New exact solution approaches for the split delivery vehicle routing problem

Abstract

In this study, we propose exact solution methods for the split delivery vehicle routing problem (SDVRP). We first give a new vehicle-indexed flow formulation for the problem and then a relaxation obtained by aggregating the vehicle-indexed variables over all vehicles. This relaxation may have optimal solutions where several vehicles exchange loads at some customers. We cut off such solutions, in a nontraditional way, either by extending the formulation locally with vehicle-indexed variables or by node splitting. We compare these approaches using instances from the literature and new randomly generated instances. Additionally, we introduce two new extensions of the SDVRP by restricting the number of splits and by relaxing the depot return requirement and modify our algorithms to handle these extensions.Keywords Split delivery · Vehicle routing problem · Valid inequalities · Extended formulations · Exact approaches Mathematics Subject Classification 90 (specifically 90-04 and 90-08) · 90B · 90C B Hande Yaman

A Column Generation-Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows

“…While route-based variables λ r are widely used in BP approaches for routing problems, the use of load flow variables f ij is less common, as the vehicle load is typically handled at the subproblem level. These load flow variables have been successfully used in BC approaches for the SDVRPTW and related variants [6,8,29,31]. In addition to strengthening the linear relaxation, they also enable an effective way of checking the feasibility of solutions to relaxed commodity flow formulations, i.e., whether load is transferred from one vehicle to another at a customer with multiple visits.…”

“…Constraints (2.5) model the regularity property [29,31] which avoids load transfers between vehicles visiting the same customer. In the adopted pickup perspective, a solution is said to satisfy the regularity property if, for each route, the flow on arc (h, i) traversed by the route is less than or equal to the flow in the subsequent arc (i, j ) traversed by the route.…”

“…Hence, customers may be visited multiple times if beneficial, by different vehicles, a feature commonly observed in practice in city and humanitarian logistics [1,13]. This can result in cost reductions, but introduces additional challenges to modeling and solving the problem [3,5,8,15,21,24,29,31]. The main challenge is that the traditional mechanisms used to model the vehicle capacity constraints fail to guarantee a feasible solution when multiple visits are allowed.…”

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

“…Several studies have shown the benefit of split loads for the classic VRP. (Dror et al, 1989(Dror et al, , 1990Belenguer et al, 2000;Ho and Haugland, 2004;Archetti et al, 2006aArchetti et al, , 2006bArchetti et al, , 2008aArchetti et al, , 2008bArchetti et al, , 2011Archetti et al, , 2014Derigs et al, 2010;Moreno et al, 2010;Cavalier, 2012a, 2012b;Berbotto et al, 2014;Khmelev and Kochetov, 2015;Silva et al, 2015;Ozbaygin et al, 2018). The SDVRP is reviewed by Archetti and Speranza (2008), while in Golden et al (2008), a more general overview of the literature where split deliveries are considered is presented.…”

Optimization of Multi-Products Distribution by Tabu Search Algorithm (Case Study: Fuel Distribution)

“…Interest SDVRP approach is to produce an efficient service [14]. SDVRP also tasked to find a number of these vehicles which begins and ends at the depot to meet customer demand at the lowest possible shipping costs [15].…”