GRASP strategies for a bi-objective commercial territory design problem

In this work a problem motivated by a real-world case from a beverage distribution firm in Mexico is addressed. Different planning criteria are taken into account in order to create acceptable territory designs. Namely, each territory needs to be compact, connected and balanced according to two attributes (number of costumers and product demand). Two GRASP based heuristics (BGRASP and TGRASP) are proposed for this NP-hard combinatorial optimization problem. For each of them two variants are studied: i) keeping connectivity as a hard constraint during construction and post-processing phases and, ii) ignoring connectivity during the construction phase and adding this as a minimizing objective function during the post-processing phase . The main difference between BGRASP and TGRASP is the way they consider the planning criteria during the construction phase. In BGRASP, the construction attempts to find high quality solutions based on the optimization of two criteria: compactness and balancing according to the number of customers, that is, demand is treated as a constraint. The construction phase in TGRASP considers three objectives to be optimized: compactness and balancing with respect to the two attributes (number of customers and demand). That is, the demand balancing constraints are relaxed and treated as part of the objective function. The proposed procedures are evaluated on a variety of problem instances, with 500 and 1000 basic units. We carried out an analysis of these procedures using different performance measures such as number of non-dominated points, k-distance, size of the space cover (SSC), coverage of two sets measure, and time. We observed that, SSC, coverage of two sets measure and time, present significant variation depending on the GRASP procedure used. The number of points and k-distance measures did not present significant variation over all evaluated procedures. BGRASP-I provides good frontiers in shortest time and BGRASP-II has the best coverage of the efficient points given by the others procedures.