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A Capacitated Location Routing Problem with Semi Soft Time Windows

In this article we address The Location Routing Problem (LRP), where there is a set of customers with known demand and a set of potential depot site and there is a set of heterogeneous vehicle with a certain capacity. Due to the similarity of the problem with real world, the constraints of depot capacity and vehicle capacity as well as route length have been considered simultaneously. The model provided in this article is described concerning the semi soft time window in which that a delay in service delivery time results in delay costs. The total costs in the proposed model include, the total fixed costs of construction depot, fixed costs associated with the use of vehicles, the total distance traveled by the vehicles, the total time within the system for the vehicle and penalty cost associated with the violation of working hour of vehicles and penalty costs associated with delay time in the start of service to customers and the aim is to minimize the total cost. Due to its complexity, two Meta-Heuristic algorithms of Genetic and Tabu Search algorithm have been used. Since the performance of the Meta-Heuristic algorithms is significantly influenced by their parameters, Taguchi Method is used to set the parameters of developed algorithms. Finally, the result represents that the Genetic Algorithm and Tabu Search are significantly efficient in terms of better quality of solution and computational time respectively.