Synchronization of inventory and transportation under flexible vehicle constraint: A heuristics approach using sliding windows and hierarchical tree structure

This paper investigates the integrated inventory and transportation planning under flexible vehicle constraint. To offer better services at lower prices, more and more companies turn to outsource transportation functions to other professional service providers, namely 3rd party logistics companies. Under these vehicle rental arrangements, the number of vehicles is a decision variable instead of a fixed number, and the transportation cost includes not only the delivery cost but also the cost of vehicle rental that is proportional to the number of vehicles rented in a given planning horizon. In this paper, the problem is formulated as a mixed integer programming problem. A heuristic algorithm is developed, in which sliding windows are applied to approximate the problem by repeatedly solving a series of overlapping short-term subproblems, and a hierarchical tree structure is used to evaluate the closeness of different groups of retailers. Numerical experiments show that a better tradeoff between the inventory cost and transportation cost can be achieved through the proposed heuristic algorithm.