Scheduling Deteriorating Jobs on a Single Processor

Abstract

A^ jobs are to be processed sequentially on a single machine. While waiting for processing, jobs deteriorate, causing the random processing requirement of each job to grow at a job-specific rate. Under such conditions, the actual processing times ofthe jobs are no longer exchangeable random variables and the expected makespan is no longer invariant under any scheduling strategy that disallows idleness. In this paper, we analyze the effects of different deterioration schemes and derive optimal scheduling policies that minimize the expected makespan, and, for some models, policies that minimize the variance of the makespan. We also allow for random setup and detaching times. Applications to optimal inventory issuing policies are discussed and extensions are considered.

Combining time and position dependent effects on a single machine subject to rate-modifying activities

“…If a > 0, we have a deterioration effect and, if a < 0, we have a learning effect. For this model, polynomial-time algorithms for minimizing the makespan and for minimizing the total flow time follow from [20] and [22], respectively.…”

“…The expression (20) for the positional weights can be written in terms of the original parameters by using (7), (19), (13) and (10). All values…”

“…The quantities W [x] (r) as defined earlier for a single machine by (20) can be redefined as W [i,x] (r) , with the group index [x] being replaced by [i, x], so that an explicit reference can be made to the machine a particular group is associated with. Additionally, the factors W [i,x] (r) , will also incorporate the speed s i , 1 ≤ i ≤ m, of a machine, as shown in [2].…”

“…Similarly, to solve problem 1 |P osi, RM P (k − 1)| C j , the required positional weights can be obtained by making relevant substitutions in (20), so that we have…”

“…Similarly, to solve problem 1 |T ime, RM P (k − 1)| C j , the required positional weights can be obtained by making relevant substitutions in (20), so that we have Thus, each of the problems 1 |T ime, RM P (k − 1)| C max and 1 |T ime, RM P (k − 1)| C j can be solved by Algorithm Generate in O n k log n (k−1)! time; see Theorem 1.…”