Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan

2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Single-machine scheduling with deteriorating jobs under a series-parallel graph constraint

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

Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants

Scheduling problems with the effects of deterioration and learning

Author name used in this publication: T. C. E. Cheng2006-2007 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models

AbstractThis paper concerns scheduling problems with the aging effect and additional resource allocation. A measurable result of the aging phenomenon is that the time required to perform a job increases whereas the additional resource allocation allows one to decrease it. As an example of a deteriorating system that can be described and optimized by the application of the models and algorithms considered, we choose the pickling process, where cleaning of metal items decreases the efficiency of the pickling (cleaning) bath (i.e., one containing an active substance), whereas heating it up can improve the efficiency. In particular, we focus on the optimization problems for such systems and model them as single-machine scheduling problems with job processing times dependent on the fatigue of a machine and on the allocation of additional resources. The objectives considered are the minimization of time criteria (the maximum completion time and the maximum lateness) under a given resource consumption as well as the minimization of the resource consumption under given time criteria. The computational complexity of the problems is determined and solution properties are proved. On the basis of these, we construct optimal polynomial time algorithms for some cases of the problems considered

Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming (MIP) model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions

Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming (MIP) model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions

Single machine scheduling with a generalized job-dependent cumulative effect

We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time