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Citation for this version held on GALA:Rustogi, Kabir and Strusevich, Vitaly (2014) Combining time and position dependent effects on a single machine subject to rate-modifying activities. London: Greenwich Academic Literature Archive. We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and timedependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, e.g., maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects, on one hand, and between the positional effects and the start-time dependent effects, on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

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.

We consider the classical scheduling problems of processing jobs on identical parallel machines to minimize (i) the makespan (the maximum completion time) or (ii) the total flow time (the sum of the completion times). The focus of this study is on the impact that additional machines may have, if added to the system. We measure such a machine impact by the ratio of the value of the objective function computed with the original number of machines to the one computed with extra machines. We give tight bounds on the machine impact for the problem of minimizing the makespan, for both the preemptive and non-preemptive versions, as well as for the problem of minimizing the total flow time. We also present polynomial-time exact and approximation algorithms to make a cost-effective choice of the number of machines, provided that each machine incurs a cost and the objective function captures the trade-off between the cost of the used machines and a scheduling objective.

We study single machine scheduling problems with linear time-dependent deterioration e¤ects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration e¤ects, i.e., all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional e¤ects.

We address the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date. This is a basic problem with applications to the just-in-time manufacturing. The problem is linked to a Boolean programming problem with a quadratic objective function, known as the half-product. An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the problem is identified and implemented. The running time matches the best known running time for an FPTAS for minimizing a half-product with no additive constant.