The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools.
The DARP is characterized by multiple objectives such as the maximization of the number of costumers served, the minimization of the number of vehicles used and the maximization of the level of service provided on average to the costumer (costumer waiting time, total time spent in vehicles, difference between actual and desired drop-off times). The DARP can be formulated as multiobjective mixed integer program. Exact algorithms for the single-vehicle DARP have been developed in @cite_47 @cite_38 . Recently, a branch-and-cut algorithm has been proposed in @cite_87 . Heuristics and meta-heuristics are proposed for dealing with the dynamic problem with time-dependent network @cite_50 . For a recent overview of the DARP, see @cite_61 .
@cite_61 @cite_38 @cite_87 @cite_50 @cite_47
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We study a setting where electric vehicles (EVs) can be hired to drive from pick-up to drop-off points in a mobility-on-demand (MoD) scheme. Each point in the MoD scheme is equipped with a battery swap facility that helps cope with the EVs' limited range. The goal of the system is to maximise the number of customers that are serviced. Thus, we first model and solve this problem optimally using Mixed-Integer Programming (MIP) techniques and show that the solution scales up to medium sized problems. Given this, we develop a greedy heuristic algorithm that is shown to generate near-optimal solutions and can scale to thousands of consumer requests and EVs. Both algorithms are evaluated in a setting using data of real locations of shared vehicle pick-up and drop-off stations and the greedy algorithm is shown to be on average 90 of the optimal in terms of average task completion. An investigation of the single-vehicle, many-to-many, immediate-request dial-a-ride problem is developed in two parts I and II. Part I focuses on the “static” case of the problem. In this case, intermediate requests that may appear during the execution of the route are not considered. A generalized objective function is examined, the minimization of a weighted combination of the time to service all customers and of the total degree of “dissatisfaction” experienced by them while waiting for service. This dissatisfaction is assumed to be a linear function of the waiting and riding times of each customer. Vehicle capacity constraints and special priority rules are part of the problem. A Dynamic Programming approach is developed. The algorithm exhibits a computational effort which, although an exponential function of the size of the problem, is asymptotically lower than the corresponding effort of the classical Dynamic Programming algorithm applied to a Traveling Salesman Problem of the same size. Part II extends this approach to solving the equivalent “dynamic” case. In this case, new customer requests are automatically eligible for consideration at the time they occur. The procedure is an open-ended sequence of updates, each following every new customer request. The algorithm optimizes only over known inputs and does not anticipate future customer requests. Indefinite deferment of a customer's request is prevented by the priority rules introduced in Part I. Examples in both “static” and “dynamic” cases are presented. This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported. This paper considers a single-vehicle Dial-a-Ride Problem in which customers may experience stochastic delays at their pickup locations. If a customer is absent when the vehicle serves the pickup location, the request is fulfilled by an alternative service (e.g., a taxi) whose cost is added to the total cost of the tour. In this case, the vehicle skips the corresponding delivery location, which yields a reduction in the total tour cost. The aim of the problem is to determine an a priori Hamiltonian tour minimizing the expected cost of the solution. This problem is solved by means of an integer L-shaped algorithm. Computational experiments show that the algorithm yields optimal solutions on several instances within reasonable CPU times. It is also shown that the actual cost of an optimal solution obtained with this algorithm can be significantly smaller than that of an optimal solution obtained with a deterministic formulation.