Showing papers on "Single-machine scheduling published in 1978"

Technical Note—Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties

Abstract: We consider a single-machine scheduling problem where penalties occur for jobs that either commence before their target start date or are completed after their due date. The objective is to minimize the maximum penalty subject to certain assumptions on the target start times, due dates, and penalty functions. A more efficient algorithm than the existing one is presented for this problem. The number of computations in the proposed algorithm is of the order of n log n, while in the existing algorithm it is of the order of n2.

Minimization of Time-Varying Costs in Single-Machine Scheduling

Abstract: Suppose n jobs are to be processed consecutively by a single machine, without interruption and without idle time. Each job j has a known processing time pj and has associated with it a time-varying cost density function cj. The cost of processing job j in the time interval [t-pj, t] is Cjt = ∫t-pjtcjudu. We show that if the cost density functions of the jobs satisfy certain simple conditions, a sequence minimizing total cost is easily obtained. This result generalizes the well-known "ratio rule" of W. E. Smith for minimizing total weighted completion time and is applicable to problems involving discounted linear delay costs, discounted linear processing costs, discounted resetting and processing costs, and linear combinations of these costs. Moreover, we show that for such costs, sequences that are optimal subject to series parallel precedence constraints can be found in 0n log n time.