Heterogeneous Fleet Research Articles

Bus scheduling with heterogeneous Fleets: Formulation and hybrid metaheuristic algorithms

This paper focuses on optimizing mixed-fleet bus scheduling (MFBS) with vehicles of different sizes in public transport systems. We develop a novel mixed-integer nonlinear programming (MINLP) model to address the MFBS problem by optimizing vehicle assignment and dispatching programs. The model considers user costs, operator costs, and the crowding inconvenience of standing and sitting passengers. To tackle the complexity of the MFBS problem, we employ Genetic Algorithm (GA) and Grey Wolf Optimizer (GWO). Besides, we develop two hybrid metaheuristics, including GA-SA [a combination of GA and Simulated Annealing (SA)] and GWO-SA (a combination of GWO and SA), to improve optimization capabilities for the MFBS problem. We also employ a Taguchi approach to fine-tune the metaheuristics’ parameters. We widely examine and compare the metaheuristics’ performance across various-sized samples (small, medium, and large), considering solution quality, computational time, and the result stability of each algorithm. We also compare the metaheuristics’ solutions with the optimal solutions acquired by GAMS software in small and medium-scale samples. Our findings show that the GWO-SA outperforms the other metaheuristics. Applying our model to a real bus corridor in Santiago, Chile, we find that precise dispatching plans generated by more sophisticated/advanced algorithms (GA-SA and GWO-SA) lead to larger cost savings and improved performance compared to simpler algorithms (GA and GWO). Interestingly, utilizing more advanced algorithms makes a difference in terms of fleet planning in crowded scenarios, whereas for low and medium-demand cases, simpler dispatching algorithms could be used without a drop in accuracy.

Optimizing task assignment and routing operations with a heterogeneous fleet of unmanned aerial vehicles for emergency healthcare services

This paper studies the optimization of task assignment and pickup and delivery operations using a heterogeneous fleet of unmanned aerial vehicles (UAVs). We specifically address the distribution of emergency medical supplies, including medications, vaccines, and essential medical aid, as well as the collection of biological blood samples for testing and analysis. Unique challenges, such as supply shortages, time windows, and geographical considerations, are explicitly taken into account. The problem is first formulated as a mixed-integer linear programming model aimed at maximizing the total profit derived from the execution of a set of emergency healthcare pickup and delivery tasks. An enhanced Q-learning-based adaptive large neighborhood search (QALNS) is proposed for large-scale benchmark instances. QALNS exhibits a superior performance on benchmark instances. It also improves the quality of the solutions on average by 5.49% and 6.86% compared to the Gurobi solver and a state-of-the-art adaptive large neighborhood search algorithm, respectively. Sensitivity analyses are performed on critical factors contributing to the performance of the QALNS algorithm, such as the learning rate and the discount indicator. Finally, we provide managerial insights on the use of the fleet of UAVs and the design of the network.

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.

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.

Maritime Inventory Routing with Speed Optimization: A MIQCP Formulation for a Tanker Fleet Servicing FPSO Units

This paper presents a continuous-time formulation for the management of deep-sea floating production storage and offloading (FPSO) units, which process and store crude oil from nearby oil platforms while waiting for a shuttle tanker to arrive and collect it. A heterogeneous fleet of tanker vessels travelling between the FPSO units and a port refinery is available, with the optimization deciding on the number and type of vessels to use, their route and travelling speed. The goal is to achieve an environmentally friendly solution featuring vessels travelling at lower speeds to minimize fuel consumption (a quadratic function of speed), which may require renting additional shuttle tankers to maintain production. The resulting mixed-integer quadratically constrained problems (MIQCP) can be solved by GUROBI, but not to global optimality, whereas a mixed-integer linear programming (MILP) relaxation that underestimates the total operating cost can tackle moderate problem sizes (5 FPSOs and 4 shuttle tankers).

Two-phase matheuristic for assignment and truck loading problems

We introduce a novel two-phase matheuristic for assignment and truck loading. The scope of our approach involves scenarios with an extensive amount of items requiring assignment to a heterogeneous fleet of trucks and subsequent transportation. A distinguishing feature of our matheuristic lies in the fact that the complex underlying problem is divided into subproblems which later are merged into a global solution. The proposed matheuristic tackles the assignment problem in its first phase, followed by a complex truck loading algorithm to validate the assignment solution in the second phase. This enables the identification of optimal solutions and adaptability to diverse use cases. This approach is motivated by the ROADEF/EURO challenge 2022 and is awarded with the scientific prize of the challenge. We demonstrate superior performance on selected instances, showcasing the potential for significant cost reduction in Renault’s supply chains.

A time-driven simulation–optimization framework for the dynamic heterogeneous order-courier assignment problem for instant deliveries

In recent years, instant delivery services have become very popular for transporting meals to urban areas, with an extensive range of products now available to order. The platforms that offer these services rely on crowdsourced couriers who utilize their personal vehicles, resulting in heterogeneous fleets. Furthermore, the competition among companies to retain both customers and couriers is very intense, which underscores the importance of developing superior decision support systems. These systems must generate real-time assignments that meet the expectations of service providers, customers, and couriers. In this study, we designed a time-driven simulation–optimization framework that addresses the dynamic heterogeneous order-courier assignment problem and incorporates order-vehicle restrictions. The framework efficiently manages real-time order arrivals, courier movements, and positional updates while considering dynamic factors such as traffic congestion and regional speed limits for various vehicle types. Extensive testing using literature instances demonstrated the framework’s ability to satisfactorily address the defined problem. Additionally, the time-driven simulation–optimization framework was applied to a realistic case study, resulting in an approximately 4.5% reduction in the total delivery times (from the submission of the order until the delivery to the client) for all orders when compared to the original assignment.

Toward green container liner shipping: joint optimization of heterogeneous fleet deployment, speed optimization, and fuel bunkering

AbstractContainer liner shipping companies, under the international shipping carbon reduction indicators proposed by the International Maritime Organization, must transform two key aspects: technology and operations. This paper defines a green liner shipping problem (GLSP) that integrates the deployment of a heterogeneous fleet, speed determination, and fuel bunkering. The objective is to achieve low‐carbon operations in liner shipping, taking into consideration the diversification of power systems, the use of alternative fuels in ships, and the continuous improvement of alternative fuel bunkering systems. For this purpose, we present a bi‐objective mixed integer nonlinear programming model and develop two methodologies: an epsilon‐constraint approach and a heuristic‐based multi‐objective genetic algorithm. We validate the effectiveness of our model and methods through a case study involving container ships of various sizes deployed on intra‐Asian short sea routes by SITC International Holdings Co., Ltd. The experimental results highlight the crucial role of dual‐fuel (DF) ships in the pursuit of low‐carbon strategies by liner companies, with liquefied natural gas and ammonia DF ships being the most widely used. Additionally, fuel cell (FC) ships, particularly those powered by ammonia and hydrogen, demonstrate significant carbon reduction potential. Furthermore, ships with larger container capacities have a greater cost advantage. For the GLSP, speed determination is an auxiliary decision, and the lowest speed is not necessarily the optimal choice. Decision‐makers must carefully balance competing economic and carbon emission reduction objectives, as deploying more alternative fuel ships may increase fuel bunkering and fuel consumption, resulting in a higher total operating cost.

Comprehensive Task Optimization Architecture for Urban UAV-Based Intelligent Transportation System

This paper tackles the problem of resource sharing and dynamic task assignment in a task scheduling architecture designed to enable a persistent, safe, and energy-efficient Intelligent Transportation System (ITS) based on multi-rotor Unmanned Aerial Vehicles (UAVs). The addressed task allocation problem consists of heterogenous pick-up and delivery tasks with time deadline constraints to be allocated to a heterogenous fleet of UAVs in an urban operational area. The proposed architecture is distributed among the UAVs and inspired by market-based allocation algorithms. By exploiting a multi-auctioneer behavior for allocating both delivery tasks and re-charge tasks, the fleet of UAVs is able to (i) self-balance the utilization of each drone, (ii) assign dynamic tasks with high priority within each round of the allocation process, (iii) minimize the estimated energy consumption related to the completion of the task set, and (iv) minimize the impact of re-charge tasks on the delivery process. A risk-aware path planner sampling a 2D risk map of the operational area is included in the allocation architecture to demonstrate the feasibility of deployment in urban environments. Thanks to the message exchange redundancy, the proposed multi-auctioneer architecture features improved robustness with respect to lossy communication scenarios. Simulation results based on Monte Carlo campaigns corroborate the validity of the approach.

Vehicle routing in precooling logistics with dynamic temperature-dependent product quality decay

This study focuses on precooling operations for post-harvest fruits and vegetables in smallholder countries, aiming to provide an effective way to reduce product losses in the early stage of food supply chains. In this study, we consider the traditional centralized precooling and emerging mobile precooling to fulfill a series of small-scale and scattered precooling requests, with the goal of minimizing the total operating cost while guaranteeing the product quality of farmers. The resulting problem is a variant of the classic heterogeneous fleet vehicle routing problems with time windows, with the additional consideration of heterogeneous service and temperature-dependent product quality decay. The vehicle routing model is formulated by integrating product quality as a constraint in which a dedicated function is developed to capture the quality dynamics under changing temperatures. We design an improved adaptive large neighborhood search method to solve this problem by identifying a strategy that is able to deal with the interactions among decisions. Experiment results quantify the advantages of managing product quality in the early stage of supply chains for perishable products and provide management insights on conducting quality-based precooling services. Numerical experiments based on small-scale instances of the studied problem as well as large-scale benchmark instances verify the effectiveness and efficiency of the proposed algorithm by comparing it with CPLEX and three state-of-the-art algorithms.

Optimizing the organization of the first mile in agri-food supply chains with a heterogeneous fleet using a mixed-integer linear model

Consumers are increasingly demanding high-quality food, which presents significant challenges for agricultural supply chains. While the majority of research in the agri-food sector has concentrated on optimizing logistics costs and meeting demand by focusing on minimizing the last mile, the complexity of the first mile in the agricultural supply chain has been less explored. Farmers must efficiently manage the harvesting process and the transportation of harvested produce to consolidation centers to ensure the delivery of high-quality products. This paper addresses this research gap by introducing a mixed-integer programming model that leverages vehicle routing problem concepts to optimize the logistics processes involved in transporting harvested products from various fields to a central depot. The primary objective is to minimize total logistics costs associated with visiting different fields during a pick-up round using multiple vehicles. The model has been applied to a case study involving an agricultural cooperative in Greece as part of the European BBTWINS project, which aims to enhance agri-food value chain digitalization for improved resource efficiency. The results demonstrate that organizing the first mile of the agri-food supply chain with a cooled vehicle for pick-up rounds can reduce logistics costs by up to 40% compared to the current practices.

Techno-economic analysis of mixed battery and fuel cell electric bus fleets: A case study

Electric city buses are promising to reduce traffic-related emissions in city centres as their drive train emits zero local emissions in an urban context. However, battery electric buses (BEBs) have limited driving range and long charging times. Although this can be managed, as city buses operate on predetermined routes, fuel cell electric buses (FCEBs) can meet more operational requirements in terms of range and charging. Thus, many bus network operators want to design a mixed full electric bus network with BEBs and FCEBs, which involves several complex and interdependent planning tasks. We extend an existing planning model to accommodate the planning of BEBs and FCEBs with their respective charging and fuelling infrastructure, and apply it to a real-world case study. Our results indicate that a heterogeneous BEB fleet with a mix of depot and opportunity charging results in lower total costs than a depot charging concept or a homogeneous FCEB fleet. We additionally find that a heterogeneous fleet including FCEBs and BEBs with a mix of charging concepts can be beneficial under specific circumstances. More specifically, the results indicate, that FCEB are a viable technology to supplement full electric bus fleets as soon as the costs for FCEB fall below 625,000€or the costs for hydrogen fall below 4.33 €/kg H2. Interestingly, rising energy prices would not increase the utilization of FCEBs, but rather influence the choice of BEB-types.

Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels

Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels

Integrated planning approach for fleet sizing and fleet management of freight railcars

AbstractDespite the general support for rail as sustainable and efficient transport mode, its share on modal split remains rather low. One of the reasons for this is the low flexibility and adaptability of rail system to changes in, e.g., demand due to the complex multi-stage planning processes that are partly done manually. In our paper we focus on the fleet planning process for freight railcars and we propose an integrated planning approach consisting of two parts. Firstly, a fleet sizing optimization model is applied to obtain the optimal assignment of railcars to customers’ orders. Within this model, we consider a heterogeneous fleet and take into account substitution between clusters and customers’ preferences. The optimal fleet size is computed on a monthly basis for a planning horizon of multiple years, accounting also for railcar flows between months and years. Secondly, a fleet management model in form of knowledge-based decision support system is applied to help the planner to make changes in the fleet mix by investing into or leasing new railcars, performing revisions and decommissioning of old or unutilized railcars. As also illustrated in the designed real-world case study, the integrated planning approach is able to provide the planner with an overview of possible actions including their direct impact on the fleet mix for a mid-term planning horizon.

A practical vehicle routing problem in small and medium cities for fuel consumption minimization

Today, reducing fossil fuel consumption in the transport sector is one of the important requirements to preserve the ecological environment. In this paper, we investigated a logistics problem in small and medium cities. We proposes the time-dependent vehicle routing problem model in small and medium cities considering heterogeneous fleets, time windows, multi-trip, time dependency, and road network. We conducted a numerical analysis on fuel consumption minimizing path selection between two customer nodes and found that the path selection is independent of the payload in most cases. The model is formulated as a mathematical integer linear programming model, and small problems are solved using a commercial optimization solver. For large-scale instances, we proposed a heuristic algorithm based on the variable neighborhood search and evaluated its performance. The proposed algorithm can decrease fuel consumption by 25 % compared to manual routing and scheduling. Furthermore, for provide useful managerial insights, sensitivity analyses were performed considering different vehicle capacities.

Cold chain distribution network design with heterogeneous fleet under carbon reduction policy application effect

ABSTRACT To integrate cold chain distribution network design problem with heterogeneous fleet, a multi-objective optimisation model is proposed to simultaneously optimise distribution routes, the quantity of internal combustion and electric refrigerated trucks (ERTs), and the number and location of distribution centres and charging stations with time window constraints, where the cold chain distribution operating cost and the customer dissatisfaction cost are minimised. A hybrid solution methodology, combining a multi-objective artificial fish swarm algorithm with a label-based optimisation algorithm, is presented to address this model. Extensive computational experiments verify the effectiveness of the proposed method. Moreover, a sensitivity analysis, focusing on the range of ERTs, the purchase subsidy for ERTs, the carbon tax and the carbon emission quota, informs the development of diverse carbon reduction policies. A comparative analysis of the implementation effect of carbon reduction policies can provide optimisation decision support for promoting sustainability in the electrification of cold chain distribution.

A Sectoral Application for Green Vehicle Routing Problem Optimization with Capacity Constrained and Heterogeneous Fleet

A Sectoral Application for Green Vehicle Routing Problem Optimization with Capacity Constrained and Heterogeneous Fleet

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.

Multi-objective location-routing model and algorithm study of material reserve bases for large-scale railway engineering construction projects

Material supply is an important support for engineering construction and an important factor affecting the progress and quality of engineering construction. A multi-objective mixed-integer nonlinear programming model is proposed for the location routing problem of the material reserve base of large-scale railway engineering construction projects, considering realistic factors like the construction period, the cycle of the material reserve, the variety of materials, the heterogeneous fleet, and demand splitting. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA- II) is developed for solving this model. This paper optimises obtaining the initial population based on the linear feature of railway engineering, improves the fitness function, and designs a two-stage crossover operator. In addition, the algorithm is compared with the augmented ϵ-constraint method with the help of a practical example. Three metrics are used to assess the performance of the algorithm's outputs, and two metrics are used to assess the similarity of the Pareto fronts obtained by the two algorithms. The results show that the proposed algorithm performs better in terms of ‘quantity’ and ‘spacing’, that the Pareto solutions obtained are accurate, and that the speed of solution is almost 10 times that of the augmented ϵ-constraint (AUGMECON) method.

An exact method for vehicle routing problem with backhaul discounts in urban express delivery network

The surge in e-commerce has led to an increased demand for urban express services, requiring the strategic development of delivery networks that are both efficient and cost-effective. This study addresses a practical vehicle routing problem (VRP) in an urban express delivery network to minimize transportation costs. Specifically, it considers the implementation of backhaul discounts, a factor disregarded in the existing literature. This VRP is further complicated by various realistic constraints, including pickup and delivery, time windows, multiple trips, heterogeneous fleets, and docking capacity limitations, which make most general VRP solvers inapplicable. This study proposes a trip-based formulation to overcome this challenge and develop a tailored branch-and-price algorithm. Feasible trips are classified into four types to simplify the computation of backhaul discounts, thereby enhancing solution efficiency. Validation with real-world data from SF Express substantiates the efficacy of our method and yields insights for sustainable city logistics management. Moreover, our simplified column generation algorithm exhibits competitive performance, achieving optimal solutions expeditiously for the tested instances.