چکیده:
Single machine, distinct due dates, early (lately) machine problem and fuzzy environment closely to the situation faced by '' just in time '' manufacture. This paper attempts to sequence the jobs on a single machine scheduling problem with distinct due dates under fuzzy environment so as to minimize the total penalty cost. This cost is the composition of all the total earliness and tardiness cost. A method to minimize the total penalty cost due to earliness or lateness of job in fuzzy environment is proposed. A numerical example is given in the sake of the paper to support this study.
خلاصه ماشینی:
A. Khalifa* Mathematics Department, College of Science and Arts, Al- Badaya, Qassim University, Saudi Arabia Abstract This research article proposes a single machine scheduling problem subject to distinct due dates in fuzzy environment.
Mohamad and Said in (2011) studied -job single machine scheduling problem with common due date so as to minimize the sum of the total inventory and penalty costs.
Jadhav and Bajaj (2012) proposed - jobs to processed on single machine scheduling problem with fuzzy processing and fuzzy due dates so as to minimize the total penalty cost in the schedule.
Ponnalagu and Mounika (2018) considered the sequence performance measurements and job mean Koulamas and Kyparisis (2019) shown that the single machine scheduling problem with past- sequence- dependent setup times and either the minimum maximum lateness/ tardiness objective was solvable by an index priority rule followed by backward intentions of certain qualifying jobs.
In this article, the research objective is to consider the sequence of the jobs on a single machine with fuzzy due dates so as to minimize the total penalty cost.
Section 4 formulate single machine scheduling problem with processing time represented as (α, β) interval valued fuzzy bi-objective criteria.
Penalty cost for earliness {مراجعه شود به فایل جدول الحاقی} jobs having( , )interval- valued fuzzy numbers due dates [( , , ; ), (a, s, b; β)] which are converted into its average high ranking using the signed distance as in Definition 4 and referring to the solution approach in Section 5, the near optimal sequence is S=2>5>1>4>7>3>6.