A genetic algorithm based heuristic optimization technique for solving balanced allocation problem involving overall shipping cost minimization with restriction to the number of serving units as well as customer hubs

In the context of balanced allocation of products from different warehouses to different customer hubs, a company may have to take decision on the maximum number of customer hubs to which products are to be supplied by each warehouse. Further decision on the number of warehouses, that should be associated with supplying products to each hub is also crucial. In this paper, a technique has been developed to facilitate the above -mentioned decision making related to balanced allocation problem (BAP) with a restriction to the maximum number of warehouses that can cater to the demand of each customer hub, and also with restriction to the maximum number of customer hubs that each warehouse can serve. The delivery cost of unit quantity of the product from each warehouse to each customer hub is fixed. The problem thus formulated has been solved with the help of Genetic algorithm (GA). The solution consists of the quantity distributed by each warehouse to each customer hub, the customer hubs chosen for allocation by each of the warehouses and the minimum total shipping cost. The model has been illustrated with a few numerical examples. Further, the effect on total optimum cost has been studied by altering the maximum number of warehouses that can cater to each customer hub, and also altering maximum number of customer hubs that each warehouse can serve. Finally, sensitivity analyses with respect to different GA parameters, as well as with respect to some model parameters have been done and displayed graphically.