The Joint Decision-Making Support through Piecewise Objective Optimization Model for Integrated Supplier Selection, Inventory Management, and Production Planning Involving Discounts

- Widowati - Diponegoro University, Semarang, 50275, Indonesia
- Sutrisno - Diponegoro University, Semarang, 50275, Indonesia
Robertus Utomo - Diponegoro University, Semarang, 50275, Indonesia

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The decision-makers in manufacturing industries continuously optimize every supply-chain part to achieve optimal profit. In this paper, three crucial activities in the supply chain are observed as profit contributors: supplier selection, inventory management, and production planning. Decision-making support is needed to optimize those activities, especially when prices/costs involve discounts. Therefore, this study aims to develop integrated decision-making support for supplier selection, inventory management, and production planning involving discounted prices. The problem was considered with multi-supplier, multi-raw material, multi-product, and multi-observation time instant. The objective was based on maximizing the profit for the entire activity, i.e., from the raw material procurement and storage to the production. This supply chain was modeled as mixed-integer linear programming with a piecewise objective function representing the profit, which was maximized. It was also modeled with a bunch of constraint functions, including product demand satisfaction. The proposed model was tested with computational simulations using randomly generated supply chain data. The primal simplex algorithm was also employed to calculate the real value of the optimal decision, which was combined with the Branch-and-Bound approach to calculate the appropriate integer solution. The results showed that the optimal decision was achieved, namely (1) The optimal quantity of raw materials ordered to each supplier, (2) The optimal production quantity, and (3) The optimal inventory level, which provided the maximal profit for the whole optimization time horizon. This indicated that the proposed decision-making support model is implementable for industrial decision-makers.


Joint decision-making support; primal simplex; linear programming; supplier selection; integrated supply chain

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