience to build the membership function of the demand. The model proposed in this study is suitable for applications on new brands of products where demand data have not been collected. It was formulated by minimizing the expected total operating cost subject to demand fulfillment and capacity limits, and then was tested by computational simulations. The results show that the proposed model is successful in providing the optimal decision, which proves that it can be utilized by decision-makers in relevant industries.