Designing routes to minimize fleet operating costs

A route-planner must try to schedule the delivaries by a fleet of vehicles such that customer requirements are met and management objectives are satisfied. In most cases, the number of feasible arrangements is legion, and calculations relating to individual vehicle loads, mileages, delivery times, etc. are tedious, allowing only a small fraction of possible route plans to be established and compared. The problem presents an ideal opportunity for computer application, not least to ensure that solutions are timely and error free.Several algorithms have been developed to improve the quality of vehicle routes, but in practice only those that rely on simple selection rules have found widespread acceptance, due to the innate complexity of the calculations that follow from a more rigorous approach and to the great variety of customer, vehicle, and operational characteristics that distinguish transport systems and which must be accomodated.The method presented here is based upon the well-known ‘savings’ criterion, but avoids many of its deficiencies by employing a random selection mode and producing (efficiently) a large sample of schedules from which to choose the most suitable. In particular, this allows greater flexibility in defining management objectives, and has led to substantial reductions in both fleet sizes and distances travelled, compared to published results, for a set of nine test cases each involving more than 200 customer locations.     

Optimal empty vehicle repositioning and fleet-sizing for two-depot service systems

This paper considers the problem of determining optimal control policies for empty vehicle repositioning and fleet-sizing in a two-depot service system with uncertainties in loaded vehicle arrival at depots and repositioning times for empty vehicles in the fleet. The objective is to minimise the sum of the costs incurred by vehicle maintenance, empty vehicle repositioning and vehicle leasing. A novel integrated model is presented. The optimal empty repositioning policy for a particular fleet size is shown to be of the threshold control type. The explicit form of the cost function under such threshold controls is obtained. The optimal threshold values and fleet-size are then derived. Numerical examples are given to demonstrate the results.     

A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

An Iteration Method for Reliability Evaluation of a Fleet System

The fleet system considered here consists of n identical units (members) which are operated together under an operational program which specifies the schedule of the operation of the system and maintenance performed on the units in the system. Introduction of this operational program makes the reliability evaluation of the fleet system more realistic but complicated. A conventional Markov approach is effective only when a fleet system consists of a few units. This paper presents a new method for the reliability evaluation of a fleet system. This method reduces the problem of the reliability evaluation of the system to that of each unit by introducing a ‘utilization factor’. Therefore, the size of the problem is irrelevant to the number of the units in the system. An iteration method is used to obtain the unique solution of the problem.     

Vehicle Scheduling with Timed and Connected Calls: A Case Study

A manual method was developed for scheduling the vehicle fleet of a contract transport undertaking. The main requirements were observance of time limits on individual calls and the ability to allocate pairs or groups of related calls to the same vehicle. These objectives were achieved by introducing an initial allocation of calls to vehicles prior to sequential routing of the calls. The allocation was based on a model relating work density (calls per unit area) to vehicle loading (calls per unit of vehicle time), and on fact-finding research on the main parameters of calling time, travelling speed and distance. This relationship was embodied in a visual scheduling aid for use by the route planners. Implementation was successful and resulted in about 15 per cent of vehicle time being made available for additional revenue-earning work without increase in fleet size. When utilized this represented an effective saving in operating costs of about 12 per cent.     

Vehicle routing and scheduling with time-varying data: A case study

A heuristic algorithm is described for vehicle routing and scheduling problems to minimise the total travel time, where the time required for a vehicle to travel along any road in the network varies according to the time of travel. The variation is caused by congestion that is typically greatest during morning and evening rush hours. The algorithm is used to schedule a fleet of delivery vehicles operating in the South West of the United Kingdom for a sample of days. The results demonstrate how conventional methods that do not take time-varying speeds into account when planning, except for an overall contingency allowance, may still lead to some routes taking too long. The results are analysed to show that in the case study using the proposed approach can lead to savings in CO₂ emissions of about 7%.     

Joint optimization of fleet size and maintenance capacity in a fork-join cyclical transportation system

This article presents an asset management-oriented multi-criteria methodology for the joint estimation of a mobile equipment fleet size, and the maintenance capacity to be allocated in a productive system. Using a business-centred life-cycle perspective, we propose an integrated analytical model and evaluate it using global cost rate, availability and throughput as performance indicators. The global cost components include: (i) opportunity costs associated with lost production, (ii) vehicle idle time costs, and (iii) maintenance resources idle time costs. This multi-criteria approach allows a balanced scorecard to be built that identifies the main trade-offs in the system. The methodology uses an improved closed network queueing model approach to describe the production and maintenance areas. We test the proposed methodology using an underground mining operation case study. The decision variables are the size of a load-haul-dump fleet and specialized maintenance crew levels. Our model achieves savings of 20.6% in global cost terms with respect to a benchmark case. We also optimize the system to achieve desired targets of vehicle availability and system throughput (based on system utilization). The results show increments of 7.1% in vehicle availability and 13.5% in system throughput with respect to baseline case. For the case studied, these criteria also have a maximum, which allows for further improvement if desired. The results also show the importance of using balanced performance measures in the decision process. A multi-criteria optimization was also performed, showing the Pareto front of considered indicators. We discuss the trade-offs among different criteria, and the implications in finding balanced solutions. The proposed analytical approach is easy to implement and requires low computational effort. It also allows for an easy re-evaluation of resources when the business cycle changes and relevant exogenous factors vary.     

Synchronized routing of seasonal products through a production/distribution network

This paper presents a multi-period vehicle routing problem for a large-scale production and distribution network. The vehicles must be routed in such a way as to minimize travel and inventory costs over a multi-period horizon, while also taking retailer demands and the availability of products at a central production facility into account. The network is composed of one distribution center and hundreds of retailers. Each retailer has its demand schedule representing the total number of units of a given product that should have been received on a given day. Many high value products are distributed. Product availability is determined by the production facility, whose production schedule determines how many units of each product must be available on a given day. To distribute these products, the routes of a heterogeneous fleet must be determined for a multiple period horizon. The objective of our research is to minimize the cost of distributing products to the retailers and the cost of maintaining inventory at the facility. In addition to considering product availability, the routing schedule must respect many constraints, such as capacity restrictions on the routes and the possibility of multiple vehicle trips over the time horizon. In the situation studied, no more than 20 product units could be carried by a single vehicle, which generally limited the number of retailers that could be supplied to one or two per route. This article proposes a mathematical formulation, as well as some heuristics, for solving this single-retailer-route vehicle routing problem. Extensions are then proposed to deal with the multiple-retailer-route situation.     

Operational aircraft maintenance routing problem with remaining time consideration

The aircraft maintenance routing problem is one of the most studied problems in the airline industry. Most of the studies focus on finding a unique rotation that will be repeated by each aircraft in the fleet with a certain lag. In practice, using a single rotation for the entire fleet is not applicable due to stochasticity and operational considerations in the airline industry. In this study, our aim is to develop a fast responsive methodology which provides maintenance feasible routes for each aircraft in the fleet over a weekly planning horizon with the objective of maximizing utilization of the total remaining flying time of fleet. For this purpose, we formulate an integer linear programming (ILP) model by modifying the connection network representation. The proposed model is solved by using branch-and-bound under different priority settings for variables to branch on. A heuristic method based on compressed annealing is applied to the same problem and a comparison of exact and heuristic methods are provided. The model and the heuristic method are extended to incorporate maintenance capacity constraints. Additionally, a rolling horizon based procedure is proposed to update the existing routes when some of the maintenance decisions are already fixed.     

Improved vehicle scheduling in public transport through systematic changes in the time-table

Vehicle scheduling for a fixed time-table is easy to formulate and solve as a minimal-cost-flow problem. Normally, however, there is considerable flexibility in the time-table. We propose here a method for exploiting this flexibility in order to improve the vehicle scheduling.A given set of trips must be assigned to a fleet of identical vehicles, starting from a common garage. Each trip is characterized by initial stop, final stop, duration, earliest departure time, and latest departure time.The problem is to decide which vehicle should be assigned to each individual trip and when the trip should start, so that a generalized cost is minimized.The minimum-cost-flow problem is first solved for the ‘kernels’ of every trip in order to make clear when the critical time-periods occur and obtain a lower bound for the solution. The kernel is defined as a trip that starts at the latest possible departure time and finishes at the earliest possible arriving time.The departure time for each trip is then chosen, thereby increasing the chances of obtaining a good schedule. The minimum-cost-flow problem is then solved for this fixed time-table.Finally, the departure times for each vehicle are adjusted (blocked) so that each vehicle (and driver) is efficiently used. This method is used as an integral part of the Volvo Traffic Planning Package.     

A perturbation metaheuristic for the vehicle routing problem with private fleet and common carriers

The purpose of this article is to propose a perturbation metaheuristic for the vehicle routing problem with private fleet and common carrier (VRPPC). This problem consists of serving all customers in such a way that (1) each customer is served exactly once either by a private fleet vehicle or by a common carrier vehicle, (2) all routes associated with the private fleet start and end at the depot, (3) each private fleet vehicle performs only one route, (4) the total demand of any route does not exceed the capacity of the vehicle assigned to it, and (5) the total cost is minimized. This article describes a new metaheuristic for the VRPPC, which uses a perturbation procedure in the construction and improvement phases and also performs exchanges between the sets of customers served by the private fleet and the common carrier. Extensive computational results show the superiority of the proposed metaheuristic over previous methods.     

A benders decomposition approach for an integrated airline schedule design and fleet assignment problem with flight retiming, schedule balance, and demand recapture

The airline’s ability to offer flight schedules that provide service to passengers at desired times in competitive markets, while matching demand with an aircraft fleet of suitable size and composition, can significantly impact its profits. In this spirit, optional flight legs can be considered to construct a profitable schedule by optimally selecting among such alternatives in concert with assigning the available aircraft fleet to all the scheduled legs. Examining itinerary-based demands as well as multiple fare-classes can effectively capture network effects and realistic demand patterns. In addition, allowing flexibility on the departure times of scheduled flight legs can increase connection opportunities for passengers, hence yielding robust schedules while saving fleet assignment costs within the framework of an integrated model. Airlines can also capture an adequate market share by balancing flight schedules throughout the day, and recapture considerations can contribute to more realistic accepted demand realizations. We therefore propose in this paper a model that integrates the schedule design and fleet assignment processes while considering flexible flight times, schedule balance, and recapture issues, along with optional legs, path/itinerary-based demands, and multiple fare-classes. A polyhedral analysis is conducted to generate several classes of valid inequalities, which are used along with suitable separation routines to tighten the model representation. Solution approaches are designed by applying Benders decomposition method to the resulting tightened model, and computational results are presented using real data obtained from United Airlines to demonstrate the efficacy of the proposed procedures.     

Vehicle Fleet Composition

In this paper we consider the problem of determining the optimal composition of a vehicle fleet (i.e. the best fleet size and the best fleet mix). A literature review is given and a new formulation of the problem is presented.     

A heuristic for vehicle fleet mix problem using tabu search and set partitioning

The vehicle fleet mix problem is a special case of the vehicle routing problem where customers are served by a heterogeneous fleet of vehicles with various capacities. An efficient heuristic for determining the composition of a vehicle fleet and travelling routes was developed using tabu search and by solving set partitioning problems. Two kinds of problems have appeared in the literature, concerning fixed cost and variable cost, and these were tested for evaluation. Initial solutions were found using the modified sweeping method. Whenever a new solution in an iteration of the tabu search was obtained, optimal vehicle allocation was performed for the set of routes, which are constructed from the current solution by making a giant tour. Experiments were performed for the benchmark problems that appeared in the literature and new best-known solutions were found.     

O.R. in the Company Car Fleet: When Simple is Efficient

The management of a large fleet of company vehicles represents a significant administrative activity, particularly when the company is a motor vehicle manufacturer and the fleet consists of its own products. The approach taken by the Operational Research Group was to cross departmental boundaries to smooth vehicle ordering, reduce inventories of vehicles awaiting delivery and optimize resale values. The method steers between two potential pitfalls: that of ‘optimizing’ one affected department to the detriment of others, and that of developing sophisticated scheduling and forecasting algorithms which the users would not understand and therefore not trust.     

Dynamic Optimization of Vehicle Fleet Size

This paper extends previous work on the fleet size problem. A dynamic programming model, based on a regeneration sequence, is developed for the more general case where the optimum fleet size is time dependent. The model can cater for vehicle obsolescence and is computationally simple.     

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 rich vehicle routing problem dealing with perishable food: a case study

This paper presents a successful application of operations research techniques in guiding the decision making process to achieve a superior operational efficiency in core activities. We focus on a rich vehicle routing problem faced by a Portuguese food distribution company on a daily basis. This problem can be described as a heterogeneous fleet site dependent vehicle routing problem with multiple time windows. We use the adaptative large neighbourhood search framework, which has proven to be effective to solve a variety of different vehicle routing problems. Our plans are compared against those of the company and the impact that the proposed decision support tool may have in terms of cost savings is shown. The algorithm converges quickly giving the planner considerably more time to focus on value-added tasks, rather than manually correct the routing schedule. Moreover, contrarily to the necessary adaptation time of the planner, the tool is quite flexible in following market changes, such as the introduction of new customers or new products.     

Optimal dispatching strategy on an airline network after a schedule perturbation

It often happens that one or more aeroplanes from an airline fleet are taken out of operation for technical reasons and the airline has to operate on the existing network with a reduced number of planes. This paper presents the results of an effort to define a new ad hoc schedule for this situation, so that the total passenger delay on an airline network is minimized. A network is formed, in which nodes represent flights on a given airline network, and arcs are the total time losses on individual flights. The problem of determining a new routing and scheduling plan for the airline fleet is solved by branch and-bound methods. A numerical example illustrates the efficiency of the model.     

Multifleet routing and multistop flight scheduling for schedule perturbation

Efficient and effective incidental scheduling techniques for schedule perturbation are essential to an airline carrier's operations. This research aims at developing a framework to assist carriers in fleet routing and flight scheduling for schedule perturbations in the operations of multifleet and multistop flights. The framework is based on a basic multifleet schedule perturbation model constructed as a timespace network from which strategic models are developed to research incidental scheduling. These network models are formulated as multiple commodity network flow problems. Lagrangian relaxation with subgradient methods accompanied by the network simplex method, a Lagrangian heuristic and a modified subgradient method are developed to solve the problems. A case study regarding the international operations of a major Taiwan airline carrier is presented.