Single‐Source Capacitated Multi‐Facility Weber Problem–An iterative two phase heuristic algorithm

Multi‐Facility Weber Problem (MFWP), also known as continuous location–allocation problem, entails determining the locations of a predefined number of facilities in a planar space and their related customer allocations. In this paper, we focus on a new variant of the problem known as Single‐Source Capacitated MFWP (SSCMFWP). To tackle the problem efficiently and effectively, an iterative two‐phase heuristic algorithm is put forward. At the phase I, we aim to determine proper locations for facilities, and during the phase II, assignment of customers to these facilities is pursued. As an alternative solution method, a simulated annealing (SA) algorithm is also proposed for carrying out the phase I. The proposed algorithms are validated on a comprehensive set of test instances taken from the literature. The proposed iterative two‐phase algorithm produces superior results when assessed against the proposed SA algorithm as well as a general MINLP Solver known as BARON. The latter is applied to produce optimal solutions for small sized instances and generate upper bound for medium ones.