This article studies a multi-product and multi-period location-routing-inventory problem in which location-allocation, inventory and routing decisions are to be taken in a three-level supply chain including suppliers, depots and customers. Products are distributed from depots to customers by a homogeneous fleet of vehicles. Backlogging is allowable on condition that the backlog quantity of each customer does not exceed a predefined fraction of his demand. A mixed-integer programming formulation is presented to describe the problem then a new hybrid heuristic algorithm based on the simulated annealing and imperialist competitive algorithm is designed to solve the model. Comprehensive numerical examples are presented to evaluate the efficiency of proposed algorithm. In addition, the proposed algorithm is compared with simulated annealing algorithm in small and large size instances. The results show that imperialist competitive-simulated annealing (IC-SA) algorithm outperforms simulated annealing (SA) algorithm in terms of solution quality and CPU time.
['Atiye Ghorbani', 'Mohammad Reza Akbari Jokar']
A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem