Damla KIZILAY, Hande ÖZTOP, Zeynel Abidin ÇİL

Mathematical models for the periodic vehicle routing problem with timewindows and time spread constraints

The periodic vehicle routing problem (PVRP) is an extension of the well-knownvehicle routing problem. In this paper, the PVRP with time windows and timespread constraints (PVRP-TWTS) is addressed, which arises in the high-valueshipment transportation area. In the PVRP-TWTS, period-specific demands of thecustomers must be delivered by a fleet of heterogeneous capacitated vehicles overthe several planning periods. Additionally, the arrival times to a customer shouldbe irregular within its time window over the planning periods, and the waiting timeis not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming(CP) models for the PVRP-TWTS. Furthermore, we develop several validinequalities to strengthen the proposed MILP and CP models as well as a lowerbound. Even though CP has successful applications for various optimizationproblems, it is still not as well-known as MILP in the operations research field.This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance ofthe proposed MILP and CP models by modifying the well-known benchmark setfrom the literature. The extensive computational results show that the CP modelperforms much better than the MILP model in terms of the solution quality. 4

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