Proposta de modelo matemático para o problema de transporte com carga fixa e N produtos

Abstract

The pursuit of revenue is a constant challenge in any organization. In this context, avoiding revenue loss due to stockouts — defined as the frustration of sales caused by the unavailability of products — represents an efficient way to increase revenue without raising costs. Stockouts negatively affect financial results by reducing revenue, while logistics impacts operational expenses. Therefore, it is essential to understand in which situations logistical costs can be offset by the increase in revenue from preventing stockouts. This study aims to propose a solution that determines the items, quantities to be transported, origins, and destinations in an internal product transfer process within the organization Gentil Negócios. The proposal involves an exact optimization approach for up to 9 stores and a metaheuristic approach, based on Simulated Annealing, for any number of stores and products. The mathematical model used is a variation of the fixed-charge transportation problem, classified as NP-Hard — meaning it has no known solution in polynomial time. To enable the exact solution, "clusters" of stores were defined based on geographic proximity, along with scenarios including all stores but limiting the number of products (3, 6, 9, and 12 items). The Simulated Annealing approach was applied to all stores and products, as well as in the clustered and filtered-product scenarios. This allowed for a comparison between the results obtained from Simulated Annealing and the exact solution. The Simulated Annealing method reduced the objective function cost from R$ 52 million to R$ 38 million, representing a 25% improvement in the full-scope scenario (all stores and all products). However, when comparing the metaheuristic results with the exact solution in the clustered scenarios, Simulated Annealing's performance was up to 50% worse.