J. Mittenthal et M. Raghavachari, STOCHASTIC SINGLE-MACHINE SCHEDULING WITH QUADRATIC EARLY-TARDY PENALTIES, Operations research, 41(4), 1993, pp. 786-796
Citations number
20
Categorie Soggetti
Management,"Operatione Research & Management Science","Operatione Research & Management Science
We address the problem of scheduling n jobs on a single machine, which
is subject to random breakdowns, to minimize an expected sum of nonre
gular penalty functions. A simple recourse model is considered when th
e penalty function is the squared deviation of job completion times fr
om a common due date, and a deterministic equivalent objective functio
n is developed. Characterizations of optimal schedules for this quadra
tic objective function are established both when the common due date i
s a decision variable and when it is given and fixed. Most importantly
, the V-shaped nature of optimal schedules is investigated for a class
of Poisson processes, {N(t), t > 0}, describing the number of breakdo
wns in the interval (0, t). In addition, relationships to a class of b
icriteria models are demonstrated.