Optimization-based Decision-Making Support for Fuzzy and Probabilistic Order Allocation Planning

Abstract

This paper proposed optimization-based decision-making support for solving the planning problems of raw material/product order allocation. A few parameters (prices, demand values, defective product rate, and late delivery) are uncertain and are treated as probabilistic or fuzzy depending on the data availability. Meanwhile, the parameters with historical/trial data are treated as probabilistic with some distribution functions. However, the parameters without any data are treated as fuzzy, and their corresponding membership functions are built by managers based on intuition and experience. Therefore, this study aims to determine optimal values for the decision variables, namely the number of raw materials planned to be ordered and its corresponding suppliers such that the total operational cost is expected to be minimal. These optimal decisions are calculated from the proposed optimization model in LINGO software by implementing the generalized Gradient algorithm. To evaluate and illustrate the proposed decision-making support, a numerical simulation was demonstrated. The results showed the optimal decisions were successfully attained and the expected minimal total operational cost was achieved. Furthermore, it proved that the proposed decision-making support could be implemented in manufacturing or retail industries to solve their order allocation problems.