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

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

Stochastic lot sizing problem with controllable processing times

Cataloged from PDF version of article.In this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities

An anticipative scheduling approach with controllable processing times

In practice, machine schedules are usually subject to disruptions which have to be repaired by reactive scheduling decisions. The most popular predictive approach in project management and machine scheduling literature is to leave idle times (time buffers) in schedules in coping with disruptions, i.e. the resources will be under-utilized. Therefore, preparing initial schedules by considering possible disruption times along with rescheduling objectives is critical for the performance of rescheduling decisions. In this paper, we show that if the processing times are controllable then an anticipative approach can be used to form an initial schedule so that the limited capacity of the production resources are utilized more effectively. To illustrate the anticipative scheduling idea, we consider a non-identical parallel machining environment, where processing times can be controlled at a certain compression cost. When there is a disruption during the execution of the initial schedule, a match-up time strategy is utilized such that a repaired schedule has to catch-up initial schedule at some point in future. This requires changing machine–job assignments and processing times for the rest of the schedule which implies increased manufacturing costs. We show that making anticipative job sequencing decisions, based on failure and repair time distributions and flexibility of jobs, one can repair schedules by incurring less manufacturing cost. Our computational results show that the match-up time strategy is very sensitive to initial schedule and the proposed anticipative scheduling algorithm can be very helpful to reduce rescheduling costs

Stochastic lot sizing problem with controllable processing times

In this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities. © 2014 Elsevier Ltd

Comparison of the formulations for a hub-and-spoke network design problem under congestion

In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set