Branch and price for the vehicle routing problem with discrete split deliveries and time windows

Abstract

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles' capacity and customer time windows. The delivery request of a customer is discrete since it consists of several items that cannot be split further. The problem belongs to the class of split delivery problems since each customer's demand can be split in orders, i.e. feasible combinations of items, and each customer can be visited by more than one vehicle. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance and that each vehicle can serve at most one order per customer. Remarkably, service time at customer's location depends on the serviced combination of items, which is a modeling feature rarely found in literature. We present a mixed integer program for the DSDVRPTW based on arcflow formulation, we reformulate it via Dantzig-Wolfe and we apply column generation. We propose a branch-and-price algorithm, implemented using state-of-the-art techniques for the pricing and the master problem. Computational results on instances based on Solomon's data set are presented and discussed.2

Exploring a Column Generation Approach for a Routing Problem with Sequential Packing Constraints

“…All these columns are validated using lower bounds and the bottom-left heuristic with sequential constraints. In order to solve the subproblem, we use the dynamic programming approach algorithm of Righini and Salani (2008) which performed good results in other works (Salani and Vacca, 2011;Vacca et al, 2013).…”

An ant colony system for responsive dynamic vehicle routing

“…At the opposite, the first contribution of our work is to simultaneously integrate a very large set of characteristics so as to allow companies to easily use our framework for real-life problems. More precisely, we have simultaneously integrated in our framework the constraints separately studied in the following VRP subfields: Capacitated VRP (CVRP), VRP with Time Windows (VRPTW) (see, e.g., Bräysy and Gendreau, 2005;Cordeau et al, 2002;Kallehauge et al, 2005), VRP with heterogeneous fleet (see, e.g., Choi and Tcha, 2007;Seixas and Mendes, 2013), VRP with multi-trips and Split Deliveries (see, e.g., Archetti and Speranza, 2012;Dror et al, 1994;Salani and Vacca, 2011). Other constraints for variations like VRP with Backhauls or with Pickup and Delivery, VRP with multi-depots, Dial-A-Ride Problems are not included in our approach, even if it would be a natural and possible extension.…”

Workforce scheduling and routing problems: literature survey and computational study

“…When using exact approaches, researchers tend to model the problem as multi-commodity network flow problems (Desaulniers et al, 1998;Salani and Vaca, 2011) or following a set partitioning/covering formulation (Bredström and Rönnqvist, 2007). Such models have been tackled using constraint programming, branch and bound, and branch and price (column generation) (Barnhart et al, 1998;Desrosiers and Lübbecke, 2005).…”