Combining time and position dependent effects on a single machine subject to rate-modifying activities

Abstract

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.

Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance

“…For their respective models, both these papers claim to solve the problem of minimizing the makespan and the problem of minimizing the total ‡ow time in O n K+1 log n time each. However, Rustogi and Strusevich (2014) show that both these papers underestimate the running time needed to solve the problem of minimizing the total ‡ow time and calculate the running time to be O n K+2 for both cases. Rustogi and Strusevich (2014) also show that the running times of O n K+1 log n and O n K+2 are applied to a range of much more general problems with group dependent combined e¤ects.…”

“…O n K+1 log n O n2 K K log K Rustogi and Strusevich (2014) This paper Table 1: Running times of the algorithms for the relevant problems K MPs to include into a schedule, in which order to perform them, and when to start each of them in order to minimize an objective function F of the job completion times. The jobs are subject to job-independent group-dependent deterioration e¤ects, while the duration of an MP is either constant or also depends on its starting time.…”

“…The resulting algorithms can be applied to handling simpler problems, with job-independent start-time e¤ects only. However, as shown by Rustogi and Strusevich (2014), in the case of minimizing the total ‡ow time P C j it is not possible to reduce the multiple n K in the running time estimates, even if simpler problems, with start-time dependent e¤ects only, are considered. For the problems in which is it required to determine how many of K available MPs should be inserted into a schedule and how to order the groups and the jobs within the groups, Table 1 demonstrates how the running times of known solution algorithms change for various e¤ects and objective functions.…”

“…The decision-maker determines how many of Linear Start-Time Dependent Group-Dependent Deterioration E¤ects P C j C max Group-Dependent O n K+2 O n K+1 log n Positional E¤ects Rustogi and Strusevich (2014) Rustogi and Strusevich (2014) …”

Multitasking Scheduling Problems with Deterioration Effect

“…The work then was extended in two aspects. Most focused on the machine perspective (e.g., [31][32][33][34][35][36]). However, some work focused on the human behavior perspective (e.g., [17,37,38]).…”