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

Document Type: Research/Original/Regular Article


1 Department of Industrial Engineering, South Tehran Branch, Islamic Azad University,

2 School of Industrial & Systems Engineering, College of Engineering, University of Tehran, Tehran, Iran

3 Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran


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.