Capacitated Routing Problem Research Articles

Real-time optimization for integrated R2 charging and refueling stations in a multi-carrier energy system considering hydrogen chain management

This study presents a real-time optimization-based strategy for sustainable energy management using an energy hub that integrates combined heat and power (CHP) units, heat pumps, and fuel-cell technology to meet community electricity, heating, and cooling demands. It incorporates renewable-based R2 stations that leverage photovoltaic and wind power, integrated with hydrogen production and storage, to supply stationary energy consumers and the transportation sector. The system provides hydrogen for fuel cell electric vehicles (FCEVs) and electricity for electric vehicles (EVs). Integrating the R2 station with the primary energy hub optimizes the use of locally generated power, reducing dependence on external sources. Hydrogen fuel is produced on-site and off-site, focusing on solving the capacitated routing problem for efficient delivery. The system's architecture is modeled using a mixed-integer linear programming (MILP) approach. According to the results, no energy is drawn from the grid to meet the end-user's electricity demand.

Solving the humanitarian multi-trip cumulative capacitated routing problem via a grouping metaheuristic algorithm

Solving the humanitarian multi-trip cumulative capacitated routing problem via a grouping metaheuristic algorithm

Optimization of Distributed Maintenance: Design, Scheduling and Capacitated Routing Problem

This paper deals with scheduling maintenance operations for a set of geographically distributed production equipment. The problem emerges in distributed maintenance context, where a central maintenance workshop (CMW) aims to monitor and repair equipment from various production sites and schedule the associated preventive actions. A mobile maintenance workshop (MMW) transports all the resources required for the maintenance tasks to replace the equipment with spare parts provided by the CMW following the predefined schedule. This study proposes a general approach and a model to minimize the maintenance and routing costs while optimizing equipment reliability. The novelty of the proposed model is the consideration of the MMW capacity while designing and scheduling distributed maintenance. We perform several experiments based on a real-world case study to implement the model and highlight its relevance. The studied approach allows choosing the CMW position and the MMW capacity while making a trade-off between the costs and the availability of production equipment.

A FRAMEWORK TO MANAGE UNCERTAINTY IN THE COMPUTATION OF WASTE COLLECTION ROUTES AFTER A FLOOD

Abstract. In this paper, we describe a framework to find a good quality waste collection tour after a flood, without having to solve a complicated optimization problem from scratch in limited time. We model the computation of a waste collection tour as a capacitated routing problem, on the vertices or on the edges of a graph, with uncertain waste quantities and uncertain road availability. Multiple models have been conceived to manage uncertainty in routing problems, and we build on the ideas of discretizing the uncertain parameters and computing master solutions that can be adapted to propose an original method to compute efficient solutions. We first introduce our model for the progressive removal of the uncertainty, then outline our method to compute solutions: our method first considers a low-dimensional set of random variables that govern the behaviour of the problem parameters, discretizes these variables and computes a solution for each discrete point before the flood, and then uses these solutions as a basis to build operational solutions when there are enough information about the parameters of the routing problem. We then give computational tools to implement this method. We give a framework to compute the basis of solutions in an efficient way, by computing all the solutions simultaneously and sharing information (that can lead to good quality solutions) between the different problems based on how close their parameters are, and we also describe how real solutions can be derived from this basis. Our main contributions are our model for the progressive removal of uncertainty, our multi-step method to compute efficient solutions, and our intrusive framework to compute solutions on the discrete grid of parameters.

Distribution with Quality of Service Considerations: The Capacitated Routing Problem with Profits and Service Level Requirements

Inspired by a problem arising in cash logistics, we propose the Capacitated Routing Problem with Profits and Service Level Requirements (CRPPSLR). The CRPPSLR extends the class of Routing Problems with Profits by considering customers requesting deliveries to their (possibly multiple) service points. Moreover, each customer imposes a service level requirement specifying a minimum-acceptable bound on the fraction of its service points being delivered. A customer-specific financial penalty is incurred by the logistics service provider when this requirement is not met. The CRPPSLR consists in finding vehicle routes maximizing the difference between the collected revenues and the incurred transportation and penalty costs in such a way that vehicle capacity and route duration constraints are met. A fleet of homogeneous vehicles is available for serving the customers. We design a branch-and-cut algorithm and evaluate the usefulness of valid inequalities that have been effectively used for the capacitated vehicle routing problem and, more recently, for other routing problems with profits. A real-life case study taken from the cash supply chain in the Netherlands highlights the relevance of the problem under consideration. Computational results illustrate the performance of the proposed solution approach under different input parameter settings for the synthetic instances. For instances of real-life problems, we distinguish between coin and banknote distribution, as vehicle capacities only matter when considering the former. Finally, we report on the effectiveness of the valid inequalities in closing the optimality gap at the root node for both the synthetic and the real-life instances and conclude with a sensitivity analysis on the most significant input parameters of our model.

The probabilistic vehicle routing problem with service guarantees

We develop a two-phase approach to solving the capacitated routing problem (CVRP) with stochastic demand. A nonlinear chance-constrained optimization model is solved to determine delivery quantities, and a tabu search metaheuristic is used to determine vehicle routes. The goal of this research is to assure that a logistics company would satisfy the demands of customers with a high probability, while minimizing the overall transportation cost. We introduce the concept of premium customers, who are guaranteed a higher level of service. We show that our chance-constrained method has some strategic advantages over the CVRP with recourse approach. We examine the possibility of the logistics company charging customers selectively with an additional service fee to assure a high level of service. Moreover, we provide managerial insight on when the best time is to pay for the premium membership. We present computational results on commonly studied small to large-scale CVRP instances. A simulation study is conducted to explore the performance of the proposed chance-constrained approach using the CVRP with recourse. We conclude that our chance-constrained CVRP model could serve a logistics company well when resource costs and service guarantees are of concern.

An Ant Colony algorithm hybridized with insertion heuristics for the Time Dependent Vehicle Routing Problem with Time Windows

This paper presents an Ant Colony System algorithm hybridized with insertion heuristics for the Time-Dependent Vehicle Routing Problem with Time Windows (TDVRPTW). In the TDVRPTW a fleet of vehicles must deliver goods to a set of customers, time window constraints of the customers must be respected and the fact that the travel time between two points depends on the time of departure has to be taken into account. The latter assumption is particularly important in an urban context where the traffic plays a significant role. A shortcoming of Ant Colony algorithms for capacitated routing problems is that, at the final stages of the algorithm, ants tend to create infeasible solutions with unrouted clients. Hence, we propose enhancing the algorithm with an aggressive insertion heuristic relying on the minimum delay metric. Computational results confirm the benefits of more involved insertion heuristics. Moreover, the resulting algorithm turns out to be competitive, matching or improving the best known results in several benchmark problems.

Bounds for the general capacitated routing problem

AbstractThis paper presents heuristics that are based on a tour splitting of a general routing tour for solving the general capacitated routing problem (GCRP). This problem is a generalization of the vehicle routing problem (VRP) and the capacitated arc routing problem (CARP). For the VRP, heuristics that consist of an optimum partitioning of a TSP tour generated by Christofides are known and have a worst‐case error of 7/2 − 3/q for even q, where q is the capacity of the vehicles. If we apply a partitioning to an optimum TSP tour, the worst‐case error becomes 3 − 2/q for even q. We generalize these results to the GCRP and give also some lower bounds. © 1993 John Wiley & Sons, Inc.

A Vehicle Routing Problem with Stochastic Demand

We consider a natural probabilistic variation of the classical vehicle routing problem (VRP), in which demands are stochastic. Given only a probabilistic description of the demand we need to design routes for the VRP. Motivated by applications in strategic planning and distribution systems, rather than resolving the problem when the demand becomes known, we propose to construct an a priori sequence among all customers of minimal expected total length. We analyze the problem using a variety of theoretical approaches. We find closed-form expressions and algorithms to compute the expected length of an a priori sequence under general probabilistic assumptions. Based on these expressions we find upper and lower bounds for the probabilistic VRP and the VRP re-optimization strategy, in which we find the optimal route at every instance. We propose heuristics and analyze their worst case performance as well as their average behavior using techniques from probabilistic analysis. Our results suggest that our approach is a strong and useful alternative to the strategy of re-optimization in capacitated routing problems.

Bounds and Heuristics for Capacitated Routing Problems

In a capacitated routing problem, the objective is to minimize the total distance travelled by vehicles of limited capacity to serve a set of customers that are located in the Euclidean plane. We develop asymptotically optimal bounds and heuristics for this problem, under the assumption that the capacity of a vehicle is expressed in terms of an upper bound on the number of customers that it can serve. The analysis culminates in an algorithm that, for a given capacity and given ϵ, will find a solution with relative error at most ϵ in time polynomial in the number of customers.