V-shape property for job sequences that minimize the expected completion time variance

Article Abstract:

A new sufficient condition for an optimal sequence to be V-shaped in job sequences where the expected variance of job completion times is to be minimized has been derived. The condition is satisfied by several problem instances, including those where processing times follow varying distribution patterns. The optimal sequence is V-shaped in terms of mean processing times when the number of jobs is greater than or equal to three.

Stochastic processes, Shop mathematics

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Minimization of agreeably weighted variance in single machine systems

Article Abstract:

The variance minimization problem in the presence of job-dependent weights is analyzed. It is shown that the optimal sequence to the problem is V-shaped in terms of weighted processing time when the problem is weighted in an agreeable manner. However, the job-dependent nature of the weights makes it difficult to answer many issues through the generalization of the known results for the equal weight problem.

Numerical analysis, Optimization theory, Mathematical programming

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Time-varying minimum cost flow problems

Article Abstract:

A minimum cost flow problem is studied on a time-varying network, with the objective of determining an optimal schedule to send a flow at minimum cost, from the origin to the destination.

Models, Testing, Time, Dynamic programming, Cost control

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