Probabilistic Piecewise-Objective Optimization Model for Integrated Supplier Selection and Production Planning Problems Involving Discounts and Probabilistic Parameters: Single Period Case

In manufacturing and retail industries, supplier selection problems deal with allocating the optimal raw material amount that should be purchased to each supplier such that the procurement cost is minimal. Meanwhile, production planning problems deal with maximizing the product amount to be produced. Decision-makers need to take optimal decisions for those problem to gain the maximal revenue. In this paper, a novel mathematical model in the class of probabilistic piecewise programming is proposed as a decision-making support that can be used to find the optimal decision in solving both integrated supplier selection and production planning problems involving discounts and probabilistic parameters. The objective is to gain the optimal performance of the supply chain, i.e., maximizing the profit from the production activity. The model covers multi-raw material, multi-supplier, multi-product, and multi-buyer situations. Numerical experiments were conducted to evaluate the proposed model and to illustrate how the optimal decision is taken. Results showed that the proposed decision-making support successfully solved the problem and provided the optimal decision for the given problem. Therefore, the proposed model can be implemented by decision-makers/managers in industries.