Heuristics for the single source capacitated multi-facility Weber problem

The Single Source Capacitated Multi-facility Weber Problem (SSCMWP) is concerned with locating I capacitated facilities in the plane to satisfy the demand of J customers with the minimum total transportation cost of a single commodity such that each customer satisfies all its demand from exactly one facility. The SSCMWP is a non-convex optimization problem and difficult to solve. In the SSCMWP, customer locations, customer demands and facility capacities are known a priori. The transportation costs are proportional to the distance between customers and facilities. We consider both the Euclidean and rectilinear distance cases of the SSCMWP. We first present an Alternate Location and Allocation type heuristic and its extension by embedding a Very Large Scale Neighborhood search procedure. Then we apply a Discrete Approximation approach and propose both lower and upper bounding procedures for the SSCWMP using a Lagrangean Relaxation scheme. The proposed heuristics are compared with the solution approaches from the literature. According to extensive computational experiments on standard and randomly generated test sets, we can say that they yield promising performance.

► We consider both the rectilinear and Euclidean distance cases of the SSCMWP.
► We propose several approximate solution procedures for the SSCMWP.
► We suggest an exact solution procedure for the rectilinear distance SSCMWP.
► We devise lower bounding procedures for the SSCWMP using a LR scheme.
► We report computational experiments on standard and randomly generated instances.