A Location Routing Problem with Time Windows Consideration: A Metaheuristics Approach

A substantial distribution system is achievable to attain through the simultaneous design of the location facility and route generation. This problem is generally called a location routing problem (LRP), where both strategic decision and operational decisions are considered during the decision initial phase. Nevertheless, for some real applications, a consideration of time restriction due to several reasons should be included in the model. Some examples include the distribution system of perishable goods, a company’s objective towards a high level of customer service, or emergency/disaster situations. Consequently, this research incorporates the location routing problem (LRP) with time window constraints, including the working hour and also time restriction in each customer. The location routing problem with time windows (LRPTW) could not be solved easily, especially for a large-sized problem and or one which is considered an NP-hard problem. In consideration with its large solution pools, this paper suggests an integration of variable neighborhood search (VNS) with path relinking (PR) to solve LRPTW. The method is first applied in the LRP benchmark to validate the effectiveness and the robustness of the proposed method. Computational results clarify that VNSPR can achieve some of the best and most competitive solutions for the LRP when compared to existing approaches. Further, we developed LRPTW instances from the best solution found in LRP datasets. The proposed VNSPR method is also able to yield nearly optimal solutions for LRPTW instances.