2,642 research outputs found

    Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product

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    We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizing the total weighted flow time with controllable processing times, minimizing the makespan with controllable release dates, minimizing the total weighted flow time for two models of scheduling with rejection

    A survey of scheduling problems with setup times or costs

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    Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

    Notes on Max Flow Time Minimization with Controllable Processing Times

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    In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the identical parallel machines max flow time minimization problem with controllable processing times. We address the preemptive and non-preemptive version of the problem. For the preemptive case, a linear programming formulation is presented which solves the problem optimally in polynomial time. For the non-preemptive problem it is shown that the First In First Out (FIFO) heuristic has a tight worst-case performance of 3−2/m, when jobs processing times and costs are set as in some optimal preemptive schedul

    Time/cost trade-offs in machine scheduling with controllable processing times

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    Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 166-175Processing time controllability is a critical aspect in scheduling decisions since most of the scheduling practice in industry allows controlling processing times. A very well known example is the computer numerically controlled (CNC) machines in flexible manufacturing systems. Selected processing times for a given set of jobs determine the manufacturing cost of the jobs and strongly affect their scheduling performance. Hence, when making processing time and scheduling decisions at the same time, one must consider both the manufacturing cost and the scheduling performance objectives. In this thesis, we have studied such bicriteria scheduling problems in various scheduling environments including single, parallel and non-identical parallel machine environments. We have included some regular scheduling performance measures such as total weighted completion time and makespan. We have considered the convex manufacturing cost function of CNC turning operation. We have provided alternative methods to find efficient solutions in each problem. We have particularly focused on the single objective problems to get efficient solutions, called the -constraint approach. We have provided efficient formulations for the problems and shown useful properties which led us to develop fast heuristics to generate set of efficient solutions. In this thesis, taking another point of view, we have also studied a conic quadratic reformulation of a machine-job assignment problem with controllable processing times. We have considered a convex compression cost function for each job and solved a profit maximization problem. The convexity of cost functions is a major source of difficulty in finding optimal integer solutions in this problem, but our strengthened conic reformulation has eliminated this difficulty. Our reformulation approach is sufficiently general so that it can also be applied to other mixed 0-1 optimization problems with separable convex cost functions.Our computational results demonstrate that the proposed conic reformulation is very effective for solving the machine-job assignment problem with controllable processing times to optimality. Finally, in this thesis, we have considered rescheduling with controllable processing times. In particular, we show that in contrast to fixed processing times, if we have the flexibility to control the processing times of the jobs, we can generate alternative reactive schedules in response to a disruption such as machine breakdown. We consider a non-identical parallel machining environment where processing times of the jobs are compressible at a certain cost which is a convex function of the compression on the processing time. When rescheduling, it is critical to catch up the initial schedule as soon as possible by reassigning the jobs to the machines and changing their processing times. On the other hand, one must keep the total cost of the jobs at minimum. We present alternative match-up scheduling problems dealing with this trade-off. We use the strong conic reformulation approach in solving these problems. We further provide fast heuristic algorithms.Gürel, SinanPh.D

    Rescheduling parallel machines with controllable processing times

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    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

    Resource Management in Machine Scheduling Problems: A Survey

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    The paper is a survey devoted to job scheduling problems with resource allocation. We present the results available in the scientific literature for commonly used models of job processing times and job release dates, i.e., the models in which the job processing time or the job release date is given as a linear or convex function dependent on the amount of the additional resource allotted to the job. The scheduling models with resource dependent processing times or resource dependent release dates extend the classical scheduling models to reflect more precisely scheduling problems that appear in real life. Thus, in this paper we present the computational complexity results and solution algorithms that have been developed for this kind of problems
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