A Cross Entropy-based heuristic for the capacitated multi-source Weber problem with facility fixed cost

• A capacitated multi-source Weber problem with fixed cost is investigated.
• An evolutionary algorithm based on Cross Entropy (CE) is proposed.
• A mathematical model is developed yielding optimal solutions for small instances.
• The proposed CE algorithm performs well when compared with GAMS software.
• Benchmarks results are provided that could be used for future research.

This paper investigates a capacitated planar location–allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones.