Deterministic and random single machine sequencing with variance minimization
Operations Research
V-shaped policies for scheduling deteriorating jobs
Operations Research
On the minimization of completion time variance with a bicriteria extension
Operations Research
New results on the completion time variance minimization
Proceedings of the workshop on Discrete algorithms
Job scheduling to minimize the weighted waiting time variance of jobs
Computers and Industrial Engineering
An efficient local search for minimizing completion time variance in permutation flow shops
Computers and Operations Research
An efficient local search scheme for minimizing mean absolute deviation of completion times
Computers and Industrial Engineering
| Hi-index | 0.01 |
We consider the problem of minimising variance of completion times when n-jobs are to be processed on a single machine. This problem is known as the CTV problem. The problem has been shown to be difficult. In this paper we consider the polytope Pn whose vertices are in one-to-one correspondence with the n! permutations of the processing times [p1, p2, …, pn]. Thus each vertex of Pn represents a sequence in which the n-jobs can be processed. We define a V-shaped local optimal solution to the CTV problem to be the V-shaped sequence of jobs corresponding to which the variance of completion times is smaller than for all the sequences adjacent to it on Pn. We show that this local solution dominates V-shaped feasible solutions of the order of 2n−3 where 2n−2 is the total number of V-shaped feasible solutions.Using adjacency structure an Pn, we develop a heuristic for the CTV problem which has a running time of low polynomial order, which is exact for n ≤ 10, and whose domination number is Ω(2n−3). In the end we mention two other classes of scheduling problems for which also ADJACENT provides solutions with the same domination number as for the CTV problem.