Opsearch, Vol. 34, No. 2, 1997
0030-3887/95 $ 2.00 + 0.00
© Operational Research Society of India
SHORT NOTE
Sequencing with Restrictions in Processing Times
P.C. Bagga
Moti Lal Nehru College (E), University of Delhi
&
Ambika Bhambani
Jesus and Mary College, University of Delhi
Abstract
Johnson, Szwarc gave the algorithm for obtaining the sequence which
minimizes the total elapsed time for n-jobs-3 machines problem when the
processing time of jobs on these machines possess certain conditions.
This paper yields the algorithm for general flow shop problems.
1. INTRODUCTION
In-n-job m-machine flow shop problem, the aim is to obtain a sequence
of jobs which' when processed on these machines (in the predefined order
of machines) minimizes the total elapsed time.
Johnson gave the algorithm for n-job 3-machine problem when
(i) Y(i,l) Y(j,2)
( ii ) Y ( i , 3) Y ( j , 2 )
Szwarc gave the algorithm when
-tt-i & j ; i :F j
-V-i & j ; i :F j
(iii) Y ( i , 1 ):S; Y ( j , 2) ; -tt- i & j ; i :F j
(iv ) Y ( i , 3):s; Y ( j , 2 ) ; -V- i & j ; i :F j
Where Y ( i, k) is the processing time of job i on machine k
(i= 1,2, ... ,n; k= 1,2,3)
The present paper extends these to m machine case and provides a
simple algorithm when the processing time of jobs satisfy certain conditions.