efficiency of a multi-objective imperialist competitive algorithm: a bi-objective location-routing-inventory problem with probabilistic routes

an integrated model considers all parameters and elements of different deficiencies in one problem. this paper presents a new integrated model of a supply chain that simultaneously considers facility location, vehicle routing and inventory control problems as well as their interactions in one problem, called location-routing-inventory (lri) problem. this model also considers stochastic demands representing the customers’ requirement. the customers’ uncertain demand follows a normal distribution, in which each distribution center (dc) holds a certain amount of safety stock. in each dc, shortage is not permitted. furthermore, the routes are not absolutely available all the time. decisions are made in a multi-period planning horizon. the considered bi-objectives are to minimize the total cost and maximize the probability of delivery to customers. stochastic availability of routes makes it similar to real-world problems. the presented model is solved by a multi-objective imperialist competitive algorithm (moica). then, well-known multi-objective evolutionary algorithm, namely anon-dominated sorting genetic algorithm ii (nsga-ii), is used to evaluate the performance of the proposed moica. finally, the conclusion is presented.