An Exact Algorithm for the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints

Abstract

One of our industry partners distributes a multitude of orders of fibre boards all over each of the Australian capital cites, a problem that has been formalised as the Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints (3L-HFVRPTW). The fleet consists of two types of trucks with flat loading surfaces and slots for spacers that allow a subdivision into stacks of different sizes. A customer’s delivery can be positioned on more than one partition, but the deliveries have to be loaded in a strict LIFO order. Optimising the truck loads beyond the 75% that can be achieved manually provides value to the company because the deliveries are generally last-minute orders and the customers depend on the deliveries for their contract work on refurbishments. This paper presents an exact integer linear programming model that serves two purposes: (1) providing exact solutions for problems of a modest size as a basis for comparing the quality of heuristic solution methodologies, and (2) for further exploration of various relaxations, stack generation, and decomposition strategies that are based on the ILP model. We solved a few real-life instances by obtaining the exact optimal solution using CPLEX 12.61, whereas previously, the problem was solved manually by staff members of the furniture company.