The Transportation Service Procurement Problem With Total Quantity Discounts

With the trend of the globalization,many companies choose to outsource their logistics operations and focus on their core competencies.To procure logistics services,companies aims to choose excellent carriers to meet their own transportation service needs.In the transportation service procurement auctions,shippers that act as the auctioneers announce their shipping demands on the shipping network,and carriers that act as the bidders submit bids reporting their capacities,shipping rates and other factors on different shipping lanes.The shipper then decides carrier selection and freight allocation based on the bids from different carriers.In the shipper's decisions of the transportation service procurement problem,transportation cost is most concerned by the shipper.In order to secure more freight volume and improve profits,carriers often use different pricing strategies to improve interests of both parties.Among them,total quantity discounts are widely used in practice.In light of this fact,this work investigates the transportation service procurement problem with total quantity discounts,and decides how to select winning carriers and allocate freight volume to them,which aims to minimize the total transportation cost,taking into consideration various practical business constraints.Particularly,the shipping demands of the shipper and the capacities of the carriers on the shipping lanes,the minimum quantity commitments,and total quantity discounts provided by the carriers are considered.The transportation services procurement problem with total quantity discounts is an NP-hard problem.With the increase of the problem size,the computational time required by commercial integer programming solvers increases significantly,which is ineffective in practice.We first formulate the problem into a mixed integer programming model.Then,the solution of the original problem can be converted to finding the set of discount intervals for carriers.Finally,an effective hybrid heuristic is designed,considering the global search feature of Estimation of Distribution Algorithms and the local search feature of Neighborhood Search Algorithms.Acceleration strategies are also proposed.Computational experiments based on random test instances show that the hybrid algorithm performs better than a commercial solver and an estimation of distribution algorithm.Our algorithm can solve practical transportation service procurement problems and reduce transportation costs,and the high-quality solutions can assist the shipper to make better decisions.