The single machine scheduling problem with setup times under an extension of the general learning and forgetting effects

This paper addresses the optimization of a single machine scheduling problem with additional constraints which are sequence-independent setup times and time-dependent learning and forgetting effects. The considered objective function is to minimize the maximum completion time (makespan). We define a...

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Bibliographic Details
Published in:Optimization letters Vol. 15; no. 4; pp. 1327 - 1343
Main Authors: Muştu, Settar, Eren, Tamer
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Setup time
Pseudo polynomial time algorithm
Learning effect
Forgetting effect
Complexity
ISSN:1862-4472, 1862-4480
Online Access:Get full text
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Summary:This paper addresses the optimization of a single machine scheduling problem with additional constraints which are sequence-independent setup times and time-dependent learning and forgetting effects. The considered objective function is to minimize the maximum completion time (makespan). We define a bivariate general learning and forgetting model consisting of two independent variables which are the sum of normal processing times of previous jobs in the schedule and the setup time of the present job. We demonstrate some global properties of an optimal schedule and prove that the problem is ordinary NP-hard by means of a polynomial transformation from a known decision problem to the decision version of the considered problem. Furthermore, we propose an integer non-linear programming model and a dynamic programming model which can be executed in pseudo-polynomial time.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-020-01641-9