Parallel machine scheduling with a convex resource consumption function

Shabtay, Dvir; Kaspi, Moshe

doi:10.1016/j.ejor.2004.12.008

Cited by 60 publications

(27 citation statements)

References 19 publications

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“…Shabtay employed this function to model operations in scheduling problems, where job-processing times are controllable. His research includes the minimization of makespan (Shabtay and Kaspi 2004a), maximum lateness (Shabtay 2004) and total weighted flowtime (Shabtay and Kaspi 2004b) on a single machine, and special cases on parallel-machine (Shabtay and Kaspi 2006a) and open-shop (Shabtay and Kaspi 2006b) scheduling. However, in these early research, it is assumed that job-processing times can take any positive value (that is, p j > 0), such that the equivalent load method can be applied to yield close-form solution for the resource allocation problem.…”

Section: Introductionmentioning

confidence: 99%

A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

Feng

2010

Ann Oper Res

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In most deterministic scheduling problems, job-processing times are regarded as constant and known in advance. However, in many realistic environments, job-processing times can be controlled by the allocation of a common resource to jobs. In this paper, we consider the problem of scheduling jobs with arbitrary release dates and due dates on a single machine, where job-processing times are controllable and are modeled by a nonlinear convex resource consumption function. The objective is to determine simultaneously an optimal processing permutation as well as an optimal resource allocation, such that no job is completed later than its due date, and the total resource consumption is minimized. The problem is strongly N P-hard. A branch and bound algorithm is presented to solve the problem. The computational experiments show that the algorithm can provide optimal solution for small-sized problems, and near-optimal solution for medium-sized problems in acceptable computing time.

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Section: Introductionmentioning

confidence: 99%

A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

Feng

2010

Ann Oper Res

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“…Moreover, we have a lower bound on the processing time of each job due to surface quality and CNC machine power requirements. All these complicating issues make our problem more difficult and the analysis of Shabtay and Kaspi [12] cannot be extended to our case.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent study, Shabtay and Kaspi [12] considered minimizing the total completion time subject to a maximal resource constraint on parallel machines. They assume a nonlinear convex resource consumption function r j = w j p k j where p j is the processing time of job j, r j is the amount of resource allocated to job j, w j is a job specific constant and k is a negative exponent which is same for all jobs.…”

Section: Introductionmentioning

confidence: 99%

Scheduling parallel CNC machines with time/cost trade-off considerations

Gürel

Aktürk

2007

Computers & Operations Research

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When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well-known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. We also know that scheduling decisions are quite sensitive to the processing times. Therefore, this paper considers minimizing total manufacturing cost (F 1 ) and total completion time (F 2 ) objectives simultaneously on identical parallel CNC turning machines. Since decreasing processing time of a job increases its manufacturing cost, we cannot minimize both objectives at the same time, so the problem is to generate non-dominated solutions. We consider the problem of minimizing F 1 subject to a given F 2 level and give an effective formulation for the problem. For this problem, we prove some optimality properties which facilitated designing an efficient heuristic algorithm to generate approximate non-dominated solutions. Computational results show that proposed algorithm performs almost equal with the GAMS/MINOS commercial solver although it spends much less computation time. ᭧

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“…Jansen and Mastrolilli [11] develop approximation schemes, Gürel et al [9] use an anticipative approach to form an initial solution, Türkcan et al [37] use a linear relaxation based algorithm for the scheduling problem with controllable processing times. Shabtay and Kaspi [25], Shabtay and Kaspi [26] and Shabtay and Steiner [28] study the scheduling problem with convex resource consumption functions. The reader is referred to Shabtay and Steiner [27] for a detailed review on scheduling with controllable processing times.…”

Section: Literature Reviewmentioning

confidence: 99%

Stochastic lot sizing problem with controllable processing times

Koca

Yaman

Aktürk

2015

Omega

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a b s t r a c tIn 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.

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Parallel machine scheduling with a convex resource consumption function

Cited by 60 publications

References 19 publications

A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

Scheduling parallel CNC machines with time/cost trade-off considerations

Stochastic lot sizing problem with controllable processing times

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