Flow-shop scheduling with a learning effect

Abstract

The paper is devoted to some flow-shop scheduling problems with a learning effect. The objective is to minimize one of the two regular performance criteria, namely, makespan and total flowtime. A heuristic algorithm with worst-case bound m for each criteria is given, where m is the number of machines. Furthermore, a polynomial algorithm is proposed for both of the special cases: identical processing time on each machine and an increasing series of dominating machines. An example is also constructed to show that the classical Johnson's rule is not the optimal solution for the two-machine flowshop scheduling to minimize makespan with a learning effect. Some extensions of the problem are also shown.

On flowshop scheduling problems with the aging effect and resource allocation

“…Proof The proof is similar to that provided by Wang and Xia [30] for a problem with the learning effect. Thus, based on [21] and Eq.…”

Genetic algorithm applied to the flow shop scheduling problem under effects of fuzzy learning and deterioration with a common fuzzy due date

“…4(10), 306-316. Available from: www.prosoc.eu 308 (2008), Wang and Xia (2005), Lee and Wu (2004), Janiak and Rudek (2009). Deterioration effect denotes that processing time of a job increases as regards to a function dependent on its starting time while that job is being processed on a machine or waiting in the queue.…”

“…Wang and Xia (2006) investigated linear deterioration effect on flow shop scheduling problems these are makespan minimisation and weighted sum of completion time minimisation, respectively. In another study of Wang and Xia (2005), learning effect was considered for flow shop scheduling makespan and flow time problems. Lee and Wu (2004) considered learning effect in a two-machine scheduling problem that's objective is to minimise the total completion time.…”

Review on Job-Shop and Flow-Shop Scheduling Using

“…When there are no further improvements in the current Pareto front, the second phase starts. Wang 83 devoted to some flow-shop scheduling problems with a learning effect. The objective is to minimize one of the two performance criteria, makespan and total flowtime.…”