Heuristic to solve bi-objective allocation problem in distribution logistics

Generalised assignment problem (GAP) is a well-known non-deterministic polynomial (NP) hard combinatorial optimisation problem to find the minimum cost during assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded. In this research, we look at the GAP from a bi-objective point of view to accommodate some real world situations. The application of BGAP for a typical practical supply chain problem of allocating a set of retailers to multiple distributors possessing different capacities with two specific performance objectives such as travel distance and travel time is considered. We propose a simulated annealing for an intensive search to find the Pareto optimal solutions to solve BGAP in a shorter period of time. Extensive computational experiments are carried out to evaluate the performance of the proposed method. Trials on benchmark data-sets and on a large number of test-problems have yielded encouraging results.