Weighted tardiness single machine scheduling with proportional weights

Article Abstract:

Solutionto the single machine weighted tardiness scheduling problem is examined. This problem, first studied by Arkin and Roundy (1991), involves scheduling a specific number of jobs on a single machine such that total tardiness is minimized. The special case wherein tardiness penalties are proportional to theprocessing times is analyzed using a decomposition mechanism that can either solve the problem or reduce it significantly into a smaller version. Problem decomposition involves three types of adjacent job orderings, which successfully solves 155 out of 320 test problems with job sizes between 20 and 150. Arkin and Roundy's algorithm is then used to solve the the 163 unsolved but reduced problems with a maximum job size of 25. The two remaining unsolved problems have job sizes of 30 and 45.

Models, Scheduling (Management), Methods engineering

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Reduced system algorithms for Markov chains

Article Abstract:

The steady state probabilities of a Markov chain can be found by solving a reduced system of equations. The reduced set of equations is derived from partitioning the transition probability matrix. Markov chains are categorized as standard or nonstandard depending on the location of an invertible submatrix. A backward recursion is used for finding algorithms for determining the steady state probabilities for standard systems, and a forward recursion is used for nonstandard systems. The first passage time distribution and its mean and variance can be found with the backward recursion.

Operations research, Research, Management science, Analysis, Algorithms, Queuing theory

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