Distribution Cost Sharing in Collaborative Logistics: Theoretical, Post Hoc and A Priori Analytics

Abstract

In collaborative logistics, multiple participants share the same route for product distribution to reduce total costs. However, each one is only willing to pay a reasonable price for its own portion. The core question in this dissertation is how to fairly determine the distribution cost to serve each participant. Three problems are investigated: cost allocation when a delivery route is known; cost estimation when real delivery routes are unknown (for example for new customers); and the traveling salesman game which provides important theoretical concepts for fairness underpinning the first two problems. In the cost allocation problem, a fixed delivery route is given but may not be optimal, with the real application we studied usually having 5 to 20 customers per route. To identify the objective and evaluate different cost allocation methods, five fairness criteria are introduced. A location constrained moat model and corresponding algorithms are proposed, and impacts of the non-optimum of routes on allocation methods are analyzed. A computational study demonstrates that the proposed method satisfies an important set of fairness axioms and improves cost allocation from the existing allocation schemes within acceptable time requirements. The cost estimation problem is targeted to forecast the long-term cost to serve new customers with limited knowledge. Based on the causes leading to distribution costs, we construct appropriate attributes for estimation using geographic factors. Combined with a search based data selection approach, linear regression, artificial neural network and stepwise polynomial regression methods are applied to build predictive models. Experiments demonstrate the benefit of the constructed attributes and the accuracy of the proposed cost estimation method. The impact of data instability is also examined to provide support for implementation in practice. The traveling salesman game addresses a problem of allocating the cost of a route that is optimal to the traveling salesman problem (TSP). A measurement of the quality of cost allocation, excess rate, is defined and derived to a simple form through induction from a proposed long-run TSP. The lower and upper bounds of an excess rate are derived and we build a relationship between core emptiness and the well-known integrality gap of TSP. An allocation model based on the duality of the Held-Karp linear relaxation model for TSP is analyzed and improved by reducing the number of variables from exponential to polynomial scale. In addition, a complete allocation method is developed to approach a fair allocation.