Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponentialtime algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions

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

Random Keys Genetic Algorithms Scheduling and Rescheduling Systems for Common Production Systems

The majority of scheduling research deals with problems in specific production environments with specific objective functions. However, in many cases, more than one problem type and/or objective function exists, resulting in the need for a more generic and flexible system to generate schedules. Furthermore, most of the published scheduling research focuses on creating an optimal or near optimal initial schedule during the planning phase. However, after production processes start, circumstances like machine breakdowns, urgent jobs, and other unplanned events may render the schedule suboptimal, obsolete or even infeasible resulting in a rescheduling problem, which is typically also addressed for a specific production environment, constraints, and objective functions. This dissertation introduces a generic framework consisting of models and algorithms based on Random Keys Genetic Algorithms (RKGA) to handle both the scheduling and rescheduling problems in the most common production environments and for various types of objective functions. The Scheduling system produces predictive (initial) schedules for environments including single machines, flow shops, job shops and parallel machine production systems to optimize regular objective functions such as the Makespan and the Total Tardiness as well as non-regular objective functions such as the Total Earliness and Tardiness. To deal with the rescheduling problem, and using as a basis the same RKGA, a reactive Rescheduling system capable of repairing initial schedules after the occurrence of unexpected events is introduced. The reactive Rescheduling system was designed not only to optimize regular and non-regular objective functions but also to minimize the instability, a very important aspect in rescheduling to avoid shop chaos due to disruptions. Minimizing both schedule inefficiency and instability, however, turns the problem into a multi-objective optimization problem, which is even more difficult to solve. The computational experiments for the predictive model show that it is able to produce optimal or near optimal schedules to benchmark problems for different production environments and objective functions. Additional computational experiments conducted to test the reactive Rescheduling system under two types of unexpected events, machine breakdowns and the arrival of a rush job, show that the proposed framework and algorithms are robust in handling various problem types and computationally reasonable

Generating all efficient solutions of a rescheduling problem on unrelated parallel machines

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and stability measures. Our efficiency measure is the total flow time and stability measure is the total reassignment cost caused by the differences in the machine allocations in the initial and new schedules. We propose a branch and bound algorithm to generate all efficient solutions with respect to our efficiency and stability measures. We improve the efficiency of the algorithm by incorporating powerful reduction and bounding mechanisms. Our computational tests on large sized problem instances have revealed the satisfactory behaviour of our algorithm

Approximate Algorithms for the Combined arrival-Departure Aircraft Sequencing and Reactive Scheduling Problems on Multiple Runways

The problem addressed in this dissertation is the Aircraft Sequencing Problem (ASP) in which a schedule must be developed to determine the assignment of each aircraft to a runway, the appropriate sequence of aircraft on each runway, and their departing or landing times. The dissertation examines the ASP over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneously. To prevent the dangers associated with wake-vortex effects, separation times enforced by Aviation Administrations (e.g., FAA) are considered, adding another level of complexity given that such times are sequence-dependent. Due to the problem being NP-hard, it is computationally difficult to solve large scale instances in a reasonable amount of time. Therefore, three greedy algorithms, namely the Adapted Apparent Tardiness Cost with Separation and Ready Times (AATCSR), the Earliest Ready Time (ERT) and the Fast Priority Index (FPI) are proposed. Moreover, metaheuristics including Simulated Annealing (SA) and the Metaheuristic for Randomized Priority Search (Meta-RaPS) are introduced to improve solutions initially constructed by the proposed greedy algorithms. The performance (solution quality and computational time) of the various algorithms is compared to the optimal solutions and to each other. The dissertation also addresses the Aircraft Reactive Scheduling Problem (ARSP) as air traffic systems frequently encounter various disruptions due to unexpected events such as inclement weather, aircraft failures or personnel shortages rendering the initial plan suboptimal or even obsolete in some cases. This research considers disruptions including the arrival of new aircraft, flight cancellations and aircraft delays. ARSP is formulated as a multi-objective optimization problem in which both the schedule\u27s quality and stability are of interest. The objectives consist of the total weighted start times (solution quality), total weighted start time deviation, and total weighted runway deviation (instability measures). Repair and complete regeneration approximate algorithms are developed for each type of disruptive events. The algorithms are tested against difficult benchmark problems and the solutions are compared to optimal solutions in terms of solution quality, schedule stability and computational time

Rescheduling parallel machines with controllable processing times

Ankara : The Department of Industrial Engineeringand the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical references.In many manufacturing environments, the production does not always endure as it is planned. Many times, it is interrupted by a disruption such as machine breakdown, power loss, etc. In our problem, we are given an original production schedule in a non-identical parallel machine environment and we assume that one of the machines is disrupted at time t. Our aim is to revise the schedule, although there are some restrictions that should be considered while creating the revised schedule. Disrupted machine is unavailable for a certain time. New schedule has to satisfy the maximum completion time constraint of each machine. Furthermore, when we revise the schedule we have to satisfy the constraint that the revised start time of a job cannot be earlier than its original start time. Because, we assume that jobs are not ready before their original start times in the revised schedule. Therefore, we have to find an alternative solution to decrease the negative impacts of this disruption as much as possible. One way to process a disrupted job in the revised schedule is to reallocate the job to another machine. The other way is to keep the disrupted job at its original machine, but to delay its start time after the end time of the disruption. Since the machines might be fully utilized originally, we may have to compress some of the processing times in order to add a new job to a machine or to reallocate the jobs after the disruption ends. Consequently, we assume that the processing times are controllable within the given lower and upper bounds. Our first objective is to minimize the sum of reallocation and nonlinear compression costs. Besides, it is important to deliver the orders on time, not earlier or later than they are promised. Therefore, we try to maintain the original completion times as much as possible. So, the second objective is to minimize the total absolute deviations of the completion times in the revised schedule from the original completion times. We developed a bi-criteria non-linear mathematical model to solve this nonidentical parallel machine rescheduling problem. Since we have two objectives, we handled the second objective by giving it an upper bound and adding this bound as a constraint to the problem. By utilizing the second order cone programming, we solved this mixed-integer nonlinear mathematical model using a commercial MIP solver such as CPLEX. We also propose a decision tree based heuristic algorithm. Our algorithm generates a set of solutions for a problem instance and we test the solution quality of the algorithm solving same problem instances by the mathematical model. According to our computational experiments, the proposed heuristic approach could obtain close solutions for the first objective for a given upper bound on the second objective.Muhafız, MügeM.S

A Robust Reactive Scheduling System with Application to Parallel Machine Scheduling

In this turbulent world, scheduling role has become crucial in most manufacturing production, and service systems. It allows the allocation of limited resources to activities with the objective of optimizing one performance measure or more. Resources may be machines in a factory, operating rooms in a hospital, or employees in a company, while activities can be jobs in a manufacturing plant, surgeries in a hospital, or paper work in a company. The goal of each schedule is to optimize some performance measures, which could be the minimization of the schedule makespan, the jobs\u27 completion times, jobs\u27 earliness and tardiness, among others. Until very recently, research has concentrated on scenarios that assume a predefined schedule that is failure free. Initial schedules produced in advance are being followed hoping no delays will occur, because once they do, the whole schedule may be compromised as it is not designed to adapt to change. Researchers focused on the generation of good schedules in the presence of complex constraints while assuming fixed processing times, known job arrival times, unbreakable machines, and immune employees. However, this is not the case in the real world, where processing times are stochastic, job arrival times could be unknown, machines do break down, and employees get sick. In fact, most environments including manufacturing are dynamic by nature and not static, vulnerable to many unpredictable events, which leads the initial schedule to become obsolete once it is executed. The reason these deterministic schedules fail is because they do not account for variability, scheduling the activities directly after each other, so when a certain activity is delayed, all its successors will be delayed too. In this dissertation, new repair and rescheduling algorithms, and robust systems equipped with learning capability are developed for the unrelated parallel machine environment, a known NP-hard problem. The introduced rules and algorithms were subjected to different stochastic rates of breakdowns and delays and were judged based on several performance measures to ensure the optimization of both the schedule quality and stability. Schedule quality is assessed based on the schedule Makespan (time to finish all jobs) and CPU, while schedule stability is based on the number of shifted jobs from one machine to another and the time to match up with the original schedule after the occurrence of a breakdown. The extensive computational tests and analyses show the superiority of the proposed algorithms and systems compared to existing methods in the literature, especially when implemented with the learning capability. Moreover, the rules were ranked based on their performance for different performance measure combinations, allowing the decision maker to easily determine the most appropriate repair/rescheduling rule depending on the performance measure(s) desired

Rescheduling in job-shop problems for sustainable manufacturing systems

[EN] Manufacturing industries are faced with environmental challenges, so their industrial processes must be optimized in terms of both profitability and sustainability. Since most of these processes are dynamic, the previously obtained solutions cannot be valid after disruptions. This paper focuses on recovery in dynamic job-shop scheduling problems where machines can work at different rates. Machine speed scaling is an alternative framework to the on/off control framework for production scheduling. Thus, given a disruption, the main goal is to recover the original solution by rescheduling the minimum number of tasks. To this end, a new match-up technique is developed to determine the rescheduling zone and a feasible reschedule. Then, a memetic algorithm is proposed for finding a schedule that minimizes the energy consumption within the rescheduling zone but that also maintains the makespan constraint. An extensive study is carried out to analyze the behavior of our algorithms to recover the original solution and minimize the energy reduction in different benchmarks, which are taken from the OR-Library. The energy consumption and processing time of the tasks involved in the rescheduling zone will play an important role in determining the best match-up point and the optimized rescheduling. Upon a disruption, different rescheduling solutions can be obtained, all of which comply with the requirements but that have different values of energy consumption. The results proposed in this paper may be useful for application in real industries for energy-efficient production rescheduling.This research has been supported by the Seventh Framework Programme under the research project TETRACOM-GA609491 and the Spanish Government under research projects TIN2013-46511-C2-1, TIN2015-65515-C4-1-R and TIN2016-80856-R. The authors wish to thank reviewers and editors for their positive comments to improve the quality of the paper.Salido Gregorio, MA.; Escamilla Fuster, J.; Barber Sanchís, F.; Giret Boggino, AS. (2017). Rescheduling in job-shop problems for sustainable manufacturing systems. Journal of Cleaner Production. 162(20):121-132. https://doi.org/10.1016/j.jclepro.2016.11.002S1211321622

Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. Although some methods have been developed to address such problems, they remain inherently difficult to solve by any single approach. This paper presents a novel decomposition-based approach (DBA), which combines both the shortest processing time (SPT) and the genetic algorithm (GA), to minimizing the makespan of a flexible flow shop (FFS) with stochastic processing times. In the proposed DBA, a neighbouring K-means clustering algorithm is developed to firstly group the machines of an FFS into an appropriate number of machine clusters, based on their stochastic nature. Two optimal back propagation networks (BPN), corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either SPT or GA to each machine cluster for sub-schedule generation. Finally, an overall schedule is generated by integrating the sub-schedules of machine clusters. Computation results show that the DBA outperforms SPT and GA alone for FFS scheduling with stochastic processing times. © 2012 Elsevier Ltd. All rights reserved.postprin