A Hybrid Algorithm for a Two-Echelon Location- Routing Problem with Simultaneous Pickup and Delivery under Fuzzy Demand

Location-Routing Problem (LRP) emerges as one of the hybrid optimization problems in distribution networks in which, total cost of the system would be reduced significantly by simultaneous optimization of locating a set of facilities among candidate locations and routing vehicles. In this paper, a mixed integer linear programming model is presented for a two-echelon location-routing problem with simultaneous pickup and delivery. In the investigated problem, one echelon of facilities, which is called the middle depot echelon, is positioned between central distribution centers and customers echelons. The number and capacity of middle depots and vehicles are considered to be limited. Besides, each network customer demands for both receiving a type of commodities and delivering another type to vehicles to be returned to the depot. In the literature of location routing problem, the majority of researches have been conducted in the deterministic conditions. However, we present a model in which data uncertainty is also taken into account and customers' demand is assumed to be a fuzzy parameter. We utilize a fuzzy programming approach to cope with uncertain demands. Moreover, a combined heuristic method based on simulated annealing (SA) algorithm and genetic algorithm (GA) is devised for solving the presented model. The results achieved from solving the problem in different sizes of numerical examples imply that the proposed hybrid algorithm outperforms other algorithms within reasonable length of time. The effectiveness of the proposed solution method is examined through a comprehensive numerical experiments. Finally, valuable insights are provided via conducting a number of sensitivity analyses.