Airport runway scheduling

Airport runway optimization is an ongoing challenge for air traffic controllers. Since demand for air-transportation is predicted to increase, there is a need to realize additional take-off and landing slots through better runway scheduling. In this paper, we review the techniques and tools of operational research and management science that are used for scheduling aircraft landings and take-offs. The main solution techniques include dynamic programming, branch and bound, heuristics and meta-heuristics.     

Airport noise modelling and aircraft scheduling so as to minimize community annoyance

A mathematical model of the annoyance created at an airport by aircraft operations is developed. The model incorporates population distribution considerations around an airport and the annoyance caused by aircraft noise. The objective function of this model corresponds to seeking to minimize total population annoyance created by all aircraft operations in a 24-hour period. Several factors are included in this model as constraint relationships. Aircraft operations by type and time period are upper bounded. Demand for flight services is incorporated by including lower bounds on the number of operations by type of aircraft, runway used and time period. Also upper bounds on the number of operations for each runway are included. The mathematical model as formulated is recognized as corresponding to a nonlinear integer mathematical programming problem.The solution technique selected makes use of a successive linear approximation optimization algorithm. An especially attractive feature of this solution algorithm is that it is capable of obtaining solutions to large problems. For example, it would be feasible to attempt the solution of problems involving several thousand variables and over 500 linear constraints. This suggested solution algorithm was implemented on a computer and computational results obtained for example problems.     

Generating,scheduling and rostering of shift crew-duties: Applications at the Hong Kong International Airport

In the context of manpower planning, goal programming (GP) is extremely useful for generating shift duties of fixed length. A fixed-length duty consists of a fixed number of contiguous hours of work in a day, with a meal/rest break somewhere preferably around the middle of these working hours. It is such properties that enable the straightforward, yet flexible GP modeling. We propose GP models for an integrated problem of crew duties assignment, for baggage services section staff at the Hong Kong International Airport. The problem is solved via decomposition into its duties generating phase—a GP planner, followed by its GP scheduling and rostering phase. The results can be adopted as a good crew schedule in the sense that it is both feasible, satisfying various work conditions, and “optimal” in minimizing idle shifts.     

Distributed personnel scheduling—negotiation among scheduling agents

This paper introduces a model for Distributed Employee Timetabling Problems (DisETPs) and proposes a general architecture for solving DisETPs by using a Multi Agent System (MAS) paradigm. The architecture is composed of a set of autonomous software Scheduling Agents (SAs) that solve the Employee Timetabling Problems (ETP) for each department. Each agent has its own local ETP problem and its own goals. The Scheduling Agents must coordinate their local solution with the other agents in order to achieve a global solution for the whole organization that yields a better result with respect to the organization’s global targets. To achieve a coherent and consistent global solution, the SAs make use of a sophisticated negotiation protocol among scheduling agents that always ends in an agreement (not ensured to be optimal). The main functionalities of this protocol are agent to agent relation definition, a mechanism to approve a chain of Request for Changes and an electronic marketplace for bidding on preferred common time slots. Experimental analysis of the implemented Multi Agent System for the Soroka medical center is presented. The results of our study indicate that the proposed framework has the potential to reduce the cost of transportation for the nurses that traveling to and from the hospital.     

Polynomial reduction of time-space scheduling to time scheduling

We study the University Course Timetabling Problem (UCTP). In particular we deal with the following question: is it possible to decompose UCTP into two problems, namely, (i) a time scheduling, and (ii) a space scheduling. We have arguments that it is not possible. Therefore we study UCTP with the assumption that each room belongs to exactly one type of room. A type of room is a set of rooms, which have similar properties. We prove that in this case UCTP is polynomially reducible to time scheduling. Hence we solve UCTP with the following method: at first we solve time scheduling and subsequently we solve space scheduling with a polynomial O(n³) algorithm. In this way we obtain a radical (exponential) speed-up of algorithms for UCTP. The method was applied at P.J. Šafárik University.     

Pattern scheduling

A pattern is a sequence of disjoint intervals on a circle together with fixed distances between these intervals. The intervals may be interpreted as tasks of a job which is produced perio-dically on one machine. How shouldr patterns be moved relative to each other to minimize the maximum overlapping of intervals (machines needed)? An enumerative procedure for solving this problem is given.     

V-shop scheduling

This paper deals with V-shop scheduling where the route by which a job passes through the machines is: M₁ → M₂ → ? → M_m?1 → M_m → M_m?1 → ? → M₂ → M₁. Flowshop scheduling is a special case of V-shop. The two-machine, minimum schedule length V-shop scheduling problem is proved to be binary NP-complete. Efficient solvable algorithms are presented for some simple special cases of NP-complete V-shop problems; specifically n/2/V/C_max with a dominating machine and n/m/V, t_ij = 1/(C_max ∩ ΣC_i). n/m/V/C_max, m?2, with an increasing series of dominating machines is discussed.     

Asymptotic scheduling

We deal with the following scheduling problem: a finite set of jobs is given and each job consists in the execution of an infinite number of tasks. A task is a sequence of operations and each operation requires a specific machine. A machine can process only one operation at a time and preemption is not allowed. Performance measures of the processing system involve fixing a time horizon T, counting the number of tasks completed within T for each job and maximizing a specified function of these numbers to estimate the throughput of the schedule. Whilst computing the throughput for a given T is in general an extremely difficult problem, it is shown in this paper that the limit, as T tends to infinity, of the average throughput (i.e. the throughput divided by T) can be easily computed via Linear Programming under fairly mild conditions. This quantity, which may be called the asymptotic throughput, can be used to assess a bound on performance measures of real systems. Buffers play a crucial role and buffer sizes can be taken care of in assessing the system performance. Mathematics Subject Classification (2000):90B35, 90C05, 90C27, 90C90     

Reversible-shop scheduling

Consider n jobs (J₁,…,J_n) and m machines (M₁,…,M_m). The route by which a job passes through the machines is either M₁ → M₂ → … → M_m or M_m → M_m−1 → … M₁, i.e. reversible-shop. It is proved that for three machines, the problem of minimizing the schedule length is NP-hard. Efficient algorithms are developed for the following special cases: three machines of which one or more are dominated; arbitrary number of machines where all operations have equal processing times; three machines, route-dependent reversible-shop where the second machine dominates the other two.     

Airport management: taxi planning

The Taxi Planning studies the aircraft routing and scheduling on the airport ground. This is a dynamic problem, which must be updated almost every time that a new aircraft enters or exits the system. Taxi Planning has been modelled using a linear multicommodity flow network model with side constraints and binary variables. The flow capacity constraints are used to represent the conflicts and competence between aircrafts using a given airport capacity. The “Branch and Bound” and “Fix and Relax” methodologies have been used. The computational tests have been run at the Madrid-Barajas airport, using actual data from the airport traffic.     

The just-in-time scheduling problem in a flow-shop scheduling system

We study the problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O(n³) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP-hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O(n³) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O(n log n) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O(mn²) time optimization algorithm.     

Railway scheduling reduces the expected project makespan over roadrunner scheduling in a multi-mode project scheduling environment

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (Critical chain, 1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.     

Extension of algorithm list scheduling for a semi-online scheduling problem

A general algorithm, called ALG, for online and semi-online scheduling problem Pm||C _max with m ≥ 2 is introduced. For the semi-online version, it is supposed that all job have their processing times within the interval [p, rp], where p > 0,1 < r ≤ m/m − 1. ALG is a generalization of LS and is optimal in the sense that there is not an algorithm with smaller competitive ratio than that of ALG.     

Cyclic nurse scheduling

This paper presents an algorithm for scheduling nurses in a hospital. The resulting schedules are cyclic and optimal. The advantage of this algorithm is that it can be implemented easily on a microcomputer.     

Surgical case scheduling as a generalized job shop scheduling problem

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.     

Rational preemptive scheduling

In scheduling jobs subject to precedence constraints that form a partial order, it is advantageous to interrupt (preempt) jobs, and return to complete them at a later time in order to minimize total completion time. It is clearly desirable to see that such preemptive scheduling by finitely many machines requires only intervals of work, and not a more general assignment of tasks over measurable sets, for optimal completion. It is a deeper fact that arbitrarily small intervals are required for a fixed number of machines m>-3 for optimal preemptive scheduling. On the other hand, if the number of jobs is fixed, say n, then it is intuitively clear that it suffices to use only comparatively large intervals (but less clear how large will suffice!). The authors address these and certain related questions.     

Decentralized list scheduling

Classical list scheduling is a very popular and efficient technique for scheduling jobs for parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single centralized list becomes too prohibitive. A suitable approach to reduce the contention is to distribute the list among the computational units: each processor only has a local view of the work to execute. Thus, the scheduler is no longer greedy and standard performance guarantees are lost. The objective of this work is to study the extra cost that must be paid when the list is distributed among the computational units. We first present a general methodology for computing the expected makespan based on the analysis of an adequate potential function which represents the load imbalance between the local lists. We obtain an equation giving the evolution of the potential by computing its expected decrease in one step of the schedule. Our main theorem shows how to solve such equations to bound the makespan. Then, we apply this method to several scheduling problems, namely, for unit independent tasks, for weighted independent tasks and for tasks with precedence constraints. More precisely, we prove that the time for scheduling a global workload W composed of independent unit tasks on m processors is equal to W/m plus an additional term proportional to log₂ W. We provide a lower bound which shows that this is optimal up to a constant. This result is extended to the case of weighted independent tasks. In the last setting, precedence task graphs, our analysis leads to an improvement on the bound of Arora et al. (Theory Comput. Syst. 34(2):115–144, 2001). We end with some experiments using a simulator. The distribution of the makespan is shown to fit existing probability laws. Moreover, the simulations give a better insight into the additive term whose value is shown to be around 3log₂ W confirming the precision of our analysis.     

Outsourcing and scheduling for two-machine ordered flow shop scheduling problems

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement p_j, and machine i a characteristic q_i. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, p_j/q_i. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{p_j, q_i} (min{p_j, q_i}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.