Fleet Mix Problem Research Articles

A holistic approach to introducing a light electric freight vehicle (LEFV) system in a historic urban environment: The case of Quito

In this paper we propose a comprehensive approach for introducing a first/last mile system based on Light Electric Freight Vehicles (LEFVs) in the historical centre of Quito (Ecuador). The approach includes four crucial steps for successful launching and establishment of a LEFVs system. The first step considers organizational aspects by proposing a number of alternative cooperative business models. In the second step, the LEFVs fleet mix problem is defined as a Multicriteria Decision Making Problem (MCDM) and solved by the Analytic Network Process (ANP). The third step includes the problem of optimal micro hub location as well as the problem of optimal routing of LEFVs. The micro hub location problem is modelled as a capacitated p-median problem and solved by an exact solution algorithm. The problem of optimal LEFVs routing is defined as the capacitated pickup and delivery with time windows addressed by a web-based optimization tool. The fourth step includes an assessment of the existing policy framework and proposing a set of additional legal instruments for facilitating the LEFVs market uptake. Based on the proposed four-step approach, the first/last mile system is currently being implemented in the historical centre of Quito. The initial results appear promising regarding the success of the new LEFVs first/last mile system.

Service Operation Vessels Fleet Size and Mix Location Routing for the Maintenance of an Offshore Floating Wind Farm

Mixed-integer linear programming is adopted to translate the routing of service operation vessels that support the logistic aspects of the maintenance of offshore floating wind farms into mathematical language. The models attempt to help the decision-makers by providing quantified tools to screen out the optimal planning for preventive maintenance. The models search for the optimal offshore base location, vessel’s routing per day, vessel’s capacity, and vessel fleet composition that minimize the total fixed and variable infrastructure cost. The integration of the vehicle fleet size and mix problem, facility location–allocation problem, and vehicle-routing problem with time window advances the state of the art. A realistic case study is shown, and the results and discussions demonstrated that the practical insights of the solutions, as well as the identification of the route patterns through a navigation route table, may improve the decision planning of preventive maintenance.

Developing the optimal vessel fleet size and mix model to minimize the transportation cost of offshore wind farms

It is crucial for the present generation of offshore wind farms to develop ways to reduce their operation and maintenance expenses to sell electricity at competitive market pricing. A wind farm located offshore will typically consist of a huge number of turbines, each of which must be maintained regularly. It is vital to make maintenance plans that reduce production losses and downtime. Also, it is essential to effectively use expensive resources such as service vessels and technician hours. This article starts with an overview of the vessel fleet size and mix problem that arises while maintaining offshore wind farms using a fleet of maintenance vessels. The main emphasize of this work is to establish the best assignments of vessels to the routes and technicians on the vessels in terms of cost. In this paper an integer programming model is formulated taking into consideration the relevant characteristic peculiarities and limits encountered in the vessel management of offshore wind farm. An algorithm is developed that has been implemented using a commercial solver. A case study is done to show the computational and dimensional perspectives of the problems in real-life settings. The findings give not only the optimal cost but also the comprehensive arrangements, both of which are directly applicable to the process of planning for maintenance vessel fleet size and mix selection.

A military fleet mix problem for high-valued defense assets: A simulation-based optimization approach

The military fleet mix problem is traditionally used when several modernization operations are required to transition a force from an outdated fleet to a more modern one over a planning period. The main objective of such a transition is to enhance the capability of a military fleet to deploy its forces for missions at any moment by continually improving its operational readiness with minimum cost and time. The complexity of the problem is significantly increased with the increase in the number of assets to be modernized, sub-divisions (Brigades) and the length of the planning period. In this paper, to effectively address the fleet mix problem in the military context, a simulation–optimization approach is introduced with the aim of providing decision-makers with a fleet modernization schedule that enables the military to achieve maximum deployment of its available assets/forces while minimizing the total cost and full deployment time. The proposed approach uses a combination of (1) an enhanced genetic algorithm (GA) to generate initial solutions, explore and exploit the generated solutions till achieving the optimal one, and (2) a capability simulation model to evaluate each solution and determine its quality. Furthermore, the proposed GA comprises several enhanced components to further improve its performance and hence find the optimal solution in lesser computational time. (a) A heuristic repairing method, to provide feasible solutions through repairing a certain number of solutions from the initial population which can significantly guide GA search towards (near-)optimal solutions, (b) a new solution representation, that better represents the fleet schedule decision variables and characteristics, (c) improved designs of crossover and mutations, that can help GA to reach optimum solutions in a faster manner, and (d) new sorting and selection functions, that use many objectives values to allow the better solutions to survive through generations, are all examples of such enhanced GA’s components. The proposed approach has been validated by solving a case study that addresses recent fleet modernization strategies of the Australian Army to recapitalize its forces over the next decade and in a continual process. Two scenarios of the case study with different scales have been used. The experimental results show that the proposed approach can effectively provide efficient modernization fleet schedules for both scenarios which allow the maximum deployment with the minimum cost and time. Compared with traditional GA and Differential Evolution (DE), the proposed approach yields 2.37% and 7.17% more deployability, and 99.59% and 98.81% less total cost than DE and GA, respectively. A surrogate model is also presented to replace the computationally expensive simulation model for fitness evaluation. The results show that the surrogate model can significantly reduce the computational time but its accuracy for expecting the optimal objectives still need more enhancements.

A Military Fleet Mix Problem For High-Valued Defense Assets: A Simulation-Based Optimization Approach

A Military Fleet Mix Problem For High-Valued Defense Assets: A Simulation-Based Optimization Approach

A dual-level stochastic fleet size and mix problem for offshore wind farm maintenance operations

This paper studies the strategic problem of finding a cost optimal fleet of vessels to support maintenance operations at offshore wind farms. A dual-level stochastic model is formulated, taking into account both long-term strategic uncertainty and short-term operational uncertainty in a single optimization model. The model supports wind farm owners in making strategic decisions regarding the number, placement, charter length, and types of vessels to charter, to meet maintenance demands throughout the lifetime of a wind farm. To evaluate the quality of strategic fleet size and mix decisions, the model also considers the operational decisions of how to utilize the fleet to support maintenance operations. The model accounts for strategic uncertainties that have not been considered in previously developed optimization models for offshore wind, such as uncertainty related to long-term trends in electricity prices and subsidy levels, the stepwise development of wind farms, and technology development in the vessel industry. To solve the proposed stochastic programming model we have developed an ad hoc integer L-shaped method, with customized optimality cuts. The computational experiments show that the proposed method outperforms solving the deterministic equivalent using a commercial MIP solver.

Comparing Implications of ‘Robustness’ and ‘Optimality’ for Decision Support under Uncertainty

AbstractConventional simulation‐optimisation approach in decision support under uncertainty aims to find optimal decisions which can meet decision objective(s) under reference scenarios with well‐characterised uncertainty. However, futures often emerge with unexpected circumstances which cannot be predicted in our pre‐specified reference scenarios, and their uncertainty cannot be fully characterised a priori. This article uses robust optimisation based on simulation models as an alternative approach to address such uncertainties of decision support. To show how the two approaches work and how better robust optimisation can be, we formulate a fleet mix problem under uncertainty and implement it in two experiments to compare the results. We conclude that robust optimisation could lead to decisions with probably lower performance than conventional optimisation at imagined future scenarios. However, the advantage of robust optimisation is that the results have better performance in overall and are more reliable over a wide variety of scenarios in the future.

A Fleet Efficiency Factor for fleet size and mix problems using particle swarm optimisation

ABSTRACTFinding the optimal fleet composition under uncertainties is crucial for the economic success of a business. This paper presents the Fleet Efficiency Factor, a decision support tool for fleet size and mix problems and fleet composition problems. The method is based on a particle swarm optimisation algorithm combined with a stochastic model to include uncertainties into the decision-making progress. This combination allows selecting the best option out of a pool of available vessels, vehicles and aircrafts. Additionally, the FEF is based on the classical ship merit factor and thus capable of comparing different fleet compositions according to their economic efficiency, by describing the efficiency in a simple factor. A case study for the supply of an offshore platform in the high North is conducted. The approach proved to be flexible and applicable to different strategical and tactical planning problems in maritime transportation.

Bulk ship scheduling in industrial shipping with stochastic backhaul canvassing demand

This paper studies a ship scheduling problem for an industrial corporation that manages a fleet of bulk ships under stochastic environments. The considered problem is an integration of three interconnected sub-problems from different planning levels: the strategic fleet sizing and mix problem, the tactical voyage planning problem, and the operational stochastic backhaul cargo canvassing problem. To obtain the optimal solution of the problem, this paper provides a two-step algorithmic scheme. In the first step, the stochastic backhaul cargo canvassing problem is solved by a dynamic programming (DP) algorithm, leading to optimal canvassing strategies for all feasible voyages of all ships. In the second step, a mixed-integer programming (MIP) model that jointly solves the fleet sizing and mix problem and the voyage planning problem is formulated using the results from the first step. To efficiently solve the proposed MIP model, this paper develops a tailored Benders decomposition method. Finally, extensive numerical experiments are conducted to demonstrate the applicability and efficiency of the proposed models and solution methods for practical instances.

Electric bus fleet size and mix problem with optimization of charging infrastructure

Battery electric buses are seen as a well-suited technology for the electrification of road-based public transport. However, the transition process from conventional diesel to electric buses faces major hurdles caused by range limitations and required charging times of battery buses. This work addresses these constraints and provides a methodology for the cost-optimized planning of depot charging battery bus fleets and their corresponding charging infrastructure. The defined problem covers the scheduling of battery buses, the fleet composition, and the optimization of charging infrastructure in a joint process. Vehicle schedule adjustments are monetized and evaluated together with the investment and operational costs of the bus system. The resulting total cost of ownership enables a comparison of technical alternatives on a system level, which makes this approach especially promising for feasibility studies comprising a wide range of technical concepts. Two scenarios of European cities are analyzed and discussed in a case study, revealing that the cost structure is influenced significantly by the considered bus type and its technical specifications. For example, the total energy consumption of the considered lightweight bus is up to 32% lower than the total consumption of the high range bus, although the deadheading mileage increases. However, the total costs of ownership for operating both bus types are relatively close, due to the increased fleet size and driver expenses required for the lightweight bus system. The case study furthermore reveals that a mixed fleet of different bus types could be advantageous depending on the operational characteristics of the bus route.

Model Penentuan Jumlah Kapal dan Komposisinya untuk Short Sea Shipping Pulau Jawa

This research aims to determine the amount and mixture composition of vessels in short sea shipping (SSS) operation in Java. SSS in Java is proposed to mitigate the surface transportation problem and move freight off the overcrowded North-Coast highways and rail systems onto the waterways. A mathematical model based on non-linear integer programming was developed to calculate the amount and the composition mix of vessels required for the proposed system. The model was solved by Lingo software and the computational results reveal that the proposed system would require daily shipment using 1 unit of type B vessel and 1 unit of type C vessel. The calculation results also show that the SSS in Java would require 6 vessels to operate. Overall, the model and the obtained solutions in this paper provide an alternative to raise awareness of short sea shipping’s potential with the government, logistic companies, and executive policymakers. Finally, this paper also contribute to research of maritime fleet size and mix problems.

A stochastic fleet size and mix model for maintenance operations at offshore wind farms

A fleet of vessels and helicopters is needed to support maintenance operations at offshore wind farms. The cost of this fleet constitutes a major part of the total maintenance costs, hence keeping an optimal or near-optimal fleet is essential to reduce the cost of energy. In this paper we study the vessel fleet size and mix problem that arises for the maintenance operations at offshore wind farms, and propose a stochastic three-stage programming model. The stochastic model considers uncertainty in vessel spot rates, weather conditions, electricity prices and failures to the system. The model is tested on realistic-sized problem instances, and the results show that it is valuable to consider uncertainty and that the proposed model can be used to solve instances of a realistic size.

Evaluating the Flexibility of Military Air Mobility Fleets

The ability of an organization to perform some critical military tasks in a timely manner may depend on the availability of a sufficient number of appropriate vehicles. Therefore, the decision of which is the best military fleet-mix for a given set of requirements should take into consideration, in addition to cost, the ability of the fleet to perform tasks when some of its vehicles are unavailable. In this paper, a measure of the flexibility of military air mobility fleets is presented that evaluates their ability to perform tasks in a timely manner taking into account the possibility that some aircraft in the fleet may be unavailable at any given time. This measure computes the number of aircraft that must be unavailable in order to render a fleet incapable of performing each task in a timely manner. The utility of the flexibility measure is demonstrated by using it as an objective in a multiobjective optimization framework to compute nondominated fleets with respect to cost and flexibility. An artificial data set that is representative of real military air mobility data is used to illustrate how the new flexibility measure may be used to aid decision makers with their fleet mix problems.

Implicit depot assignments and rotations in vehicle routing heuristics

Vehicle routing variants with multiple depots and mixed fleet present intricate combinatorial aspects related to sequencing choices, vehicle type choices, depot choices, and depots positioning. This paper introduces a dynamic programming methodology for efficiently evaluating compound neighborhoods combining sequence-based moves with an optimal choice of vehicle and depot, and an optimal determination of the first customer to be visited in the route, called rotation. The assignment choices, making the richness of the problem, are thus no more addressed in the solution structure, but implicitly determined during each move evaluation. Two meta-heuristics relying on these concepts, an iterated local search and a hybrid genetic algorithm, are presented. Extensive computational experiments demonstrate the remarkable performance of these methods on classic benchmark instances for multi-depot vehicle routing problems with and without fleet mix, as well as the notable contribution of the implicit depot choice and positioning methods to the search performance. New state-of-the-art results are obtained for multi-depot vehicle routing problems (MDVRP), and multi-depot vehicle fleet mix problems (MDVFMP) with unconstrained fleet size. The proposed concepts are fairly general, and widely applicable to many other vehicle routing variants.

A survey on maritime fleet size and mix problems

This paper presents a literature survey on the fleet size and mix problem in maritime transportation. Fluctuations in the shipping market and frequent mismatches between fleet capacities and demands highlight the relevance of the problem and call for more accurate decision support. After analyzing the available scientific literature on the problem and its variants and extensions, we summarize the state of the art and highlight the main contributions of past research. Furthermore, by identifying important real life aspects of the problem which past research has failed to capture, we uncover the main areas where more research will be needed.

Military Fleet Mix Computation and Analysis [Application Notes

A major financial expense for any military is the acquisition, operation, and maintenance of vehicles such as ships [1] and aircraft [2]. For example, the U.S. Air Force estimates that the acquisition of the F-35 fighter aircraft will cost $156 million each [3], hence even slight improvements in fleet efficiency and/or effectiveness can save governments large amounts of money or, using the same budget, can buy better equipment. Such high costs have driven the development and application of optimization and simulation methodologies to problems of military fleet mix computation and analysis. The complexity of military fleet mix problems, due in large part to the uncertainty, multi-objectivity, and temporal criticality of military missions, has resulted in the increased use of computational intelligence (CI) methods for solving them.

A hybrid evolutionary local search with depth first search split procedure for the heterogeneous vehicle routing problems

Routing Problems have been deeply studied over the last decades. Split procedures have proved their efficiency for those problems, especially within global optimization frameworks. The purpose is to build a feasible routing solution by splitting a giant tour into trips. This is done by computing a shortest path on an auxiliary graph built from the giant tour. One of the latest advances consists in handling extra resource constraints through the generation of labels on the nodes of the auxiliary graph. Lately, the development of a new generic split family based on a Depth First Search (DFS) approach during label generation has highlighted the efficiency of this new method for the routing problems, through extensive numerical evaluations on the location-routing problem. In this paper, we present a hybrid Evolutionary Local Search (hybrid ELS) for non-homogeneous fleet Vehicle Routing Problems (VRP) based on the application of split strategies. Experiments show our method is able to handle all known benchmarks, from Vehicle Fleet Mix Problems to Heterogeneous Fleet VRP (HVRP). We also propose a set of new realistic HVRP instances from 50 to more than 250 nodes coming from French counties. It relies on real distances in kilometers between towns. Since many classical HVRP instance sets are solved to optimality, this new set of instances could allow a fair comparative study of methods. The DFS split strategy shows its efficiency and attests the fact that it can be a promising line of research for routing problems including numerous additional constraints.

A decision support methodology for strategic planning in maritime transportation

This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company.

Theoretical and algorithmic results for a class of hierarchical fleet mix problems

In this paper a workforce model is studied from both a theoretical and an algorithmic point of view. In the considered hierarchical model workforce units can be substituted by higher qualified ones; external workforce can also be hired to cover low qualified jobs. An exact recursive solution algorithm is proposed to solve the problems and its efficiency is improved by means of cut conditions and discrete convexity properties. Finally, the results of a computational test are provided.

Two memetic algorithms for heterogeneous fleet vehicle routing problems

The vehicle routing problem (VRP) plays an important role in the distribution step of supply chains. From a depot with identical vehicles of limited capacity, it consists in determining a set of vehicle trips of minimum total length, to satisfy the demands of a set of customers. In general, the number of vehicles used is a decision variable. The heterogeneous fleet VRP (HFVRP or HVRP) is a natural generalization with several vehicle types, each type being defined by a capacity, a fixed cost, a cost per distance unit and a number of vehicles available. The vehicle fleet mix problem (VFMP) is a variant with an unlimited number of vehicles per type. This paper presents two memetic algorithms (genetic algorithms hybridized with a local search) able to solve both the VFMP and the HVRP. They are based on chromosomes encoded as giant tours, without trip delimiters, and on an optimal evaluation procedure which splits these tours into feasible trips and assigns vehicles to them. The second algorithm uses a distance measure in solution space to diversify the search. Numerical tests on standard VFMP and HFVRP instances show that the two methods, especially the one with distance measure, compete with published metaheuristics and improve several best-known solutions.