Two-level decomposition algorithm for crew rostering problems with fair working condition

A typical railway crew scheduling problem consists of two phases: a crew pairing problem to determine a set of crew duties and a crew rostering problem. The crew rostering problem aims to find a set of rosters that forms workforce assignment of crew duties and rest periods satisfying several working regulations. In this paper, we present a two-level decomposition approach to solve railway crew rostering problem with the objective of fair working condition. To reduce computational efforts, the original problem is decomposed into the upper-level master problem and the lower-level subproblem. The subproblem can be further decomposed into several subproblems for each roster. These problems are iteratively solved by incorporating cuts into the master problem. We show that the relaxed problem of the master problem can be formulated as a uniform parallel machine scheduling problem to minimize makespan, which is NP-hard. An efficient branch-and-bound algorithm is applied to solve the master problem. Effective valid cuts are developed to reduce feasible search space to tighten the duality gap. Using data provided by the railway company, we demonstrate the effectiveness of the proposed method compared with that of constraint programming techniques for large-scale problems through computational experiments.     

Genetic algorithm based approach for the integrated airline crew-pairing and rostering problem

Airline crew scheduling problem is a complex and difficult problem faced by all airline companies.To tackle this problem, it was often decomposed into two subproblems solved successively. First, the airline crew-pairing problem, which consists on finding a set of trips – called pairings – i.e. sequences of flights, starting and ending at a crew base, that cover all the flights planned for a given period of time. Secondly, the airline crew rostering problem, which consists on assigning the pairings found by solving the first subproblem, to the named airline crew members. For both problems, several rules and regulations must be respected and costs minimized.It is sure that this decomposition provides a convenient tool to handle the numerous and complex restrictions, but it lacks, however, of a global treatment of the problem. For this purpose, in this study we took the challenge of proposing a new way to solve both subproblems simultaneously. The proposed approach is based on a hybrid genetic algorithm. In fact, three heuristics are developed here to tackle the restriction rules within the GA’s process.     

A decomposed branch-and-price procedure for integrating demand planning in personnel staffing problems

The personnel staffing problem calculates the required workforce size and is determined by constructing a baseline personnel roster that assigns personnel members to duties in order to cover certain staffing requirements. In this research, we incorporate the planning of the duty demand in the staff scheduling problem in order to lower the staffing costs. More specifically, the demand originates from a project scheduling problem with discrete time/resource trade-offs, which embodies additional flexibility as activities can be executed in different modes. In order to tackle this integrated problem, we propose a decomposed branch-and-price procedure. A tight lower and upper bound are calculated using a problem formulation that models the project scheduling constraints and the time-related resource scheduling constraints implicitly in the decision variables. Based upon these bounds, the strategic problem is decomposed into multiple tactical subproblems with a fixed workforce size and an optimal solution is searched for each subproblem via branch-and-price. Fixing the workforce size in a subproblem facilitates the definition of resource capacity cuts, which limit the set of eligible project schedules, decreasing the size of the branching tree. In addition, in order to find the optimal integer solution, we propose a specific search strategy based upon the lower bound and dedicated rules to branch upon the workload generated by a project schedule. The computational results show that applying the proposed search space decomposition and the inclusion of resource capacity cuts lead to a well-performing procedure outperforming different other heuristic and exact methodologies.     

Scatter search for minimizing weighted tardiness in a single machine scheduling with setups

Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the weighted tardiness. To solve this problem, we propose a scatter search algorithm which uses path relinking in its core. This algorithm is enhanced with some procedures to speed-up the neighbors’ evaluation and with some diversification and intensification techniques, the latter taking some elements from iterated local search. We conducted an experimental study across a well-known set of instances to analyze the contribution of each component to the overall performance of the algorithm, as well as to compare our proposal with the state-of-the-art metaheuristics, obtaining competitive results. We also propose a new benchmark with larger and more challenging instances and provide the first results for them.     

Scheduling jobs on a single machine with release dates, delivery times and controllable processing times: worst-case analysis

The paper deals with the problem of scheduling jobs on a single machine, in which each job has a release date, a delivery time and a controllable processing time, having its own associated linearly varying cost. An approximation algorithm for minimizing the overall schedule cost is provided which has the performance guarantee of , where is the worst-case performance bound of a procedure used in the proposed algorithm for solving the pure sequencing problem. The best approximation procedure known has .     

Airline Crew Scheduling: State-of-the-Art

The airline industry is faced with some of the largest scheduling problems of any industry. The crew scheduling problem involves the optimal allocation of crews to flights. Over the last two decades the magnitude and complexity of crew scheduling problems have grown enormously and airlines are relying more on automated mathematical procedures as a practical necessity. In this paper we survey different approaches studied and discuss the state-of-the-art in solution methodology for the airline crew scheduling problem. We conclude with a discussion about promising areas for further work to make it possible to get very good solutions for the crew scheduling problem.     

Solving a manpower scheduling problem for airline catering using metaheuristics

We study a manpower scheduling problem with job time windows and job-skills compatibility constraints. This problem is motivated by airline catering operations, whereby airline meals and other supplies are delivered to aircrafts on the tarmac just before the flights take-off. Jobs (flights) must be serviced within a given time-window by a team consisting of a driver and loader. Each driver/loader has the skills to service some, but not all, of the airline/aircraft/configuration of the jobs. Given the jobs to be serviced and the roster of workers for each shift, the problem is to form teams and assign teams and start-times for the jobs, so as to service as many flights as possible. Only teams with the appropriate skills can be assigned to a flight. Workload balance among the teams is also a consideration. We present model formulations and investigate a tabu search heuristic and a simulated annealing heuristic approach to solve the problem. Computational experiments show that the tabu search approach outperforms the simulated annealing approach, and is capable of finding good solutions.     

Parallel machine scheduling with machine availability and eligibility constraints

In this paper we consider the problem of scheduling n independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the makespan. Each machine is not continuously available at all times and each job can only be processed on specified machines. A network flow approach is used to formulate this scheduling problem into a series of maximum flow problems. We propose a polynomial time binary search algorithm to either verify the infeasibility of the problem or solve it optimally if a feasible schedule exists.     

Modeling and Solving an Airline Schedule Generation Problem

Since opening a new flight connection or closing an existing flight has a great impact on the revenues of an airline, the generation of the flight schedule is one of the fundamental problems in airline planning processes.In this paper we concentrate on a special case of the problem which arises at charter companies. In contrast to airlines operating on regular schedules, the market for charter airlines is well-known and the schedule is allowed to change completely from period to period. Thus, precise adjustments to the demands of the market have a great potential for minimizing operating costs.We present a capacitated network design model and propose a combined branch-and-cut approach to solve this airline schedule generation problem. To tighten the linear relaxation bound, we add cutting planes which adjust the number of aircraft and the spill of passengers to the demand on each itinerary.For real-world problems from a large European charter airline we obtain solutions within a very few percent of optimality with running times in the order of minutes on a customary personal computer for most of the data sets.     

Novel hybrid heuristics for an extension of the dynamic relay deployment problem over disaster areas

In this paper, we propose a novel autonomous intelligent tool for the optimum design of a wireless relayed communication network deployed over disaster areas. The so-called dynamic relay deployment problem consists of finding the optimum number of deployed relays and their location aimed at simultaneously maximizing the overall number of mobile nodes covered and minimizing the cost of the deployment. In this paper, we extend the problem by considering diverse relay models characterized by different coverage radii and associated costs. To efficiently tackle this problem we derive a novel hybrid scheme comprising: (1) a Harmony Search (HS)-based global search procedure and (2) a modified version of the well-known K-means clustering algorithm as a local search technique. Single- and bi-objective formulations of the algorithm are proposed for emergency and strategic operational planning, respectively. Monte Carlo simulations are run over a emulated scenario based on real statistical data from the Castilla La Mancha region (center of Spain) to show that, in comparison with a standard implementation of the K-means algorithm followed by a exhaustive search procedure over all relay-model combinations, the proposed scheme renders on average better coverage levels and reduced costs providing, at the same time, an intelligent tool capable of simultaneously determining the number and models of the relays to be deployed.     

Constraint Programming Based Column Generation for Crew Assignment

Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.     

Crew pairing at Air France

In the airline industry, crew schedules consist of a number of pairings. These are round trips originating and terminating at the same crew home base composed of legal work days, called duties, separated by rest periods. The purpose of the airline crew pairing problem is to generate a set of minimal cost crew pairings covering all flight legs. The set of pairings must satisfy all the rules in the work convention and all the appropriate air traffic regulations. The resulting constraints can affect duty construction, may restrict each pairing, or be imposed on the overall crew schedule.The pairing problem is formulated as an integer, nonlinear multi-commodity network flow problem with additional resource variables. Nonlinearities occur in the objective function as well as in a large subset of constraints. A branch-and-bound algorithm based on an extension of the Dantzig-Wolfe decomposition principle is used to solve this model. The master problem becomes a Set Partitioning type model, as in the classical formulation, while pairings are generated using resource constrained shortest path subproblems. This primal approach implicitly considers all feasible pairings and also provides the optimality gap value on a feasible solution. A nice feature of this decomposition process is that it isolates all nonlinear aspects of the proposed multi-commodity model in the subproblems which are solved by means of a specialized dynamic programming algorithm.We present the application and implementation of this approach at Air France. It is one of the first implementations of an optimal approach for a large airline carrier. We have chosen a subproblem network representation where the duties rather than the legs are on the arcs. This ensures feasibility relative to duty restrictions by definition. As opposed to Lavoie, Minoux and Odier (1988), the nonlinear cost function is modeled without approximations. The computational experiments were conducted using actual Air France medium haul data. Even if the branch-and-bound trees were not fully explored in all cases, the gaps certify that the computed solutions are within a fraction of one percentage point of the optimality. Our results illustrate that our approach produced substantial improvements over solutions derived by the expert system in use at Air France. Their magnitude led to the eventual implementation of the approach.     

An Air Force Crew Allocation and Scheduling Problem

This paper considers an airline crew allocation and scheduling problem faced by certain divisions of the United States Air Force. Two variants of the problem under consideration were posed to us by the U.S. Air Force. This paper reports our experience with two heuristic methods developed, each applicable to either variant of the problem. Although the problem described herein is peculiar to this situation, the heuristic scheduling and dispatching rules developed have been found to be very effective and are generally applicable in other related contexts of routeing and crew and vehicle scheduling problems as well. The two algorithms developed have been applied to a coded set of real world data. The results indicate that each one of the two methods is preferable to the other for one of the two variants of the problem. This suggests an overall effective composite technique.     

Genetic algorithms for the bus driver scheduling problem: a case study

This paper describes an application of genetic algorithms to the bus driver scheduling problem. The application of genetic algorithms extends the traditional approach of Set Covering/Set Partitioning formulations, allowing the simultaneous consideration of several complex criteria. The genetic algorithm is integrated in a DSS but can be used as a very interactive tool or a stand-alone application. It incorporates the user's knowledge in a quite natural way and produces solutions that are almost directly implemented by the transport companies in their operational planning processes. Computational results with airline and bus crew scheduling problems from real world companies are presented and discussed.     

A multi-objective genetic algorithm for robust flight scheduling using simulation

Traditional methods of developing flight schedules generally do not take into consideration disruptions that may arise during actual operations. Potential irregularities in airline operations such as equipment failure are not adequately considered during the planning stage of a flight schedule. As such, flight schedules cannot be met as planned and their performance is compromised, which may eventually lead to huge losses in revenue for airlines. In this paper, we seek to improve the robustness of a flight schedule by re-timing its departure times. The problem is modeled as a multi-objective optimization problem, and a multi-objective genetic algorithm (MOGA) is developed to solve the problem. To evaluate flight schedules, SIMAIR 2.0, a simulation model which simulates airline operations under operational irregularities, has been employed. The simulation results indicate that we are able to develop schedules with better operation costs and on-time performance through the application of MOGA.     

An algorithm for large scale 0–1 integer programming with application to airline crew scheduling

We present an approximation algorithm for solving large 0–1 integer programming problems whereA is 0–1 and whereb is integer. The method can be viewed as a dual coordinate search for solving the LP-relaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems that have appeared in the literature.     

Divide-and-price: A decomposition algorithm for solving large railway crew scheduling problems

The railway crew scheduling problem consists of generating crew duties to operate trains at minimal cost, while meeting all work regulations and operational requirements. Typically, a railway operation uses tens of thousands of train movements (trips) and requires thousands of crew members to be assigned to these trips. Despite the large size of the problem, crew schedules need to be generated in short time, because large parts of the train schedule are not finalized until few days before operation.     

A hybrid scatter search for the discrete time/resource trade-off problem in project scheduling

We develop a heuristic procedure for solving the discrete time/resource trade-off problem in the field of project scheduling. In this problem, a project contains activities interrelated by finish-start-type precedence constraints with a time lag of zero, which require one or more constrained renewable resources. Each activity has a specified work content and can be performed in different modes, i.e. with different durations and resource requirements, as long as the required work content is met. The objective is to schedule each activity in one of its modes in order to minimize the project makespan. We use a scatter search algorithm to tackle this problem, using path relinking methodology as a solution combination method. Computational results on randomly generated problem sets are compared with the best available results indicating the efficiency of the proposed algorithm.     

A decomposition approach for the integrated vehicle-crew-roster problem with days-off pattern

The integrated vehicle-crew-roster problem with days-off pattern aims to simultaneously determine minimum cost vehicle and daily crew schedules that cover all timetabled trips and a minimum cost roster covering all daily crew duties according to a pre-defined days-off pattern. This problem is formulated as a new integer linear programming model and is solved by a heuristic approach based on Benders decomposition that iterates between the solution of an integrated vehicle-crew scheduling problem and the solution of a rostering problem. Computational experience with data from two bus companies in Portugal and data from benchmark vehicle scheduling instances shows the ability of the approach for producing a variety of solutions within reasonable computing times as well as the advantages of integrating the three problems.     

A scatter search algorithm for the distributed permutation flowshop scheduling problem

The distributed permutation flowshop problem has been recently proposed as a generalization of the regular flowshop setting where more than one factory is available to process jobs. Distributed manufacturing is a common situation for large enterprises that compete in a globalized market. The problem has two dimensions: assigning jobs to factories and scheduling the jobs assigned to each factory. Despite being recently introduced, this interesting scheduling problem has attracted attention and several heuristic and metaheuristic methods have been proposed in the literature. In this paper we present a scatter search (SS) method for this problem to optimize makespan. SS has seldom been explored for flowshop settings. In the proposed algorithm we employ some advanced techniques like a reference set made up of complete and partial solutions along with other features like restarts and local search. A comprehensive computational campaign including 10 existing algorithms, together with statistical analyses, shows that the proposed scatter search algorithm produces better results than existing algorithms by a significant margin. Moreover all 720 known best solutions for this problem are improved.