(658a) Diagnosis of Linear Programming Supply Chain Optimization Models: Minimizing Changes for New Parameter Values

This work addresses the challenge of updating operating decisions in supply chain optimization models in the face of changing conditions. For example, there might be increases or decreases in the demands of customers for certain products, reduction of raw materials from suppliers, changes in prices of raw materials, intermediates and products, and changes in transportation costs between suppliers and plants. To adapt to these types of changes, there are commonly trade-offs associated with implementing changes in the selection suppliers, customers, delivering or sourcing materials from sellers and buyers. Specifically, to improve profitability one may have to undertake a significant number of changes. On the other hand, to maintain stable operation one would prefer to reduce both the number and magnitude of required changes^[2].

Mathematical programming models such as LP, MILP or MINLP are used to optimize long-term/midterm planning, and short-term operations of supply chains^[3][4]. Although these models are useful, challenges arise when the optimization models must be updated for the changing conditions encountered during operation. The challenges include on the one hand the possibility of not being able to find feasible solutions, or on the other hand obtaining feasible solutions that involve a very large number of changes. Motivated by these challenges we propose formulations to minimize the changes introduced in the solution of linear programming models for supply chain optimization, and help the users to interpret the changes in the model.

Specifically, we propose three formulations to minimize the magnitude of changes, minimize the number of changes and minimize the weighted sum of both magnitude and number of changes, when there is a change in the parameters in the corresponding linear programming model. We also formulate a bi-criterion optimization model by considering the objectives of minimizing cost and minimizing the weighted sum of the number and magnitude of changes to analyze the trade-off between the two in the Pareto frontier. An ideal compromise solution is also presented to determine the trade-off solution between the two objectives that is closest to the utopia point, namely the point when both objectives are optimized independently. These algorithms are applied to several supply chain test problems to demonstrate their usefulness.

Furthermore, the formulations are extended to a large-scale supply chain problem based on Aurubis AG’s supply chain network. The features of this large-scale model such as its multi-period structure require an extension to the proposed algorithm of minimizing changes. Our goal is to demonstrate algorithms to classify the types of changes, extending from the formulation that counts distinct and new changes that occur due to the disruptions introduced in the model. The significance of this work is that it contributes to the analysis and interpretation of linear programming supply chain optimization results to minimize changes introduced due to variation in parameters.

References

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