عنوان مقاله [English]
In this study a mathematical model has been presented for multi depots, continuous location-routing problem with inventory restrictions. In this problem, a three-echelon supply chain was assumed a factory, producing one product with unlimited capacity, is on the first echelon of supply chain. In the second echelon of supply chain, several distribution centers distribute products. In the third echelon, there is a set of customers who are scattered in different geographical locations. Location of customers is pre-specified, but distribution centers should be located. In this problem, location of distribution centers will be determined in a continuous space.
As the leader of this supply chain, factory is looking for product distribution planning to minimize the total cost of this system. Model formulation of this problem is NP-hard; so a meta-heuristic algorithm with three phases has been developed for medium and large sizes of this problem. In the first phase of this algorithm, Region-rejection approach and modified saving algorithm are used to generate initial solution. In the second phase, we apply the Weiszfeld algorithm in order to improve location-routing decisions
repeatedly. In the last phase, diversification and intensification mechanisms are incorporated into the search.
The proposed algorithm is able to improve even the best solution implemented by GAMS solver with time limits of 10800 seconds and 18000 seconds, 0.62 percent in average, with much less computational effort. Also it can be seen that this algorithm is
moving toward the best solution during three phases. For this small sized problem, each of the three main phases, the average percentage deviation from optimal solution is only \% 0.07, \% 0.05, \% 0.03 and % 0.02, respectively. For
medium and large size of this problem, \% 2.83, \%1.89 and \%1.29 improvement can be seen in each phase compared to the previous phase, respectively. This improvement is impressive for the large size of this problem.