Conclusions

As a new branch of location problems, location-routing problem is still under development by various researchers. Present paper considered a location-routing problem on multimodal network. This paper aims to model and solve two problems at the same time. First problem is to select multimodal routes from supplier to potential DCs along with locating multimodal terminals. Second problem is DC location with routing tours from located DCs to retailers. An integer linear programming proposed and a genetic algorithm developed to capture the problem structure. To validate mathematical model, analyze sensitivity and demonstrate algorithm performance, two small and large size numerical instances generated based on previous papers, and different cost scenarios applied to these instances. Scenarios were different in vehicle capacity, transportation modes' costs, and mode changing cost. According to the results, for different scenarios, different multimodal routes selected. Changing mode change cost affects on establishing multimodal terminals. High mode changing cost caused products to be transported on just one transportation mode; decreasing the cost, however, led to changes in modes, requiring multimodal terminals to be established. Changing vehicle capacity cause a change in number of established DCs and retailers orders on delivery tours. Also, by changing transportation cost on multimodal network, model makes a trade-off between distance and transportation cost and selects a multimodal route with lowest cost. In large numerical instance, due to high complexity of the model, GAMS software failed to find an optimum solution within a reasonable time. In this case, genetic algorithm run under different scenarios and ended up returning solutions equal to or better than GAMS results, revealing good performance of the algorithm.

For future researches, first suggestion is to develop other solving algorithms including exact algorithms and comparing results. Other developments to LRP can be other suggestion for future research; mathematical model can be further developed considering uncertainties within data and dynamic programming issues, for example. Applying model for real cases and reporting real results can be another validation for model.