A Matheuristic Algorithm for the Multiple-Depot Vehicle and Crew Scheduling Problem

This paper examines time windows for scheduled trips in multiple depot vehicle and crew scheduling problems that arise in public bus transportation. In practice, the two planning tasks vehicle scheduling and crew scheduling are traditionally solved sequentially with the implicit understanding that the scheduled time for timetabled trips remains fixed. In order to improve cost efficiency two concepts have been developed over the last years: In order to obtain better flexibility when scheduling crews, vehicle and crew scheduling problems are tackled simultaneously. In order to extend flexibility while scheduling vehicles, variable trip departure and arrival times are considered. Obviously the combination of both concepts promises the largest savings, but probably leads to bursting computational times due to growing problem complexity. In this paper we combine both concepts by extending the integrated vehicle and crew scheduling problem with the possibility to shift scheduled trips within defined time windows. We examine the tradeoffs between solution quality and computational time for different solution approaches.

Multiple depot vehicle scheduling with controlled trip shifting

Separating valid odd-cycle and odd-set inequalities for the multiple depot vehicle scheduling problem

This paper describes the most obvious way for public transportation companies to decrease their operational cost. This is to optimize the logistics of their operations. The optimization process is a very complex operation and therefore we split the logistics into three phases: vehicle scheduling, driver scheduling and driverrostering. The phases reflect also the split of a large problem (long term optimization) to the daily operation and finally to individual trips. The individual trips are then grouped into working shifts and to these are scheduled individual drivers. In the paper we present a detail description of bus scheduling. We use its mapping to the multiple depot vehicle scheduling problem (MDVSP) using a time-space network model. Finally, we solve the problem for two different cases – the city of Szeged and the city of Ljubljana.

Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem and one or more pricing problems (PP). The total computing time taken by the method is divided between these two parts. In routing or scheduling applications, the problems are mostly defined on a network, and the PP is usually an NP-hard shortest path problem with resource constraints. In this work, we propose a new heuristic pricing algorithm based on machine learning. By taking advantage of the data collected during previous executions, the objective is to reduce the size of the network and accelerate the PP, keeping only the arcs that have a high chance to be part of the linear relaxation solution. The method has been applied to two specific problems: the vehicle and crew scheduling problem in public transit and the vehicle routing problem with time windows. Reductions in computational time of up to 40% can be obtained. Funding: The authors thank Giro, Inc., and the Natural Sciences and Engineering Research Council of Canada for financial support [Grant CRDPJ 520349-17].

This paper investigates the application of a new class of neighborhood search algorithms—cyclic transfers—to multivehicle routing and scheduling problems. These algorithms exploit the two-faceted decision structure inherent to this problem class: First, assigning demands to vehicles and, second, routing each vehicle through its assigned demand stops. We describe the application of cyclic transfers to vehicle routing and scheduling problems. Then we determine the worst-case performance of these algorithms for several classes of vehicle routing and scheduling problems. Next, we develop computationally efficient methods for finding negative cost cyclic transfers. Finally, we present computational results for three diverse vehicle routing and scheduling problems, which collectively incorporate a variety of constraint and objective function structures. Our results show that cyclic transfer methods are either comparable to or better than the best published heuristic algorithms for several complex and important vehicle routing and scheduling problems. Most importantly, they represent a novel approach to solution improvement which holds promise in many vehicle routing and scheduling problem domains.

The crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline's fleets. The problem is especially important today since costs for flying personnel of major U.S. carriers have grown and now often exceed $1.3 billion a year and are the second largest item (next to fuel cost) of the total operating cost of major U.S. carriers. Thus even small percentage savings amount to substantial dollar amounts. We present a branch-and-cut approach to solving to proven optimality large set partitioning problems arising within the airline industry. We first provide some background related to this important application and then describe the approach for solving representative problems in this problem class. The branch-and-cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree-search algorithm that uses automatic reformulation procedures, heuristics and linear programming technology to assist in the solution. Numerical experiments are reported for a sample of 68 large-scale real-world crew scheduling problems. These problems include both pure set partitioning problems and set partitioning problems with side constraints. These “base constraints” represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality. An interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground.

In this paper, the ant colony algorithms is studied, and improve the shortcomings of the algorithm, And the improved algorithm is introduced into the field of logistics transportation.Aiming at the complexity and uncertainty of logistics transportation vehicle scheduling problem, a new algorithm is designed.The experimental results show that the improved algorithm can choose the transport route, speed up the transportation speed, improve the service quality, reduce the transportation cost and increase economic benefits.

The past few decades have witnessed numerous applications of operations research in logistics, and these applications have resulted in substantial cost savings. However, the U.S. railroad industry has not benefited from the advances, and most of the planning and scheduling processes do not use modeling and optimization. Indeed, most of the planning and scheduling problems arising in railroads, which involve billions of dollars of resources annually, are currently being solved manually. The main reason for not using OR models and methodologies is the mathematical difficulty of these problems, which prevented the development of decision tools that railroads can use to obtain implementable solutions. However, now this situation is gradually changing. We are developing cutting-edge operations research algorithms, by using state-of-the-art ideas from linear and integer programming, network flows, discrete optimization, heuristics, and very large-scale neighborhood (VLSN) search, that railroads have already started using and from which they have started deriving immense benefits. This chapter gives an overview of the railroad planning and scheduling problems, including the railroad blocking problem, train scheduling problem, yard location problem, train dispatching problem, locomotive scheduling problem, and crew scheduling problem. Some of these problems are very large-scale integer programming problems containing billions or even trillions of integer variables. We will describe algorithms that can solve these problems to near-optimality within one to two hours of computational time. We present computational results of these algorithms on the data provided by several U.S. railroads, demonstrating potential benefits from tens to hundreds of millions annually.

A branch-and-price algorithm for integrating urban rail crew scheduling and rostering problems

The Vehicle Scheduling Problem is a well-known combinatorial optimization problem that emerges in mobility and transportation sectors. The heterogeneous fleet with multiple depots extension arises in major urban public transportation companies due to different demands throughout the day and some restrictions in the use of different vehicle types. This extension introduces complexity to the problem and makes the known deterministic methods unable to solve it efficiently. This paper describes an approach to create a comprehensive model to represent the Multiple Depot Vehicle Scheduling Problem as an Asymmetric Traveling Salesman Problem. To solve the A-TSP problem an Ant Colony based meta-heuristic was developed. The results achieved on solving problems from a Portuguese major public transportation planning database show the usefulness of the proposed approach.

This thesis goes deep into the vehicle scheduling problem (VSP), which is the key problem for the distribution center.This paper analyzes and optimizes the mathematical model of vehicle scheduling problem. The problem of dynamic vehicle scheduling with time windows is described in great details in the thesis, which also gives an arithmetic solution aiming at the scheduling problem.Finally, based on the research results and under the background of logistics distribution enterprises, the vehicle scheduling algorithm is exposed to experiment.

This article presents a planning problem in a distribution network incorporating two levels of inventory management. Perishable products are routed with lot-sizing, multi-sourcing and limited transport capacity using a homogeneous fleet of vehicles. A mixed integer linear programming (MILP) and a greedy heuristic have been developed to solve this real planning problem. There are some instances for which the solver cannot give a good lower bound within the limited time and for other instances it takes a lot of time to solve MILP. The greedy heuristic is an alternative to the mixed integer linear program, used to quickly solve some large instances taking into account original and difficult constraints. For some instances the gap between the solution provided by the solver (MILP) and the heuristic becomes quite significant. An iterated local search (ILS) using the variable neighborhood descent (VND) method has been implemented to improve the quality of heuristic solutions. We have included the ILS method in an APS (Advanced Planning System) and have compared it with an exact resolution of the MILP. Two types of instances are tested: models derived from actual data and models built using a random generator of instances that have wider diversity for computational evaluation. The ILS procedure significantly improves the quality of solutions and average computational time is much shorter than MILP resolution.

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O(n3). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O(n4). We demonstrate that with careful implementation it is possible, in most cases, to maintain the O(n3) complexity or, in a few cases, increase the time complexity to O(n3 log n). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics.

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances.