This article addresses the problem of sequencing a given set of jobs w
ith random processing times for uninterrupted processing on a single m
achine. The objective is to identify the ''optimal'' sequence which mi
nimizes the expected value of a ''scheduler's'' disutility (or cost) f
unction with respect to a performance measure. The general problem is
difficult to solve; however, special cases can be modeled and solved e
xactly when (1) processing times are statistically independent, (2) di
sutility functions for sequence evaluation are linear, exponential, or
quadratic, and (3) performance measures are mean flow time, mean wait
ing time, or mean lateness. Illustrative examples demonstrate that the
proposed models create sequences which are (a) influenced by both sch
edulers' risk taking behavior and the stochasticity of processing time
s, and (b) more ''realistic'' than those provided by the classical sin
gle machine models. This paper also extends the developed models to in
clude multi-dimensional deterministic single machine problems. Copyrig
ht (C) 1996 Elsevier Science Ltd