Heterogeneous Fleet Vehicle Research Articles

Applying quantum approximate optimization to the heterogeneous vehicle routing problem

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We show that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.

Optimization of Truck–Cargo Matching for the LTL Logistics Hub Based on Three-Dimensional Pallet Loading

This study investigates the truck–cargo matching problem in less-than-truckload (LTL) logistics hubs, focusing on optimizing the three-dimensional loading of goods onto standardized pallets and assigning these loaded pallets to a fleet of heterogeneous vehicles. A two-stage hybrid heuristic algorithm is proposed to solve this complex logistics challenge. In the first stage, a tree search algorithm based on residual space is developed to determine the optimal layout for the 3D loading of cargo onto pallets. In the second stage, a heuristic online truck–cargo matching algorithm is introduced to allocate loaded pallets to trucks while optimizing the number of trucks used and minimizing transportation costs. The algorithm operates within a rolling time horizon, allowing it to dynamically handle real-time order arrivals and time window constraints. Numerical experiments demonstrate that the proposed method achieves high pallet loading efficiency (close to 90%), near-optimal truck utilization (nearly 95%), and significant cost reductions, making it a practical solution for real-world LTL logistics operations.

Solving a real-world package delivery routing problem using quantum annealers.

Research focused on the conjunction between quantum computing and routing problems has been very prolific in recent years. Most of the works revolve around classical problems such as the Traveling Salesman Problem or the Vehicle Routing Problem. The real-world applicability of these problems is dependent on the objectives and constraints considered. Anyway, it is undeniable that it is often difficult to translate complex requirements into these classical formulations. The main objective of this research is to present a solving scheme for dealing with realistic instances while maintaining all the characteristics and restrictions of the original real-world problem. Thus, a quantum-classical strategy has been developed, coined Q4RPD, that considers a set of real constraints such as a heterogeneous fleet of vehicles, priority deliveries, and capacities characterized by two values: weight and dimensions of the packages. Q4RPD resorts to the Leap Constrained Quadratic Model Hybrid Solver of D-Wave. To demonstrate the application of Q4RPD, an experimentation composed of six different instances has been conducted, aiming to serve as illustrative examples.

An inventory-routing optimization model for pharmaceutical supply chain with time-dependent travel time on a multi-graph network: a case study

PurposeSpurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment.Design/methodology/approachIn this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty.FindingsAn appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term.Originality/valueApplying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

Optimizing petroleum redistribution in Sri Lanka: A cost-benefit transportation model

This case study is based on Ceylon Petroleum Corporation, Sri Lanka, the national oil and gas company and market leader in Sri Lanka. The company’s outbound logistics consists of a centralized distribution method and a redistribution process of its products across the island. However, this study mainly focused on one regional depot and one petroleum product, Kotagala depot and Lanka Auto Diesel. The currently centralized redistribution process has noticed extra routing costs due to the unreasonable consumption of additional distance. This problem is modelled as a variant of the vehicle routing problem with a heterogeneous vehicle fleet. Our objective is to minimize the routing costs (or milk-run) by imposing constraints on the capacity and the volume. The researcher introduces a centralized vehicle routing problem that is presented. The proposed vehicle routing problem has been used to find the optimal path between clusters. The computational investigation highlights the cost savings that this new VRP can accrue. Cost savings can be accrued as large as 32.35% compared to a company's existing method.

A probabilistic bi‐objective model for a humanitarian location‐routing problem under uncertain demand and road closure

AbstractEffective planning and execution of humanitarian aid logistics activities ensure that disaster‐related losses are minimized. This study addresses a tactical‐level pre‐disaster humanitarian logistics problem where a decision‐maker decides on cross‐dock locations by taking potential vehicle routes into account. A decision support model is proposed for the location selection and distribution operations in humanitarian logistics with explicit fuel consumption estimation. In the addressed problem, the demand amount of each node depends on probabilistic disaster scenarios. Probabilities of whether each arc/road is open or closed and heterogeneous vehicle fleet in terms of vehicle sizes are also respected. The model is formulated as probabilistic bi‐objective mixed integer linear programming, whose objectives are minimization of the total cost (i.e., fuel cost, vehicle fixed cost, and fixed opening cost) and total travel time. To the best of our knowledge, the proposed decision support model is unique in terms of the features considered simultaneously. The applicability of the model is demonstrated by the case study and subsequent numerical analyses of a possible earthquake in the Kartal district of Istanbul. The proposed model is shown to have the potential to support decision‐makers in preparation for a disaster. A solution approach based on a clustering algorithm has been also proposed to solve larger instances of the problem. The effectiveness of this heuristic has been demonstrated through its application to larger‐scale problems.

Optimalitas Rute pada Pengiriman Multiperjalanan dengan Armada Kendaraan Listrik Heterogen

Electric vehicles are emerging as a key trend in sustainable mobility, mitigating emissions, and reducing dependence on fossil fuels. The challenge in optimizing route modeling lies in some limitations, such as battery range, charging time, and the diversity of electric vehicle types. This article explores the optimality of routes in a multiple-trip distribution system using a heterogeneous fleet of electric vehicles. The electric vehicle routing problem is formulated as a mixed-integer linear programming aiming to find the most cost-efficient optimal route. A notable feature of the model allows electric vehicle fleets to undertake additional travel to complete distribution tasks, i.e., multiple trips. The model is implemented in two illustrative examples involving the delivery of goods using homogeneous and heterogeneous electric vehicle fleets characterized by loading and battery capacities. Each case includes one depot, 8 and 10 customers, and 2 battery swapping stations, solved using the branch-and-bound method through Lingo 18.0. Simulation results indicate that battery capacity and the presence of battery swapping stations significantly influence the routes selection.

A Bayesian Optimization Approach for Tuning a Grouping Genetic Algorithm for Solving Practically Oriented Pickup and Delivery Problems

Background: The Multi Depot Pickup and Delivery Problem with Time Windows and Heterogeneous Vehicle Fleets (MDPDPTWHV) is a strongly practically oriented routing problem with many real-world constraints. Due to its complexity, solution approaches with sufficiently good quality ideally contain several operators with certain probabilities.Thus, automatically selecting the best parameter configurations enhances the overall solution quality. Methods: To solve the MDPDPTWHV, we present a Grouping Genetic Algorithm (GGA) framework with several operators and population management variants. A Bayesian Optimization (BO) approach is introduced to optimize the GGA’s parameter configuration. The parameter tuning is evaluated on five data sets which differ in several structural characteristics and contain 1200 problem instances. The outcomes of the parameter-tuned GGA are compared to both the initial GGA parameter configuration and a state-of-the-art Adaptive Large Neighborhood Search (ALNS). Results: The presented GGA framework achieves a better solution quality than the ALNS, even for the initial parameter configuration used. The mean value of the relative error is less than 0.9% and its standard deviation is less than 1.31% for every problem class. For the ALNS, these values are up to three times higher and the GGA is up to 38% faster than the ALNS. Conclusions: It is shown that the BO, as a parameter tuning approach, is a good choice in improving the performance of the considered meta-heuristic over all instances in each data set. In addition, the best parameter configuration per problem class with the same characteristics is able to improve both the frequency of finding the best solution, as well as the relative error to this solution, significantly.

A simheuristic approach towards supply chain scheduling: Integrating production, maintenance and distribution

This study attempts to integrate production, maintenance, and delivery operations among supply chain members. Despite numerous studies in the field of supply chain management, researchers have often overlooked crucial aspects, such as uncertainties in demand and production. For instance, the significant impact of maintenance activities on production flow has been underrepresented in supply chain management literature. This study investigates these gaps in the context of a fertilizer producer case study, which is characterized by seasonal demand and the functional silos syndrome due to old-fashioned management approaches. This study proposes a mathematical model and two multi-objective simheuristics for the Integrated Production, Maintenance, and Distribution Scheduling Problem (IPMDSP) considering demand variation for multiple products and product delivery time-windows using a heterogeneous fleet of vehicles. The IPMDSP is solved using the ϵ-constraint method and simheuristics linking the simulation model to customized and tuned versions of Particle Swarm Optimization (MOPSO) and the Non-dominated Sorting Genetic Algorithm (NSGA-II). The optimization objectives include minimizing maintenance duration, distribution costs, and customer dissatisfaction due to delivery tardiness. The results demonstrate the superiority of the simheuristic empowered by NSGA-II over the MOPSO in solving the IPMDSP. The comparison between the performance of deterministic and stochastic approaches in addressing the problem reveals that neglecting uncertainty caused by maintenance activities can lead to an increase in optimization objectives. Furthermore, the proposed simheuristics achieved significant improvements in minimizing objectives in solving the fertilizer producer case study.

Sustainable supply chain resilience for logistics problems: Empirical validation using robust and computational intelligence methods

A supply chain's ability to avoid an unexpected disruption or quickly return to a normal situation defines supply chain resilience. Prior works have emphasized the integration of supply chain resilience and sustainable development goals (sustainable supply chain resilience), which is the focus of this paper. This paper proposes a four-level supply chain consisting of suppliers, intermodal hubs, manufacturers, and distributors along with a heterogeneous fleet of vehicles. Two types of manufacturers are included: large and small. The small manufacturers are moveable. To contribute to sustainable logistics problems, the objectives are cost, carbon emissions, and job opportunities when the appropriate supply chain members and flow of materials are optimized. To contribute to supply chain resilience, this paper presents a new robust approach and a new multiobjective algorithm to capture uncertain parameters (e.g., supply cost and employee availability). A numerical example based on empirical data shows the applicability of the proposed model.

Modeling and solving the fuel distribution problem with unloading precedence and loading sequence considerations

AbstractThis paper presents a real-world liquid fuel distribution problem involving a heterogeneous fleet of multi-compartment vehicles servicing a set of orders of different fuels. Two new features are introduced that affect significantly the performance of the fuel distribution process in terms of safety and efficiency: (i) loading trucks so that the payload remains balanced throughout each phase of a delivery route, and (ii) sequencing the requests for loading trucks at the depot loading facilities. A Mixed Integer Programming formulation is presented and an Adaptive Large Neighbourhood Search algorithm with various novel features is developed and benchmarked. A new loading model is formed and solved for allocating the ordered items (fuel) to vehicle compartments, as part of constructing/repairing delivery routes. The computational performance of the proposed solution approach has been tested on a series of benchmark problems. Moreover, a series of experiments were performed in order to assess the effect of the balanced loading constraints on the traveled distance. The results indicate that the effect of this type of constraint on the total traveled distance is kept at a reasonable level, reaching a maximum increase of 4.37%. The computational tools presented in this work may accommodate the dispatchers’ work in producing efficient and safe delivery routes while managing efficiently any potential bottleneck in the truck loading facilities.

Geometric zoning and selective routing for surveillance and coverage operations

Taking fast action, and effectively utilizing the available resources, are important when conducting time-critical surveillance missions. In addition, the potential complexity of the search, such as the ruggedness of the terrain or large size of the search region, should be considered. Such issues can be tackled by using a heterogeneous fleet of manned and unmanned vehicles equipped with different sensors by considering speed, coverage and flexibility. This article centres on designing a fast solution approach for planning coverage missions through zoning and routing. The challenge is to cover an area where targets can be potentially found with a variable likelihood. The search area is modelled using a scoring map to support the choice of search in sub-areas, where the scores represent the importance of tasks. Heuristic approaches are proposed to automate search processes and plan missions, given a small time budget.

A unified exact approach for a broad class of vehicle routing problems with simultaneous pickup and delivery

The vehicle routing problem (VRP) with simultaneous pickup and delivery (VRPSPD) is a classical combinatorial optimization problem in which one aims at determining least-cost routes, starting and ending at the depot, while simultaneously meeting the pickup and delivery demands of geographically dispersed customers in a single visit, and without violating the capacity of the vehicle. In this work, we propose a unified branch-cut-and-price (BCP) algorithm to solve ten variants of the problem, considering not only the standard version but also those including additional attributes such as a heterogeneous fleet of vehicles, time windows, route duration, multiple depots, and location decisions. The resulting problem that generalizes all of these variants can be formulated as a heterogeneous location routing problem with simultaneous pickup and delivery and time windows (HLRPSPDTW), for which we propose a compact formulation to serve as the basis for an extended formulation associated with the BCP approach. The proposed exact method includes many of the features developed in recent years, such as a bucket graph-based labeling algorithm, rank-1 cuts with limited memory, and dynamic ng-sets. Extensive computational experiments were performed on more than 550 benchmark instances and our algorithm was capable of obtaining a number of new optimal solutions, as well as improved lower bounds, for all variants addressed in this paper.

A mathematical model and metaheuristic approach to solve the real-time feeder vehicle routing problem

Unlike classic vehicle routing problems, real-time vehicle routing problems (RTVRPs) are real-world dynamic vehicle routing problems (DVRPs) in which customer requests are identified over the time horizon of operations without previous knowledge. In this problem, received requests are answered as quickly as possible and then dispatched to a service vehicle. Considering the RTVRP’s timing constraints, a solution must provide the best trade-off between the computation time required to find the solution and the proposed solution’s costs. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. The feeder approach also lowers the number of times the vehicle returns to the central depot for loading, resulting in cost and time savings. The present article proposes a real-time feeder vehicle routing problem (RTFVRP) in a situation where every truck and every motorcycle can join during the freight delivery process. After modeling the RTFVRP through mixed-integer linear programming, a dynamic inertia weight particle swarm optimization (DIWPSO) algorithm is offered to solve the problem. The results of the static version of the FVRP in the small and the last time slices show that the GAMS outputs outperform those of the DIWPSO and differential evolution (DE), both indicating a similar performance. The results of running these algorithms for 21 DVRP test instances revealed that the PSO outperforms the DE in quality and solution runtime in both static and dynamic versions. Overall, the PSO and DE algorithms generated 34.33% and 30.37% cost savings in implementing RTFVRP, respectively, compared to the case that all requests were available at the beginning of the working day.

Analyzing the benefits of a city hub: An inventory and routing perspective

Collaboration is one of the crucial elements in city logistics and it is often pursued by the introduction of two- or multi-echelon systems using one or more intermediate consolidation points, such as Urban Consolidation Centers (UCCs), city depots, city hubs, etc. Our literature review shows that the study of inventory aspects in such a context is relatively unexplored. Therefore, this paper studies the effect of using a UCC or city hub in a B2B city logistics system in terms of both inventory and routing aspects. A multi-period optimization model is proposed to support the operational decisions in urban B2B distribution when using a city hub. We study the effect of introducing a city hub by comparing our model with a baseline model in which urban retailers operate without a city hub. The model accounts for the complexity of urban logistics by considering a heterogeneous vehicle fleet, the option to perform multiple trips per day, and strict customer time windows. A metaheuristic algorithm based on Large Neighborhood Search (LNS) is used to solve the route optimization problem for realistic problem instances. Extensive numerical experiments are conducted according to an experimental design and a statistical analysis. Results indicate that the introduction of a city hub leads to significant reductions in operational costs and societal impacts (e.g., loading degree, number of urban trips, traveled distances). Our analysis shows that these savings are significantly impacted by the problem context (e.g., replenishment policy, number of retailers, number of suppliers, and holding cost). For example, how retailers make replenishment decisions significantly impacts the costs of the overall system and the potential savings. The most cost-efficient replenishment method is often not the most interesting one from a societal perspective. Finally, from a city’s perspective, a sufficient number of retailers and suppliers should participate in the system to maximize consolidation opportunities. However, in relative terms, the largest potential savings by introducing a city hub are reached when not too many suppliers are included and suppliers have a relatively limited number of customers to serve.

A simulated annealing with variable neighborhood descent approach for the heterogeneous fleet vehicle routing problem with multiple forward/reverse cross-docks

With a greater awareness of the challenges regarding environmental, societal, political, and economic factors, where reverse logistics has become a significant part of supply chain networks, this paper presents an integrated forward and reverse logistics network, named the Heterogeneous Fleet Vehicle Routing Problem with Multiple Forward/Reverse Cross-Docks (HF-VRPMFRCD). We consider a heterogeneous fleet of vehicles with different loading capacities and transportation costs. We also consider multiple cross-docks with two different operations: forward and reverse processes. The former focuses on delivering the demand from suppliers to customers, while the latter aims at returning unsold products from customers to suppliers. We propose a Simulated Annealing with Variable Neighborhood Descent (SAVND) algorithm for solving HF-VRPMFRCD, where Variable Neighborhood Descent (VND) is a local search heuristic embedded in the framework of Simulated Annealing (SA). SAVND outperforms the state-of-the-art algorithm in solving the Heterogeneous Fleet Vehicle Routing Problem with Multiple Cross-Docks (HF-VRPMCD), where the VND heuristic significantly improves the quality of solutions. For HF-VRPMFRCD benchmark instances, SAVND provides optimal solutions for small-scale instances and better solutions than those of the GUROBI solver for remaining larger instances. Lastly, we present and discuss the benefits of integrating the forward and reverse processes.

ANALYSIS OF LOCATION AND DECISION-MAKING OF FLEET VEHICLE TYPE WITH CVRP MULTI TRIP AND GRAVITY LOCATION MODEL FOR OPERATIONAL COST EFFICIENCY (Case Study CV. XYZ, Wonoayu-Sidoarjo)

Transportation has an important role in the logistics of a company, both in services and products. Increased orders in 2020 for wooden speaker products at CV. XYZ (Wonoayu-Sidoarjo) makes this company try to minimize transportation costs at their operational level. This study focuses on determining the relationship between changes in the type of fleet vehicle and the depot location on the operational costs of product delivery and the time to return to the depot in terms of adding trips. The methodology used in this study is the CVRP Multi Trip with Heterogeneous fleet vehicle and the Gravity Location Model based on the heuristic method. Saving heuristic method and nearest neighbor are heuristic methods used in computational studies to determine the order of visits to the formed sub-routes. There are 4 scenarios that are modeled to further analyze the results of these computations, namely: (1) CVRP multi-trip of old location with wings box truck, (2) CVRP multi-trip of old location with Fuso truck, (3) CVRP multi-trip of the new location with wings box truck, and (4) CVRP multi-trip of the new location with fuso truck. The results of the study concluded that there is a relationship between: (1) changes in fleet vehicle type with total traveling distance, (2) changes in depot location with total traveling distance, (3) fuel consumption rate on vehicle operating costs, (4) average vehicle speed on the time back to the depot. Scenario 4 is the best scenario in terms of traveling distance, fuel costs and delivery time. However, moving the depot center is not easy, so the scenario 2 is the most applicable condition considering that the fuso truck is available and has a higher utility than the wings box truck

The transportation problem with packing constraints

We address a new variant of the transportation problem, where a set of different commodities, available at several supply nodes with different prices, are distributed to demand nodes using a set of heterogeneous vehicle fleets available at each supply node. Since each commodity has a specific weight, there is a packing constraint due to the total capacity of each vehicle. The objective of this problem is to minimize the total supply cost, which includes the purchase cost of commodities and the fixed transportation cost based on the traveled distance. This novel variant of the transportation problem poses computational challenges due to its combinatorial structure. To tackle these challenges and solve large-scale instances to near-optimality in reasonable CPU times, we propose a variable neighborhood search algorithm. The proposed algorithm partitions the problem into smaller, more manageable problems to be solved. In order to initialize this methodology, we also propose a decomposition heuristic that prescribes initial feasible solutions in CPU times ranging from 0.6 s to 133.2 s on average with average optimality gaps ranging from 0.09% to 4.62%. Our proposed methodology provides solutions with 0.06% to 3.78% optimality gaps on average within average CPU times ranging from 0.2 s to 386.2 s, while the commercial solvers are unable to find integer solutions or to solve most of the instances to optimality within one CPU-hour time limit.

Determining lower bound on number of vehicle blocks in multi-depot vehicle scheduling problem with mixed fleet covering electric buses

Scheduling buses in public transport systems consists in assigning trips to vehicle blocks. To minimize the cost of fuel and environmental impact of public transport, the number of vehicle blocks used should be as small as possi-ble, but sufficient to cover all trips in a timetable. However, when solving real life transportation problems, it is difficult to decide whether the number of vehicle blocks obtained from an algorithm is minimal, unless the actual minimal number is already known, which is rare, or the theoretical lower bound on the number of vehicles has been determined. The lower bound on the number of vehicle blocks is even more important and useful since it can be used both as a parameter that controls the optimization process and as the minimum expected value of the respective optimization criterion. Therefore, methods for determining the lower bound in transportation optimiza-tion problems have been studied for decades. However, the existing methods for determining the lower bound on the number of vehicle blocks are very limited and do not take multiple depots or heterogeneous fleet of vehicles into account. In this research, we propose a new practical and effective method to assess the lower bound on the number of vehicle blocks in the Multi-Depot Vehicle Scheduling Problem (MDVSP) with a mixed fleet covering electric vehicles (MDVSP-EV). The considered MDVSP-EV reflects a problem of public transport planning encoun-tered in medium-sized cities. The experimental results obtained for a real public transport system show the great potential of the proposed method in determining the fairly strong lower bound on the number of vehicle blocks. The method can generate an estimated distribution of the number of blocks during the day, which may be helpful, for example, in planning duties and crew scheduling. An important advantage of the proposed method is its low calculation time, which is very important when solving real life transportation problems.

Solving a heterogeneous fleet multi-compartment vehicle routing problem:a case study

Vehicle Routing Problem (VRP) is a complex optimisation problem in the field of supply chain management, especially in the Oil & Gas sector. Due to the rising cost of fuel, effective planning of transportation routes has become a crucial success factor for distribution companies, increasing operational efficiency as well as the corresponding service level. In this paper, we present an optimisation model to solve a heterogeneous fleet multi-compartment vehicle routing problem (MCVRP), a variant of the conventional vehicle routing problem (VRP). Real data are obtained from a medium size oil distribution company, operating in Greece and incorporates 19 petrol stations served from a central oil depot using a fleet of various multi-compartment tanker trucks. The main objective of this research is to design an optimum set of routes minimising distance and truck operating costs. The MCVRP with a heterogeneous fleet of vehicles is modelled as a Mixed-Integer Linear Programming (MILP) problem and the proposed solution determines the number of assigned vehicles, the planning of daily routes and the allocation of different fuels to vehicles compartments, while satisfying customer demand following specific requirements, as detailed in the Carriage of Dangerous Goods (ADR) Regulations.