Multi-objective vehicle routing and loading with time window constraints:a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner

A branch-and-cut algorithm for vehicle routing problems with three-dimensional loading constraints

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously infeasible route can become feasible by adding a new customer if support constraints are enabled in the loading subproblem and call this the incremental feasibility property. Consequently, different infeasible path definitions apply to different 3L-CVRP variants and we introduce several variant-depending lifting steps to strengthen infeasible path inequalities. The loading subproblem is solved exactly using a flexible constraint programming model to determine the feasibility or infeasibility of a route. An extreme point-based packing heuristic is implemented to reduce time-consuming calls to the exact loading algorithm. Furthermore, we integrate a start solution procedure and periodically combine memoized feasible routes in a set-partitioning-based heuristic to generate new upper bounds. A comprehensive computational study, employing well-known benchmark instances, showcases the significant performance improvements achieved through the algorithmic enhancements. Consequently, we not only prove the optimality of many best-known heuristic solutions for the first time but also introduce new optimal and best solutions for a large number of instances.Comment: 33 pages, 13 figures, 7 tables, Submitted to Transportation Scienc

The value of integrating loading and routing

Location-routing, inventory-routing, multi-echelon routing, routing problems with loading constraints are classes of problems that are receiving increasing attention in the scientific community. Problems in these classes generalize classical vehicle routing problems enlarging the decision space to optimize a broader system. The resulting problems are computationally harder to solve but offer opportunities to achieve remarkable additional savings. In this paper, we address the issue of quantifying the potential benefit deriving from tackling directly such complex problems instead of solving the individual problems in a not integrated manner. To this aim, we consider as a proof of concept the Capacitated Vehicle Routing Problem (CVRP) with Two-dimensional Loading constraints (2L-CVRP), a variant of the CVRP where rectangular-shaped items have to be delivered to customers and loading constraints have to be satisfied. We consider the 2L-CVRP in an integrated manner and compare the solutions with those obtained from three not integrated approaches based on addressing separately the routing and the loading problems. The importance of an integrated approach for the 2L-CVRP is validated through the study of the worst-case performance of the not integrated approaches, and conducting computational experiments on benchmark and new instances