An adaptive large neighborhood search based approach for the vehicle routing problem with zone-based pricing

Engineering Applications of Artificial Intelligence(2023)

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Abstract
In the classical vehicle routing problems, the objective function is usually to minimize the transportation cost without considering the pricing decision-making. However, in some practical applications, such as riding-share services and fast-food delivery services, logistics companies aim to maximize profits, involving decision-making issues closely related to the pricing and route planning. This paper designs an adaptive large neighborhood search (ALNS) based approach to solve a vehicle routing problem with zone-based pricing (VRPZ). In the studied problem, the customers in the same zone share the same price for transportation, and each customer could accept or reject the price given by the logistics company. On the one hand, a too-high pricing strategy may reduce the number of served customers; on the other hand, a too-low pricing strategy may result in low earnings for logistics companies. VRPZ optimizes the routing planning and seeks an appropriate pricing strategy to maximize the total profit, which is the difference value of total earnings and costs. Considering that the studied problem is a computational challenge, we have developed an algorithm incorporating the local search into ALNS, particularly nested with two varying pricing operators: price++ and price−−, to solve the problem. The proposed algorithm has been compared with pure ALNS, variable neighborhood search (VNS) and Simulated Annealing (SA) by solving 472 benchmark instances in the published work. The compared results, which are validated by the statistic tests, highlight the efficiency and effectiveness of the proposed algorithm. To our best knowledge, this is the first heuristic to achieve a good performance in solving the benchmark instances. This study is significant for the retail industry to find a reasonable logistics pricing strategy and improve operational efficiency, as well as lays a foundation for developing a decision support system.
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Key words
adaptive large neighborhood search,vehicle routing problem,pricing,zone-based
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