Abstract
The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is 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 valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, 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 of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.
Highlights
The periodic vehicle routing problem (PVRP) is an extension of the standard vehicle routing problem (VRP), which plans the vehicle routes over the several planning periods
This paper addresses the periodic vehicle routing problem with time windows and time spread constraints (PVRP-TWTS), which arises in high-value shipment transportation
This study aims to fill this gap by proposing novel mixed-integer linear programming (MILP) and constraint programming (CP) models for this more realistic extension of the PVRP-TWTS, as exact solution methods
Summary
The periodic vehicle routing problem (PVRP) is an extension of the standard vehicle routing problem (VRP), which plans the vehicle routes over the several planning periods. This paper addresses the periodic vehicle routing problem with time windows and time spread constraints (PVRP-TWTS), which arises in high-value shipment transportation. Since the high-value shipment companies generally plan the vehicle routes over several days and most of their customers are visited each day, their transportation processes can be formulated as a PVRP. Purpose of these Cash in Transit (CIT) companies is to move valuable things like coins, banknotes, or jewels from one location to a different one safely The customers of these CIT corporations involve supermarkets and various shopping stores in addition to the banks. Since these CIT companies transport valuable products, they must arrange their daily visits using different routes due to security reasons [1,2].
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