Comparative analysis of MP-based solvers to optimize distribution problems in logistics

Abstract

Distribution related problems in logistics have many decision variables and constraints that have to be considered simultaneously. Most often, these are the problems in the discrete optimization branch, modeled and optimized using operational research, in particular mathematical programming (MP) models and methods, such as mixed integer linear programming (MILP), integer programming (IP) and integer linear programming (ILP). These methods become ineffective very quickly in the case of larger size problems. Also, the number of decision variables and constraints may exceed the capacity of available MP solvers. To improve their efficiency and reduce the effective size of the solution space of a given problem, hybrid approaches are being developed, integrating MP with other environments. This article discusses the results of comparative analysis of several MP solvers (LINGO, SCIP, GUROBI) in the context of their use for optimization of selected distribution problems.