توزیع سود در مسائل مسیریابی خودروهای مرکزی متعدد Profit distribution in collaborative multiple centers vehicle routing problem

1 Introduction The traditional vehicle routing problem (VRP) seeks to find a set of routes that serve a series of customers (Allahyari et al. 2015). Each route can be performed by a single vehicle, which starts and returns to its own depot, and fulfills all customer requirements with minimized global transportation costs (Cordeau and Maischberger 2012; Fikar and Hirsch 2015). A collaborative multiple-center vehicle routing problem (CMCVRP) is the relaxed type of traditional VRP that is usually studied as a multiple-depot VRP (MDVRP) and a collaborative problem among multiple distribution centers (DCs). CMCVRP occurs when more than one DC is utilized in the network. Each vehicle departs from a DC to serve a series of customers by following a certain route plan and finally returns to the same DC. Each customer is reasonably assigned to its adjacent DC, where merged and transshipped goods are transported by a fleet of semitrailer trucks. Each customer should be also served by one vehicle on one occasion, whereas the loading of each vehicle should not exceed the vehicle capacity (Cattaruzza et al. 2014; Allahyari et al. 2015). Properly optimizing MCVR not only mitigates city-wide traffic congestion and alleviates negative environmental effects, but also reduces individual operating costs for profit maximization (Dai and Chen 2012). Different from conventional MDVRP, CMCVRP incorporates the cooperation mechanism among depots and increases modeling difficulty. CMCVR optimization is achieved through the negotiation-facilitated collaboration among multiple participants. The ultimate objective is to minimize the total costs of MCVR optimization, including vehicle routing costs in each DC and transportation costs among DCs, which may involve a transformative process from an original, non-optimal network structure to an optimized one. This process is organized by a logistics service provider (LSP) that performs corresponding logistics operations and strategies for participants in logistics distribution networks (Zäpfel and Bögl 2008; Braekers et al. 2014). Third-party LSPs can perform logistics activities better, including transportation, warehousing, information system, and value-added service, all of which integrate transportation, storage, and information into the LSP market. The mutually beneficial situation among different logistics companies can be achieved through outsourcing non-core logistics activities by LSPs. LSPs have the capability to persuade more participants to join the coalition and save more from an original nonoptimal network structure to a newly optimized one in the logistics network optimization process. Determining a reasonable profit distribution strategy with collaboration among its participants is the critical issue during a negotiation and optimization procedure. The robustness of collaboration relies on the rationality of profit distribution. Conventional MCVRP studies neglect the collaboration mechanism in the optimization procedure and assume that any two depots are willing to share their customer resources, delivery facilities without costs and the need for third-party logistics; such an assumption is not true in reality, and a series of value-added services including warehousing, negotiation, and transportation require third-party logistics providers (i.e., LSPs) to manage certain costs.