Proof of a conjecture of Schrage about the completion time variance problem
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Cited by (52)
Time-flexible min completion time variance in a single machine by quadratic programming
2024, European Journal of Operational ResearchA multi-machine scheduling solution for homogeneous processing: Asymptotic approximation and applications
2022, International Journal of Production EconomicsAn almost exact solution to the min completion time variance in a single machine
2021, European Journal of Operational ResearchCitation Excerpt :In this respect, Schrage (1975) characterized the first position of the optimal sequence, by proving that the longest job is always scheduled first. Hall and Kubiak (1991) characterized the second and last positions of the optimal sequence, verifying that the second largest job must be placed last and the third largest job must be situated in the second position. Similarly, bounds for the position of the smallest job in the CTV problem are established by Manna and Prasad (1999).
Completion time variance minimisation on two identical parallel processors
2017, Computers and Operations ResearchCitation Excerpt :Discussion: Since start of job processing on a machine can be delayed, an optimal job sequence on any machine can be obtained as if we were solving a (1||CTV) problem. Hence, the proof follows from Theorem 1 in Hall and Kubiak (1991) and Theorem K in Merten and Muller (1972). Discussion: As the two longest jobs have to be assigned to each of the two machines, this is a direct extension of Property 3.
An exact algorithm to minimize mean squared deviation of job completion times about a common due date
2013, European Journal of Operational ResearchAn efficient local search for minimizing completion time variance in permutation flow shops
2012, Computers and Operations Research