No-wait scheduling of a two-machine flow-shop to minimise the makespan under non-availability constraints and different release dates (original) (raw)

Minimizing makespan in a two-machine no-wait flow shop with batch processing machines

The International Journal of Advanced Manufacturing Technology, 2012

Given a set of jobs and two batch processing machines (BPMs) arranged in a flow shop environment, the objective is to batch the jobs and sequence the batches such that the makespan is minimized. The job sizes, ready times, and processing times on the two BPMs are known. The batch processing machines can process a batch of jobs as long as the total size of all the jobs assigned to a batch does not exceed its capacity. Once the jobs are batched, the processing time of the batch on the first machine is equal to the longest processing job in the batch; processing time of the batch on the second machine is equal to the sum of processing times of all the jobs in the batch. The batches cannot wait between two machines (i.e., no-wait). The problem under study is NP-hard. We propose a mathematical formulation and present a particle swarm optimization (PSO) algorithm. The solution quality and run time of PSO is compared with a commercial solver used to solve the mathematical formulation. Experimental study clearly highlights the advantages, in terms of solution quality and run time, of using PSO to solve large-scale problems.

A heuristic for scheduling two-machine no-wait flow shops with anticipatory setups

Operations Research Letters, 2000

We consider a problem of scheduling jobs in two-machine no-wait ow shops for which the objective is to minimize the makespan. Each job, upon completion of its processing on the ÿrst machine, must be transferred immediately to the second machine due to a no-wait in process constraint. Every job requires a setup time on each machine before it is processed. The setup on the second machine is anticipatory, since it can be performed in advance of an arriving job, and consists of two parts. During the ÿrst part of the setup, the job should not be present in the machine, while the second part of setup can be done in the presence or absence of the job. A heuristic algorithm is proposed, and its worst-case performance ratio of 4=3 is established.

Minimising Makespan in the Two-Machine Flow-Shop with Release Times

The Journal of the Operational Research Society, 1998

This paper considers the two-machine¯ow-shop problem with the objective of minimising the makespan subject to different release times. In view of the strongly NP-hard nature of this problem, ®ve lower bounds and two new dominance criteria are proposed together with a decomposition procedure that reduces the problem size by setting jobs at the beginning of the sequence. Several branch and bound procedures are described by applying different lower bounds and branching schemes. A detailed computational campaign has been performed on different kinds of instances testing problems with size up to 200 jobs.

Two-machine flow shop scheduling problems with no-wait jobs

Operations Research Letters, 2005

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 43-approximation algorithm.