Robust vehicle routing problem with hard time windows under demand and travel time uncertainty

© 2018 Elsevier Ltd Due to an increase in customer-oriented service strategies designed to meet more complex and exacting customer requirements, meeting a scheduled time window has become an important part of designing vehicle routes for logistics activities. However, practically, the uncertainty in travel times and customer demand often means vehicles miss these time windows, increasing service costs and decreasing customer satisfaction. In an effort to find a solution that meets the needs of real-world logistics, we examine the vehicle routing problem with hard time windows under demand and travel time uncertainty. To address the problem, we build a robust optimization model based on novel route-dependent uncertainty sets. However, due to the complex nature of the problem, the robust model is only able to tackle small-sized instances using standard solvers. Therefore, to tackle large instances, we design a two-stage algorithm based on a modified adaptive variable neighborhood search heuristic. The first stage of the algorithm minimizes the total number of vehicle routes, while the second stage minimizes the total travel distance. Extensive computational experiments are conducted with modified versions of Solomon's benchmark instances. The numerical results show that the proposed two-stage algorithm is able to find optimal solutions for small-sized instances and good-quality robust solutions for large-sized instances with little increase to the total travel distance and/or the number of vehicles used. A detailed analysis of the results also reveals several managerial insights for decision-makers in the logistics industry

Routing Optimization Under Uncertainty

We consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized. The objective is to obtain optimal routing solutions that would, as much as possible, adhere to a set of specified requirements after the uncertainty is realized. These problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain, and sending multiple capacitated vehicles to different nodes to meet the customers’ uncertain demands. We introduce a precise mathematical framework for defining and solving such routing problems. In particular, we propose a new decision criterion, called the Requirements Violation (RV) Index, which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur. The criterion can handle instances when probability distributions are known, and ambiguity when distributions are partially characterized through descriptive statistics such as moments. We develop practically efficient algorithms involving Benders decomposition to find the exact optimal routing solution in which the RV Index criterion is minimized, and we give numerical results from several computational studies that show the attractive performance of the solutions

The stochastic vehicle routing problem : a literature review, part I : models

Building on the work of Gendreau et al. (Eur J Oper Res 88(1):3–12; 1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems. The numerous variants of the problem that have been studied in the literature are described and categorized. Keywords: vehicle routing (VRP), stochastic programming, SVRPpublishedVersio

A decomposition approach for commodity pickup and delivery with time-windows under uncertainty

We consider a special class of large-scale, network-based, resource allocation problems under uncertainty, namely that of multi-commodity flows with time-windows under uncertainty. In this class, we focus on problems involving commodity pickup and delivery with time-windows. Our work examines methods of proactive planning, that is, robust plan generation to protect against future uncertainty. By a priori modeling uncertainties in data corresponding to service times, resource availability, supplies and demands, we generate solutions that are more robust operationally, that is, more likely to be executed or easier to repair when disrupted. We propose a novel modeling and solution framework involving a decomposition scheme that separates problems into a routing master problem and Scheduling Sub-Problems; and iterates to find the optimal solution. Uncertainty is captured in part by the master problem and in part by the Scheduling Sub-Problem. We present proof-of-concept for our approach using real data involving routing and scheduling for a large shipment carrier’s ground network, and demonstrate the improved robustness of solutions from our approach

Demand robust counterpart open capacitated vehicle routing problem time windows and deadline model of garbage transportation with LINGO 13.0

Demand robust counterpart-open capacitated vehicle routing problem with time windows and deadline (DRC-OCVRPtw,d) model formed and explained in this paper, is the model used to find the minimum distance and the time needed for vehicles to transport garbage in Sukarami Sub-District, Palembang that consists of the time it takes for the vehicle to pass through the route. Time needed to transport garbage to the vehicle is called time windows. Combination of the thoses times is called deadline. The farther the distance passed by vehicle and the more garbage transported, the longer the deadline is needed. This DRC-OCVRPtw,d model is completed by LINGO 13.0 to obtain the optimal route and time deadline for Sukarami Sub-District. The model shows that the improved model of open vehicle routing problem involving the robustness, time windows and deadline can achieve the optimal routes that enable driver to save operational time in picking up the garbage compared to similar problem not involving no-time windows and deadline stated in previous research

The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

Dynamic planning of mobile service teams’ mission subject to orders uncertainty constraints

This paper considers the dynamic vehicle routing problem where a fleet of vehicles deals with periodic deliveries of goods or services to spatially dispersed customers over a given time horizon. Individual customers may only be served by predefined (dedicated) suppliers. Each vehicle follows a pre-planned separate route linking points defined by the customer location and service periods when ordered deliveries are carried out. Customer order specifications and their services time windows as well as vehicle travel times are dynamically recognized over time. The objective is to maximize a number of newly introduced or modified requests, being submitted dynamically throughout the assumed time horizon, but not compromising already considered orders. Therefore, the main question is whether a newly reported delivery request or currently modified/corrected one can be accepted or not. The considered problem arises, for example, in systems in which garbage collection or DHL parcel deliveries as well as preventive maintenance requests are scheduled and implemented according to a cyclically repeating sequence. It is formulated as a constraint satisfaction problem implementing the ordered fuzzy number formalism enabling to handle the fuzzy nature of variables through an algebraic approach. Computational results show that the proposed solution outperforms commonly used computer simulation methods