One Machine Scheduling Problem with Fuzzy Random Due-Dates

Authors: Takeshi Itoh¹; Hiroaki Ishii²

Source: Fuzzy Optimization and Decision Making, Volume 4, Number 1, February 2005 , pp. 71-78(8)

Publisher: Springer

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Abstract:

In many classical or basic scheduling models, jobs’ processing times and due-dates are crisp values. Recently, they have been formulated as uncertain values in some more actual models. That is the introduction of ‘‘fuzziness’’. However, in a real situation of decision making, there exists uncertainty that can not be described only by fuzziness. In this paper, we propose an n-job, one machine scheduling model, where due-dates for jobs are fuzzy random variables. In the model, jobs’ processing times are crisp, and we assign satisfaction levels to jobs’ completion times according to membership functions. They are non-increasing functions, but their support positions depend upon the expected due-dates, which are exponentially distributed random variables.

Keywords: one machine scheduling; fuzzy random variable; exponential distribution; binary search

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10700-004-5571-4

Affiliations: 1: Faculty of Information Science, University of Marketing and Distribution Sciences, 3-1 Gakuen-Nishi, Nishi, Kobe, 651-2188, Japan , Email: takeshi@umds.ac.jp 2: Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0871, Japan,

Publication date: 2005-02-01