Multiple Depots Research Articles

An exact routing optimization model for bio-waste collection in the Brussels Capital Region

This paper presents a routing optimization model for a wide range of waste collection problems which allows for multiple depots with homogeneous, capacitated vehicles, intermediate stops at multiple processing facilities, and multiple pick-ups per waste collection location. By minimizing collection routing and vehicle investment costs, the model estimates the total transportation costs for a given network design and waste volumes to be collected at different demand points. The number of feasible routes is severely reduced by restricting the number of subsequent pick-up location visits. The model’s use is illustrated through assessing four future, realistic bio-waste collection scenarios of the Brussels Capital Region (BCR). The scenarios differ with respect to assumptions on future collection rates, joint versus separate collection of food and green waste, and number and locations of processing facilities. The results show that the highest cost reduction can be achieved through joint collection of food and green waste combined with three composting locations. Moreover, we found that introducing multiple processing facilities significantly increases the complexity of the waste collection problem.

Big data analytics in Industry 4.0 ecosystems

Big data analytics in Industry 4.0 ecosystems

An Effective Heuristic for Multidepot Low-Carbon Vehicle Routing Problem

Low-carbon economy has been a hot research topic in recent years. This paper firstly considers the vehicle load weight, the key factors affecting the fuel consumption, to establish the fuel consumption model, and then constructs the vehicle routing planning model in the last mile delivery with multiple depots within time windows. In order to solve this problem, we improve the classical fruit fly algorithm which is easy to fall into the local optimum, and the improved fruit fly optimization algorithm is designed and integrated with genetic algorithm. Computational results show that our solution approach is capable of solving instances with up to 48 customers and 4 different depots. The effectiveness and efficiency of the model and multigroup fruit fly algorithm are verified through case study.

Implementing Horizontal Cooperation in Public Transport and Parcel Deliveries: The Cooperative Share-A-Ride Problem

The static share-a-ride problem (SARP) consists of handling people and parcels in an integrated way through the same vehicle, which provides a shared trip between an origin and a destination, in response to requests received in advance. When multiple providers compete on the same market (for instance, within the same city or region), horizontal cooperation can be an efficient strategy to consolidate all requests and to optimize the total payoff. This situation gives rise to the cooperative SARP (coop-SARP). In this problem, multiple depots and heterogeneous vehicles must be considered and different cooperation levels may be agreed upon by service providers. In this paper, we propose a new mathematical programming formulation for cooperative SARP along with theoretical bounds. Moreover, through numerical experiments and ad hoc statistics, we analyze the benefits of different levels of horizontal cooperation between service providers. The results show that cooperation leads to reduced travel times and to improved vehicle occupancy rates, service levels, and profits, which make such a cooperative system even more appealing for service providers.

A Heuristic for Efficient Coordination of Multiple Heterogeneous Mobile Robots Considering Workload Balance

The letter deals with a path planning problem that commonly arises in many applications involving multiple heterogeneous robots called a Multiple Depot Heterogeneous Traveling Salesman Problem (MDHTSP). Specifically, the authors seek to provide good quality of feasible solutions for a path planning problem for a given set of structurally heterogeneous mobile robots located in distinctive depots and a set of targets to visit while minimizing the maximum travel cost (min-max). A solution for MDHTSP with min-max objectives is in great demand for many applications, such as transportation and surveillance, because it is directly related to a significant reduction in the mission completion time. However, no reliable algorithm running in a reasonable computation time has been published for this specific problem. As an extension of our preliminary research on two heterogeneous robots, this letter presents a heuristic approach based on a primal-dual technique for the problem while focusing on the target assignment. The computational results of the implementation verify that the proposed algorithm produces a good quality of feasible solution within a relatively short computation time.

A hybrid variable neighborhood search approach for the multi-depot green vehicle routing problem

The Multi-Depot Green Vehicle Routing Problem (MDGVRP) is an extension of the well-known Green Vehicle Routing Problem (GVRP) where a fleet of alternative fuel-powered vehicles (AFVs) are used to serve the customers. GVRP consists of determining AFV tours such that the total distance travelled is minimum. The AFVs depart from the depot, serve a set of customers, and complete their tours at the depot without exceeding their driving range and the maximum tour duration. AFVs may refuel en-route at public refueling stations. In MDGVRP, the AFVs are dispatched from different depot locations and may refuel during the day at any depot or refueling station. We formulate MDGVRP as a mixed integer linear programming model and develop a hybrid General Variable Neighborhood Search and Tabu Search approach by proposing new problem-specific neighborhood structures to solve the problem effectively. We assess the performance of our method using the GVRP dataset from the literature. Our results show that the proposed method can provide high quality solutions in short computation times. Then, we extend these instances to the multi-depot case and compare our solutions for small-size instances with the optimal solutions. We also report our results for large-size problems and investigate the trade-offs associated with operating multiple depots and adopting different refueling policies to provide further insights for both academicians and practitioners.

A novel state transition simulated annealing algorithm for the multiple traveling salesmen problem

In this study, we consider the multiple traveling salesman problem (MTSP) with multiple depots, closed paths, and a constraint on the number of cities visited by each traveling salesman. In our previous study, we proposed a state transition simulated annealing algorithm (STASA) that employs the Metropolitan criterion for simulated annealing to solve the traveling salesman problem (TSP). The results obtained were significantly improved according to our previous experiments. In the present study, we propose a new intelligent operator to solve the MTSP called an elementary breakpoint operator, which can generate the solution space for MTSP through elementary matrix operations. A neighborhood search structure called 2opt, which can improve the quality of the solution by connecting two shorter non-adjacent arcs, is then introduced into STASA to enhance the ability to capture the global optimal solution. Finally, comparative experiments were conducted based on a wide range of TSPLIB benchmark instances using our proposed algorithm and other algorithms, and the results demonstrated the superior performance of our proposed approach compared with all other state-of-the-art approaches for MTSP.

Optimization of electric vehicle recharge schedule and routing problem with time windows and partial recharge: A comparative study for an urban logistics fleet

The use of electric vehicles (EVs) is becoming more and more widespread and the interest in these vehicles is increasing each day. EVs promise to emit less air pollution and greenhouse gas (GHG) emissions with lower operational costs when compared to fossil fuel-powered vehicles. However, many factors such as the limited mileage of these vehicles, long recharging times, and the sparseness of available recharging stations adversely affect the preferability of EVs in industrial and commercial logistics. Effective planning of EV routes and recharge schedules is vital for the future of the logistics sector. This paper proposes an electric vehicle routing problem with the time windows (EVRPTW) framework, which is an extension of the well-known vehicle routing problem (VRP). In the proposed model, partial recharging is considered for the EVRPTW with the multiple depots and heterogeneous EV fleet and multiple visits to customers. While routing a set of heterogeneous EVs, their limited ranges, interdependent on the battery capacity, should be taken into consideration and all the customers' deliveries should be completed within the predetermined time windows. To deal with this problem, a series of neighbourhood operators are developed for the local search process in the variable neighbourhood search (VNS) and variable neighbourhood descent (VND) heuristics. The proposed solution algorithms are tested in large-scale instances. Results indicate that the proposed heuristics perform well as to this problem in terms of optimizing recharging times, idle waiting times, overtime of operators, compliance with time windows, number of vehicles, depots, and charging stations used.

A novel bi-objective credibility-based fuzzy model for municipal waste collection with hard time windows

In this study, a bi-objective vehicle routing mathematical model was proposed, in which the main objectives were minimizing the total economic cost, as well as the whole time for municipal waste collection. The considered waste collection network included bins, multiple depots, multiple heterogeneous vehicles, multiple intermediate facilities, and a landfill. Besides, in each day, municipal waste was collected several times in various hard time windows by heterogeneous vehicles, which all used vehicles could trip more than once per time window. It should be noted that the amount of waste generated was uncertain, which a fuzzy credibility theory was used to cope with this uncertainty. The exact solutions of some small problems were generated by the augmented ε-constraint method. Due to the complexity of this problem in more substantial sizes, the metaheuristic of Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used. Since the performance of metaheuristic algorithms is quite sensitive to their parameters, we used the self-adaptive method to tune the parameters of NSGA-II and also compared the results with the Taguchi method. The initial solutions of the metaheuristic approach were generated by a novel heuristic algorithm. Also, the waste collection vehicle routing problem of one of Tehran’s regions was solved by the proposed model. After solving this model, the presented Pareto optimal solutions showed the total economic cost and the total time of the waste collection were improved by about 1.4% and 1.1%, respectively, which means a significant reduction, due to the high volume of costs and time.

Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper.

Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm

In “Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm,” Uit het Broek, Schrotenboer, Jargalsaikhan, Roodbergen, and Coelho present a generic branch-and-cut framework to solve routing problems with multiple depots on directed graphs. They present new valid inequalities that eliminate subtours, enforce tours to be linked to the same depot, and enforce bounds on the number of customers in a vehicle tour. This is embedded in a branch-and-cut scheme that also contains generalized and adapted versions of valid inequalities that are well known for related routing problems. The authors show that the new inequalities tighten root node relaxations considerably. In combination with a simple but effective upper-bound procedure, only requiring a MIP solver and a smart reduction of the problem size, the authors show that the overall framework solves instances of considerably larger size to optimality than have been reported in the literature.

The Mathematical Model and an Genetic Algorithm for the Two-Echelon Electric Vehicle Routing Problem

In order to cope with the challenges of high cargo load and high timeliness distribution in logistics industry, as well as to alleviate the current situation of oil resource depletion and air pollution, this study established a mathematical model of two-echelon electric vehicle routing problem (2E-EVRP) and design a heuristic algorithm. The 2E-EVRP can be divided into the multiple depot vehicle routing problem (MDEVRP) and the split delivery vehicle routing problem (SDVRP). The proposed genetic algorithm is used to solve the MDEVRP, and the actual case of a logistics company in Beijing is taken as the calculation experiment, so as to verify the feasibility of the proposed algorithm and provide decision-making reference for the development of logistics enterprises. The results show that the total path length obtained by the proposed algorithm is optimized by 20.82 kilometers compared with the traditional simulated annealing algorithm.

A Branch & Cut algorithm for the prize-collecting capacitated location routing problem

The Capacitated location routing problem (CLRP) is the combination of two well-studied problems in Operations Research: the capacitated facility location problem (CFLP) and the multiple depots vehicle routing problem (MDVRP). Given a set of available locations and a fleet of vehicles, the aim is to determine a set of depots to open and routes of the vehicles to satisfy the customers demands. The objective of the CLRP is to minimize the total cost, that is the cost of the opened depots, the fixed cost of the vehicles and the cost of the routes while satisfying vehicle and depot capacity constraints. In this work the prize-collecting capacitated location routing problem (PC-CLRP), a new variant of the CLRP is presented. In this case it is possible to leave some customers unvisited and if a customer is visited it gives a gain. The objective is to maximize the overall benefit. A two-index formulation for the PC-CLRP and a Branch & Cut algorithm based on this model are proposed. Valid inequalities for the CLRP are adapted for the PC-CLRP. Also new valid inequalities and optimality cuts are proposed together with their corresponding separation algorithms. A hierarchical branching strategy is also included. The initial solution was provided by an Ant Colony Algorithm. The algorithm is tested on a set of instances specially designed for the new problem. Computational results showed very promising. We also compare the performance of the algorithm with recent work for CLRP on instances from the literature.

A mixed-integer linear programming model for the selective full-truckload multi-depot vehicle routing problem with time windows

This article has studied a full truckload transportation problem in the context of an empty return scenario, particularly an order selection and vehicle routing problem with full truckload, multiple depots and time windows (SFTMDVRPTW). The aim is to develop a solution where a set of truck routes serves a subset of selected transportation demands from a number of full truckload orders to maximize the total profit obtained from those orders. Each truck route is a chain of selected demands to serve, originating at a departure point and terminating at an arriving point of trucks in a way that respects the constraints of availability and time windows. It is not mandatory to serve all orders, and only the profitable ones are selected. In this study, we have formulated the SFTMDVRPTW as a mixed-integer linear programming (MILP) model. Finally, Computational results are conducted on a new data set that contains thirty randomly generated problem instances ranging from 16 to 30 orders using the CPLEX software. The findings prove that our model has provided good solutions in a reasonable time.

Multi-objective Emergency Scheduling for Geological Disasters

Because of the specific time and distance constraints, emergency management departments usually build multiple depots (resource centers) to serve the widely dispersed customers (disaster areas), to more effectively fulfill customer demand, and deal with the changing road conditions in real time. Therefore, research on multi-depot dynamic emergency dispatch can be of significant value to effective disaster operations. In this paper, a multi-objective multi-depot and multi-type dynamic vehicle routing problem model is established that minimizes total distance and priority errors and considers secondary disasters, damaged roads, the limited vehicle number at the various depots, and the different vehicle capacities. To solve this model, a hybrid ant colony optimization based on the circumcenter of the polygon formed by depots is proposed. Real landslides disaster data from Hubei province and two kinds of benchmark instances test the performance of the proposed algorithm. After detailed experimental comparisons, the competitive performance of the proposed algorithm is verified.

Dynamic Multiple Depots Vehicle Routing in the Physical Internet context

Abstract This paper proposes Dynamic Multiple Depots Vehicle Routing (DMDVR) to explore the feasible solution of routing transportation between PI-hubs and retailers in the same cluster. The routing solution in this research is constructed by the daily forecasting demand of a commodity crop, Pineapple, from Thailand’s northern region. Each route is composed of a starting hub, the number of retailers, and an ending hub. The authors propose Mixed Integer Linear Programming (MILP) to construct the routes considering inventory and truck capacity constraints. Besides, another solution method is proposed by using a heuristic method named “Iterated Random Heuristic”. The empirical results are evaluated by using the total distribution cost and computational time. The routing transportation of this research is based on the daily delivery transportation from PI-hubs to retailers. The results show that Iterated Random Heuristic with Nearest Neighbor Search generates near-optimal solutions within a short computational time.

Efficient formulation for transportation scheduling of single refinery multiproduct pipelines

Multiproduct pipeline transportation scheduling is a complex operations research problem that is characterized by the movement of the cargo rather than the carrier. Hence, it cannot be solved using vehicle routing methods. While most formulations for short-term scheduling adopt a continuous-time representation, they often lead to suboptimal solutions because of the dependence on the number of time slots in the grid, which is difficult to predict. Furthermore, some of these formulations have poor linear relaxations due to the presence of inefficient big-M constraints. In this paper, we develop a discrete-time mixed integer linear programming (MILP) model for the detailed scheduling of a straight pipeline with a single refinery and multiple depots. The proposed formulation rigorously detects interface material generated between adjacent products and considers planned shutdowns in pipeline segments due to maintenance operations, as well as local market demands occurring at multiple intermediate due dates. The main novelty is that continuous tasks can span multiple time slots to enforce minimum batch sizes on injection and delivery nodes, which allows for the model to generate better schedules than those obtained with previously proposed formulations. To ensure an efficient model by design, we rely on generalized disjunctive programming (GDP) and on the convex hull reformulation of disjunctions, which results in stronger and often more computationally efficient formulations. We present numerical results for a set of benchmark instances and show that the proposed model applies to large-scale industrial cases.

A Branch-and-Cut Agorithm for the Multi-Depot Inventory-Routing Problem with Split Deliveries

In this paper, we model and solve a multi-depot inventory-routing problem with split-deliveries (MDIRPSD). The problem emerges under the vendor-managed inventory paradigm when deliveries are made from multiple depots, and the customers can be served several times in the same period. The MDIRPSD integrates supply and distribution decisions and has recently been proposed in the literature. We present a new mathematical formulation, taking into account inventory holding costs, and we also introduce a new inventory policy. We have designed and implemented a new branch-and-cut that overcome a similar approach from the literature. Finally, we report comparative results between the two inventory policies considered.

An exact solution method for a rich helicopter flight scheduling problem arising in offshore oil and gas logistics

This paper studies the problem of creating an optimal flight schedule for a heterogeneous fleet of helicopters tasked with transporting personnel to, from, and between offshore installations. The problem can be modelled as a rich vehicle routing problem and combines the following properties from the vehicle routing literature: pickup and delivery structure, heterogeneous fleet operating out of multiple depots, multi-trip, and temporal synchronization of transportation tasks. We present compact and extended mathematical models of the problem, where the extended model is based on generating all trips apriori. When solving the extended model we apply delayed constraint generation (DCG) to parts of the model to speed up the solution process. Computational results are presented that show that the extended formulation and solution method can solve realistic instances of the problem within one hour. The results further show that the DCG method works significantly better than using lazy constraints from a commercial solver, especially when the number of transportation tasks requiring temporal synchronization becomes large.

Routing automated lane-guided transport vehicles in a warehouse handling returns

Faced with high return rates, many e-commerce retailers are considering novel technical solutions to expedite the processing of returned items in their warehouses. One such solution consists of lane-guided transport (LGT) vehicles. These small, electric vehicles follow optical markers on the floor, picking up boxes of returned items at a depot and dropping them off at workstations, releasing the logistics workers to focus on the productive task of actually processing the items instead of carrying them through the warehouse. These types of systems are simple to set up from a technical perspective; however, the routes on the warehouse floor still need to be carefully planned. This gives rise to the following routing problem. Given a set of stations to be served from multiple depots by a fleet of LGT vehicles, which stations doing what type of work should be visited on what route? Only one route per depot is allowed, but multiple vehicles may use the same route. Moreover, since routes cannot be changed on short notice, we consider an infinite planning horizon where the demand rate of the stations depends on the type of work they are assigned to do (e.g., handling defective items or refurbishing). We develop a decomposition heuristic, which solves instances derived from industry data to near-optimality in less than a minute. We also show that the depot location is rather unimportant for the overall system performance, but that the depot count can have a significant influence.