Pareto optimality and a class of set covering heuristics

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.     

Crane scheduling in container yards with inter-crane interference

This paper examines the problem of scheduling multiple yard cranes to perform a given set of jobs with different ready times in a yard zone with only one bi-directional travelling lane. Due to sharing of the travelling lane among two or more yard cranes, inter-crane interference, a planned move of a yard crane blocked by the other yard cranes, may happen. The scheduling problem is formulated as an integer program. It is noted that the scheduling problem is NP-complete. This research develops a dynamic programming-based heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. Computational experiments are carried out to evaluate the performance of the heuristic and the results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 7.3% above their lower bounds.     

The hybrid flow shop scheduling problem

The scheduling of flow shops with multiple parallel machines per stage, usually referred to as the hybrid flow shop (HFS), is a complex combinatorial problem encountered in many real world applications. Given its importance and complexity, the HFS problem has been intensively studied. This paper presents a literature review on exact, heuristic and metaheuristic methods that have been proposed for its solution. The paper briefly discusses and reviews several variants of the HFS problem, each in turn considering different assumptions, constraints and objective functions. Research opportunities in HFS are also discussed.     

Algorithms for railway crew management

Crew management is concerned with building the work schedules of crews needed to cover a planned timetable. This is a well-known problem in Operations Research and has been historically associated with airlines and mass-transit companies. More recently, railway applications have also come on the scene, especially in Europe. In practice, the overall crew management problem is decomposed into two subproblems, called crew scheduling and crew rostering. In this paper, we give an outline of different ways of modeling the two subproblems and possible solution methods. Two main solution approaches are illustrated for real-world applications. In particular we discuss in some detail the solution techniques currently adopted at the Italian railway company, Ferrovie dello Stato SpA, for solving crew scheduling and rostering problems.     

Solving large set covering problems for crew scheduling

This paper presents a computationally effective heuristic method which produces good-quality solutions for large-scale set covering problems with thousands of constraints and about one million variables. The need to solve such large-scale problems arises from a crew scheduling problem of mass transit agencies where the number of work shifts required has to be minimized. This problem may be formulated as a large-scale non-unicost set covering problem whose rows are trips to be performed while columns stand for round trips. The proposed method is mainly based on lagragian relaxation and sub-gradient optimization. After the reduction of the number of rows and columns by the logical tests, “greedy” heuristic algorithms provide upper and lower bounds which are continuously improved to produce goodquality solutions. Computational results, regarding randomly generated problems and real life problems concerning crew scheduling at Italian Railways Company, show that good-quality solutions can be obtained at an acceptable computational cost. This work was supported by the project “Progetto Finalizzato Transporti 2” of National Research Council of Italy (C.N.R.) contract No. 94.01436PF74 and by “Ferrovie dello Stato S.p.A.”     

A time-based pheromone approach for the ant system

The ant system (AS) is a metaheuristic approach originally developed for solving the traveling salesman problem. AS has been successfully applied to various hard combinatorial optimization problems and different variants have been proposed in the literature. In this paper, we introduce a time-based pheromone approach for AS (TbAS). Due to this nature TbAS is applicable to routing problems involving time-windows. The novelty in TbAS is the multi-layer pheromone network structure which implicitly utilizes the service time information associated with the customers as a heuristic information. To investigate the performance of TbAS, we use the well-known vehicle routing problem with time-windows as our testbed and we conduct an extensive computational study using the Solomon (Algorithms for the vehicle routing and scheduling problems with time window constraints 35:254?C265, 1987) instances. Our results reveal that the proposed time-based pheromone approach is effective in obtaining good quality solutions.     

A Simulated Annealing Approach to the Solution of Flexible Labour Scheduling Problems

This paper presents a new solution approach to the discontinuous labour tour scheduling problem where the objective is to minimize the number of full-time employees required to satisfy forecast demand. Previous heuristic approaches have often limited the number of allowable tours by restricting labour scheduling flexibility in terms of shift length, shift start-times, days-off, meal-break placement, and other factors. These restrictions were essential to the tractability of the heuristic approaches but often resulted in solutions that contained a substantial amount of excess labour. In this study, we relaxed many of the restrictions on scheduling flexibility assumed in previous studies. The resulting problem environment contained more than two billion allowable tours, precluding the use of previous heuristic methods. Consequently, we developed a simulated annealing heuristic for solving the problem. An important facet of this new approach is an ‘intelligent’ improvement routine which eliminates the need for long run-times typically associated with simulated annealing algorithms. The simulated annealing framework does not rely on a special problem structure and our implementation rapidly converged to near-optimal solutions for all problems in the test environment.     

A dual ascent procedure for the set partitioning problem

The set partitioning problem is a fundamental model for many important real-life transportation problems, including airline crew and bus driver scheduling and vehicle routing.In this paper we propose a new dual ascent heuristic and an exact method for the set partitioning problem. The dual ascent heuristic finds an effective dual solution of the linear relaxation of the set partitioning problem and it is faster than traditional simplex based methods. Moreover, we show that the lower bound achieved dominates the one achieved by the classic Lagrangean relaxation of the set partitioning constraints. We describe a simple exact method that uses the dual solution to define a sequence of reduced set partitioning problems that are solved by a general purpose integer programming solver. Our computational results indicate that the new bounding procedure is fast and produces very good dual solutions. Moreover, the exact method proposed is easy to implement and it is competitive with the best branch and cut algorithms published in the literature so far.     

Simple and efficient heuristic approach for the multiple-depot vehicle scheduling problem

In this paper, a fast heuristic approach is proposed for solving the multiple depot vehicle scheduling problem (MDVSP), a well-known NP-hard problem. The heuristic is based on a two stage procedure. The first one applies two state space reduction procedures towards reducing the problem complexity. One procedure is based on the solutions of the single-depot vehicle scheduling for each depot, while the other uses the solution of a relaxed formulation of the MDVSP, in which a vehicle can finish its task sequence in a different depot from where it started. Next, the reduced problem is solved by employing a truncated column generation approach. The heuristic approach has been implemented in several variants, through different combinations of the reduction procedures, and tested on a series of benchmark problems provided by Pepin et al. (J Sched 12:17–30, 2009). The heuristic variants found solutions with very narrow gaps (below 0.7 %, on average) to best-known solutions (Pepin et al., J Sched 12:17–30, 2009), decreasing the required CPU time by an overall average factor of 17 in comparison with reported results in the literature (Otsuki and Aihara, J Heuristics 1–19, 2014).     

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.     

Scatter Search and Bionomic Algorithms for the aircraft landing problem

The problem of deciding how to land aircraft approaching an airport involves assigning each aircraft to an appropriate runway, computing a landing sequence for each runway and scheduling the landing time for each aircraft. Runway allocation, sequencing and scheduling for each aircraft must ensure the scheduled landing time lies within a predefined time window and meet separation time requirements with other aircraft. The objective is to achieve effective runway use.In this paper, the multiple runway case of the static Aircraft Landing Problem is considered. Two heuristic techniques are presented: Scatter Search and the Bionomic Algorithm, population heuristic approaches that have not been applied to this problem before.Computational results are presented for publicly available test problems involving up to 500 aircraft and five runways showing that feasible solutions of good quality can be produced relatively quickly.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

Scheduling aircraft landings at London Heathrow using a population heuristic

With increasing levels of air traffic, making effective use of limited airport capacity is obviously important. This paper reports on an investigation undertaken by National Air Traffic Services in the UK into improving runway utilisation at London Heathrow. This investigation centred on developing an algorithm for improving the scheduling of aircraft waiting to land. The heuristic algorithm developed (a population heuristic) is discussed and results presented using actual operational data relating to aircraft landings at London Heathrow. This data indicates that our algorithm could have improved on air traffic control decisions in such cases by between 2–5?% in terms of reducing the timespan required to land all of the aircraft considered.     

航空公司机组排班计划研究

以中国国际航空公司北京-成都航班为例,提出一种航空公司制定机组排班计划的新方法。首先以机组异地停留时间最短为目标,应用匈牙利算法生成“机组航班串”;然后,应用人员排班方法求得保证机组每周连休两日的条件下完成“机组航班串”飞行任务的最少机组数;最后,对这些机组制定具体的排班计划。应用该方法制定的机组排班计划使得航空公司在保证机组每周连休两日的条件下能够以最少的机组完成航班飞行任务,且机组在异地的停留时间最短。     

A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows

This paper presents a novel three-phase heuristic/algorithmic approach for the multi-depot routing problem with time windows and heterogeneous vehicles. It has been derived from embedding a heuristic-based clustering algorithm within a VRPTW optimization framework. To this purpose, a rigorous MILP mathematical model for the VRPTW problem is first introduced. Likewise other optimization approaches, the new formulation can efficiently solve case studies involving at most 25 nodes to optimality. To overcome this limitation, a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster-based MILP problem formulation. In this way, a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed. Phase I aims to identifying a set of cost-effective feasible clusters while Phase II assigns clusters to vehicles and sequences them on each tour by using the cluster-based MILP formulation. Ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small MILP model is finally performed at Phase III. Numerous benchmark problems featuring different sizes, clustered/random customer locations and time window distributions have been solved at acceptable CPU times.     

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.     

Heuristics for the flow line problem with setup costs

This paper presents two new heuristics for the flowshop scheduling problem with sequence-dependent setup times (SDSTs) and makespan minimization objective. The first is an extension of a procedure that has been very successful for the general flowshop scheduling problem. The other is a greedy randomized adaptive search procedure (GRASP) which is a technique that has achieved good results on a variety of combinatorial optimization problems. Both heuristics are compared to a previously proposed algorithm based on the traveling salesman problem (TSP). In addition, local search procedures are developed and adapted to each of the heuristics. A two-phase lower bounding scheme is presented as well. The first phase finds a lower bound based on the assignment relaxation for the asymmetric TSP. In phase two, attempts are made to improve the bound by inserting idle time. All procedures are compared for two different classes of randomly generated instances. In the first case where setup times are an order of magnitude smaller than the processing times, the new approaches prove superior to the TSP-based heuristic; for the case where both processing and setup times are identically distributed, the TSP-based heuristic outperforms the proposed procedures.     

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.     

Interior point method for long-term generation scheduling of large-scale hydrothermal systems

This paper presents an interior point method for the long-term generation scheduling of large-scale hydrothermal systems. The problem is formulated as a nonlinear programming one due to the nonlinear representation of hydropower production and thermal fuel cost functions. Sparsity exploitation techniques and an heuristic procedure for computing the interior point method search directions have been developed. Numerical tests in case studies with systems of different dimensions and inflow scenarios have been carried out in order to evaluate the proposed method. Three systems were tested, with the largest being the Brazilian hydropower system with 74 hydro plants distributed in several cascades. Results show that the proposed method is an efficient and robust tool for solving the long-term generation scheduling problem.     

Maximizing total job value on a single machine with job selection

This paper describes a single-machine scheduling problem of maximizing total job value with a machine availability constraint. The value of each job decreases over time in a stepwise fashion. Several solution properties of the problem are developed. Based on the properties, a branch-and-bound algorithm and a heuristic algorithm are derived. These algorithms are evaluated in the computational study, and the results show that the heuristic algorithm provides effective solutions within short computation times.