The reference point method was found to be tractable for trading-off between deviations from ideal values of all the criteria. Some criteria computations are based on dynamic programs with value iteration whose run time can be bounded by a low-degree polynomial. For designing standard PCR primers, the scheme offers in a relative gain in computing speed of up to 50: 1 over ad-hoc computational methods. Single PCR primer pairs have been used as model systems in order to simplify the quantization of the computational acceleration factors. The program has been structured so as to facilitate the analysis of large numbers of primer pairs with minor modifications. The scheme significantly increases primer design throughput which in turn facilitates the use of oligonucleotides in a wide range of applications including: multiplex PCR and other nucleic acid-based amplification systems, as well as in zip code targeting, oligonucleotide microarrays and nucleic acid-based nanoengineering.
The scheduling of jobs with stochastically independent, exponentially distributed service times on identical parallel processors is considered. General sufficient conditions for optimality in expectation of priority policies for certain cost functions are given, including cases of the weighted flow time. The priority policies under consideration may be more general than the longest expected processing time (LEPT) or the shortest expected processing time (SEPT) policy. We deal with a fixed number of processors as well as certain more general resource constraints. Finally, precedence relations between jobs given by strict interval orders are admitted and an optimality result for LEPT is stated for this situation.
n jobs are to be preemptively scheduled for processing on n machines. The machines may have differing speeds and the jobs have processing requirements which are distributed as independent exponential random variables with different means. Holding cost g(U) is incurred per unit time that the set of uncompleted jobs is U and it is desired to minimize the total expected holding cost which is incurred until all jobs are complete. We show that if g satisfies certain simple conditions then the optimal policy is one which takes the jobs in the order 1, 2, ···, n and assigns each uncompleted job in turn to the fastest available machine. In the special case in which the objective is to minimize the expected weighted flowtime, where there is a holding cost of wi
while job i is incomplete, the sufficient condition is simply w1 ≧ … ≧ wn
and λ1 w1 ≧ … ≧ λn wn
.
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