The single-machine absolute-deviation early-tardy problem with random completion times

Abstract

We consider sequencing n jobs on a single machine subject to job completion times arising from either machine breakdowns or other causes. The objective is to minimize an expected weighted combination of due dates, completion times, earliness, and tardiness penalties. The determination of optimal distinct due dates or optimal common due dates for a given schedule is investigated. The scheduling problem for a fixed common due date is considered when random completion times arise from machine breakdowns. The optimality of a V‐shaped about (a point) T sequence is established when the number of machine breakdowns follows either a Poisson or a geometric distribution and the duration of a breakdown has an exponential distribution. © 1996 John Wiley & Sons, Inc.

Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem

“…with an arbitrary pdf (i.e., p k $ f(.)) (e.g., [7]), using (7) and Corollary 2, a sequence [1], . .…”

“…. , 5, are respectively f ðtÞ ¼ 4 ffi ffi t 3 p =243, 0 < t < 27, exponential with mean 4 (i.e., exp(0.25)), gamma with shape a = 3 and scale b = 2.5 parameters (i.e., G(3, 2.5)), uniform between 1 and 13 (i.e., U [1,13]), and Weibull with scale a = 0.3 and shape b = 0.5 parameters (i.e., W(0.3, 0.5)). (In this paper, we utilize some 5-job problems to illustrate, without loss of generality, our proposed solution strategies.…”

“…, or (2) n [1] P Á Á Á P n [n] and t [1] P Á Á Á P t [n] . Jang [15] also studies the latter case and suggests that an optimal sequence exists in which job i appears before job j, i 5 j 2 N, if either (i) t i < t j and CV i PCV j , or (ii) t i P t j and n i P n j .…”

“…, n, s P 3.1 (i.e., processing time means and variances are proportional). In this case, a sequence [1], . .…”

“…The use of this measure is justified due to the emphasis on Just-In-Time (JIT) scheduling where jobs must be completed on their due dates, neither earlier nor later. The available literatures on this problem deal with either the deterministic case (e.g., [4,11,20,21,29]) or the stochastic case (e.g., [1,10,18,28]). Both of these cases consider cost functions that depend on the amount of deviations of job completion times from their due dates (i.e., job earliness time and tardiness time).…”