Scheduling aircraft landings - the static case

This is the publisher version of the article, obtained from the link below.In this paper, we consider the problem of scheduling aircraft (plane) landings at an airport. This problem is one of deciding a landing time for each plane such that each plane lands within a predetermined time window and that separation criteria between the landing of a plane and the landing of all successive planes are respected. We present a mixed-integer zero–one formulation of the problem for the single runway case and extend it to the multiple runway case. We strengthen the linear programming relaxations of these formulations by introducing additional constraints. Throughout, we discuss how our formulations can be used to model a number of issues (choice of objective function, precedence restrictions, restricting the number of landings in a given time period, runway workload balancing) commonly encountered in practice. The problem is solved optimally using linear programming-based tree search. We also present an effective heuristic algorithm for the problem. Computational results for both the heuristic and the optimal algorithm are presented for a number of test problems involving up to 50 planes and four runways.J.E.Beasley. would like to acknowledge the financial support of the Commonwealth Scientific and Industrial Research Organization, Australia

Solving Integrated Process Planning, Dynamic Scheduling, and Due Date Assignment Using Metaheuristic Algorithms

Because the alternative process plans have significant contributions to the production efficiency of a manufacturing system, researchers have studied the integration of manufacturing functions, which can be divided into two groups, namely, integrated process planning and scheduling (IPPS) and scheduling with due date assignment (SWDDA). Although IPPS and SWDDA are well-known and solved problems in the literature, there are limited works on integration of process planning, scheduling, and due date assignment (IPPSDDA). In this study, due date assignment function was added to IPPS in a dynamic manufacturing environment. And the studied problem was introduced as dynamic integrated process planning, scheduling, and due date assignment (DIPPSDDA). The objective function of DIPPSDDA is to minimize earliness and tardiness (E/T) and determine due dates for each job. Furthermore, four different pure metaheuristic algorithms which are genetic algorithm (GA), tabu algorithm (TA), simulated annealing (SA), and their hybrid (combination) algorithms GA/SA and GA/TA have been developed to facilitate and optimize DIPPSDDA on the 8 different sized shop floors. The performance comparisons of the algorithms for each shop floor have been given to show the efficiency and effectiveness of the algorithms used. In conclusion, computational results show that the proposed combination algorithms are competitive, give better results than pure metaheuristics, and can effectively generate good solutions for DIPPSDDA problems

Algorithms for Scheduling Problems

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

Scheduling the assembly process with uncertain material arrivals.

by Cheung Chit-Cheung, Gavin.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 75-77).Abstract also in Chinese.Abstract --- p.iAcknowledgment --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.2Chapter 1.2 --- Problem Description --- p.5Chapter 1.3 --- Contributions --- p.6Chapter 1.4 --- Thesis Organization --- p.6Chapter 2 --- Problem Formulation and Solution Approaches --- p.8Chapter 2.1 --- Mathematical Modeling --- p.8Chapter 2.2 --- Transformation of Problem --- p.11Chapter 2.3 --- Problem Analysis --- p.12Chapter 2.3.1 --- Optimality Criteria --- p.13Chapter 2.3.2 --- Heuristic Solutions --- p.15Chapter 2.4 --- Literatures Review on Single-Machine Scheduling --- p.18Chapter 3 --- Discussion of Some Special Cases --- p.21Chapter 3.1 --- Two Operations --- p.22Chapter 3.2 --- Identical Distributions --- p.24Chapter 3.2.1 --- Error Bound of LPTF - Maximum Distribution Approach --- p.27Chapter 3.3 --- Large Initial Time and Special Processing Times Structure --- p.29Chapter 3.3.1 --- Application of SVF to Exponential Distribution --- p.34Chapter 3.3.2 --- Error Bound of SVF 一 Switching Processing Times Approach --- p.37Chapter 3.3.3 --- Extended Error Bound Analysis --- p.41Chapter 4 --- Heuristics to Solve the General Problems --- p.47Chapter 4.1 --- Level 1 - PIPF and LPTF Rules --- p.48Chapter 4.2 --- Level 2 - Adjacent Pair wise Interchange --- p.51Chapter 4.3 --- Computational Complexity --- p.53Chapter 5 --- Experimental Results --- p.54Chapter 5.1 --- Design of Experiments --- p.54Chapter 5.1.1 --- Design of Problem Parameters --- p.55Chapter 5.1.2 --- Evaluation Methods --- p.57Chapter 5.2 --- Results Analysis --- p.59Chapter 5.2.1 --- Evaluation for Problems with Small Size --- p.60Chapter 5.2.2 --- Evaluation for Problems with Large Size --- p.63Chapter 6 --- Conclusion --- p.67Chapter 6.1 --- Summary --- p.67Chapter 6.2 --- Future Extension --- p.68Appendix --- p.69Chapter A --- Crossing Point of Normal Density Functions --- p.69Chapter B --- Probaiblity Distributions --- p.73Chapter B.1 --- Uniform Distribution --- p.73Chapter B.2 --- Exponential Distribution --- p.74Chapter B.3 --- Normal Distribution --- p.74Bibliography --- p.7

Joint optimization of allocation and release policy decisions for surgical block time under uncertainty

The research presented in this dissertation contributes to the growing literature on applications of operations research methodology to healthcare problems through the development and analysis of mathematical models and simulation techniques to find practical solutions to fundamental problems facing nearly all hospitals. In practice, surgical block schedule allocation is usually determined regardless of the stochastic nature of case demand and duration. Once allocated, associated block time release policies, if utilized, are often simple rules that may be far from optimal. Although previous research has examined these decisions individually, our model considers them jointly. A multi-objective model that characterizes financial, temporal, and clinical measures is utilized within a simulation optimization framework. The model is also used to test “conventional wisdom” solutions and to identify improved practical approaches. Our result from scheduling multi-priority patients at the Stafford hospital highlights the importance of considering the joint optimization of block schedule and block release policy on quality of care and revenue, taking into account current resources and performance. The proposed model suggests a new approach for hospitals and OR managers to investigate the dynamic interaction of these decisions and to evaluate the impact of changes in the surgical schedule on operating room usage and patient waiting time, where patients have different sensitivities to waiting time. This study also investigated the performance of multiple scheduling policies under multi-priority patients. Experiments were conducted to assess their impacts on the waiting time of patients and hospital profit. Our results confirmed that our proposed threshold-based reserve policy has superior performance over common scheduling policies by preserving a specific amount of OR time for late-arriving, high priority demand

Extending scheduling algorithms to minimise the impact of bounded uncertainty using interval programming

 This research proposed a new methodology to extend algorithms to accept interval-based uncertain parameters. The methodology is applied on scheduling algorithms, including heuristic and meta-heuristic algorithms and produced optimal results with higher accuracy. The research outcomes are effective for decision making process using uncertain or predicted data

The Integration of Maintenance Decisions and Flow Shop Scheduling

In the conventional production and service scheduling problems, it is assumed that the machines can continuously process the jobs and the information is complete and certain. However, in practice the machines must stop for preventive or corrective maintenance, and the information available to the planners can be both incomplete and uncertain. In this dissertation, the integration of maintenance decisions and production scheduling is studied in a permutation flow shop setting. Several variations of the problem are modeled as (stochastic) mixed-integer programs. In these models, some technical nuances are considered that increase the practicality of the models: having various types of maintenance, combining maintenance activities, and the impact of maintenance on the processing times of the production jobs. The solution methodologies involve studying the solution space of the problems, genetic algorithms, stochastic optimization, multi-objective optimization, and extensive computational experiments. The application of the problems and managerial implications are demonstrated through a case study in the earthmoving operations in construction projects