Ola Jabali

A Vehicle Routing Problem with Flexible Time Windows

In this paper, we introduce the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW), in which vehicles are allowed to deviate from customer time windows by a given tolerance. This flexibility enables savings in the operational costs of carriers, since customers may be served before and after the earliest and latest time window bounds, respectively. However, as time window deviations are undesired from a customer service perspective, a penalty proportional to these deviations is accounted for in the objective function. We develop a solution procedure, in which feasible vehicle routes are constructed via a tabu search algorithm. Furthermore, we propose a linear programming model to handle the detailed scheduling of customer visits for given routes. We validate our solution procedure by a number of Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances. We highlight the costs involved in integrating flexibility in time windows and underline the advantages of the VRPFlexTW, when compared to the VRPTW.

50th Anniversary Invited Article-Goods Distribution with Electric Vehicles: Review and Research Perspectives

Since the mid-2000s, electric vehicles have gained popularity in several countries even though their market share is still relatively low. However, most gains have been made in the area of passenger vehicles and most technical and scientific studies have been devoted to this case. By contrast, the potential of electric vehicular technology for goods distribution has received less attention. The issues related to the use of electric vehicles for goods distribution reveal a wide range of relevant research problems. The aims of this survey paper are to provide transportation researchers an overview of the technological and marketing background needed to conduct research in this area, to present a survey of the existing research in this field, and to offer perspectives for future research.

Thirty years of heterogeneous vehicle routing

It has been around 30 years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems.

A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited availability of vehicles. The main objective is to minimize the fixed vehicle cost and the distribution cost, where the latter can be defined with respect to en-route time (T) or distance (D). The proposed unified algorithm is able to solve the four variants of heterogeneous fleet routing problem, called FT, FD, HT and HD, where the last variant is new. The HEA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle the heterogeneous fleet dimension. Extensive computational experiments on benchmark instances have shown that the HEA is highly effective on FT, FD and HT. In particular, out of the 360 instances we obtained 75 new best solutions and matched 102 within reasonable computational times. New benchmark results on HD are also presented. HighlightsWe develop a unified algorithm for four heterogeneous routing problems.We introduce a new heterogeneous routing problem.The algorithm combines two state-of-the-art metaheuristic concepts.Out of the 360 instances we obtain 75 strictly new best solutions.

The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm

This paper introduces the fleet size and mix location-routing problem with time windows (FSMLRPTW) which extends the location-routing problem by considering a heterogeneous fleet and time windows. The main objective is to minimize the sum of vehicle fixed cost, depot cost and routing cost. We present mixed integer programming formulations, a family of valid inequalities and we develop a powerful hybrid evolutionary search algorithm (HESA) to solve the problem. The HESA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle heterogeneous fleet dimensioning and location decisions. We evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions. We also investigate the performance of the HESA. Extensive computational experiments on new benchmark instances have shown that the HESA is highly effective on the FSMLRPTW.

Multi-period Vehicle Routing Problem with Due dates

In this paper we study the Multi-period Vehicle Routing Problem with Due dates (MVRPD), where customers have to be served between a release and a due date. Customers with due dates exceeding the planning period may be postponed at a cost. A fleet of capacitated vehicles is available to perform the distribution in each day of the planning period. The objective of the problem is to find vehicle routes for each day such that the overall cost of the distribution, including transportation costs, inventory costs and penalty costs for postponed service, is minimized. We present alternative formulations for the MVRPD and enhance the formulations with valid inequalities. The formulations are solved with a branch-and-cut algorithm and computationally compared. Furthermore, we present a computational analysis aimed at highlighting managerial insights. We study the potential benefit that can be achieved by incorporating flexibility in the due dates and the number of vehicles. Finally, we highlight the effect of reducing vehicle capacity.

50th Anniversary Invited Article—Future Research Directions in Stochastic Vehicle Routing

Stochastic vehicle routing, which deals with routing problems in which some of the key problem parameters are not known with certainty, has been an active, but fairly small research area for almost 50 years. However, over the past 15 years we have witnessed a steady increase in the number of papers targeting stochastic versions of the vehicle routing problem (VRP). This increase may be explained by the larger amount of data available to better analyze and understand various stochastic phenomena at hand, coupled with methodological advances that have yielded solution tools capable of handling some of the computational challenges involved in such problems. In this paper, we first briefly sketch the state-of-the-art in stochastic vehicle routing by examining the main classes of stochastic VRPs (problems with stochastic demands, with stochastic customers, and with stochastic travel or service times), the modeling paradigms that have been used to formulate them, and existing exact and approximate solution methods that have been proposed to tackle them. We then identify and discuss two groups of critical issues and challenges that need to be addressed to advance research in this area. These revolve around the expression of stochastic phenomena and the development of new recourse strategies. Based on this discussion, we conclude the paper by proposing a number of promising research directions.

Self-imposed time windows in vehicle routing problems

We observe self-imposed time windows (SITW) whenever a logistics service provider quotes a delivery time window to his customer. Once this time window is communicated, the company strives to respect it as well as possible. We incorporate these SITW within the framework of the vehicle routing problem (VRP). Essential to SITW is the fact that the time window is determined by the carrier company and not by the customer. The resulting VRP-SITW is inherently different from the well-studied VRP with time windows (VRPTW) in that in the latter problem the time windows are exogenous constraints imposed by the customers. The second important element of the problem studied in this paper is the uncertainty in the travel times. The basic mechanism of dealing with this uncertainty is the allocation of time buffers throughout the routes, which absorb disruptions. We propose a heuristic solution approach combining an LP model and a local search heuristic. A tabu search heuristic assigns customers to vehicles and establishes the order of visit of the customers per vehicle. Detailed timing decisions are subsequently generated by the LP model, whose output also guides the local search in a feedback loop. We test our algorithm on a number of benchmark instances for the VRP and VRPTW. We highlight the costs involved in integrating SITW with the VRP and we underline the advantages of SITW as compared to VRPTW.

The traveling salesman problem with time-dependent service times

This paper introduces a version of the classical traveling salesman problem with time-dependent service times. In our setting, the duration required to provide service to any customer is not fixed but defined as a function of the time at which service starts at that location. The objective is to minimize the total route duration, which consists of the total travel time plus the total service time. The proposed model can handle several types of service time functions, e.g., linear and quadratic functions. We describe basic properties for certain classes of service time functions, followed by the computation of valid lower and upper bounds. We apply several classes of subtour elimination constraints and measure their effect on the performance of our model. Numerical results obtained by implementing different linear and quadratic service time functions on several test instances are presented.

Partial-route inequalities for the multi-vehicle routing problem with stochastic demands

Abstract This paper describes an exact algorithm for a variant of the vehicle routing problem in which customer demands to be collected are stochastic. Demands are revealed upon the vehicle arrival at customer locations. As a result, a vehicle may reach a customer and does not have sufficient capacity to collect the realized demand. Such a situation is referred to as a failure. In this paper the following recourse action is then applied when failure occurs: the vehicle returns to the depot to unload and resumes its planned route at the point of failure. The capacitated vehicle routing problem with stochastic demands (VRPSD) consists of minimizing the sum of the planned routes cost and of the expected recourse cost. The VRPSD is formulated as a two-stage stochastic programming model and solved by means of an integer L -shaped algorithm. This paper introduces three lower bounding functionals based on the generation of general partial routes, as well as an exact separation procedure to identify violated cuts. Extensive computational results confirm the effectiveness of the proposed algorithm, as measured by a substantial reduction in the number of feasible solutions that have to be explicitly eliminated. This translates into a higher proportion of instances solved to optimality, reduced optimality gaps, and lower computing times.