MILP Model Solution Steps: Implementation of Big M Simplex and Branch and Bound in the Coffee Supply Chain

Ananda Hans Islamiyah, Umu Sa'adah, Corina Karim

Abstract


This research aims to develop a Mixed-Integer Linear Programming (MILP) model to optimize the distribution of coffee from producing sub-districts to storage warehouses, and subsequently to destination markets in Malang Regency during the 2020–2024 period. This model minimizes total logistics costs, which include distribution, shipping, and warehouse operating costs. The Big M Simplex method is used to handle logical constraints in the model, while the Branch and Bound algorithm is used to determine the operational state of the warehouse as a binary variable. The optimization results show that the warehouse is actively operated every year, with a distribution flow capable of meeting all market demands. The optimal purpose function value obtained is IDR 43,265,867,761,500,-. for five years. This shows that the combination of MILP, Big M, and Branch and Bound is effective as a decision-making framework in the optimization of the agribusiness sector's supply chain. This model considers temporal, spatial, and operational cost aspects, so it can be applied practically to data-driven distribution planning. This research contributes to the development of a relevant structured optimization approach for multi-period supply chain systems and discrete decisions

Keywords


Big-M method, Branch and bound, Coffee supply chain, MILP, Optimization distribution

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References


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DOI: https://doi.org/10.18860/cauchy.v10i2.35380

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