Deterministic and Random Single Machine Sequencing with Variance Minimization

Vani Vina and Raghavacahari M

IIMA Working Papers from Indian Institute of Management Ahmedabad, Research and Publication Department

Abstract: This paper discusses the problem of ordering n jobs on a single machine with the objective of minimizing the variance of completion times. It is shown that for n> 18 jobs, there exits an optimal solution in which the job with the third largest processing time is always at the second position. Using the techniques of partitioning of variances 1 a general formula is given for the change in variance due to the interchange of two jobs whose positions hav nt been fixed in the sequence. Optimal sequences are obtained for n=6 and n=7. The results are extended to the random case when the processing times are random variables and the objective is to minimize the expected variance of the completion times.

Date: 1983-10-01
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Persistent link: https://EconPapers.repec.org/RePEc:iim:iimawp:wp00556

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