Exact distribution of the makespan in a two machines flow shop with two kinds of jobs

Abstract In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $$m \ge 2$$ m ≥ 2 of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are 0. Previously, polynomial time algorithms have only been known for two machines.

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An Optimal Algorithm for a Special Flow Shop Problem with Infinite Buffer Capacity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.101-102.379 ◽

2011 ◽

Vol 101-102 ◽

pp. 379-382

Author(s):

Qi Wei

Keyword(s):

Buffer Capacity ◽

Flow Shop ◽

Optimal Algorithm ◽

Special Flow ◽

Flow Shop Problem ◽

Two Machines

In this paper, a two-machine flow shop problem with infinite buffer capacity is considered. Each of jobs is identical and has two tasks. The first task can be processed on either machine, called flexible task, while the second task must be processed on the second machine and can't be processed unless the first task has been processed. There is infinite buffer capacity between two machines. The problem is to determine the assignment of the flexible tasks to the machines for each job, with the objective of maximizing the makespan. We present an optimal algorithm for this problem.

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TWO-MACHINE FLOW-SHOP MINIMUM-LENGTH SCHEDULING WITH INTERVAL PROCESSING TIMES

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595909002432 ◽

2009 ◽

Vol 26 (06) ◽

pp. 715-734 ◽

Cited By ~ 14

Author(s):

C. T. NG ◽

NATALJA M. MATSVEICHUK ◽

YURI N. SOTSKOV ◽

T. C. EDWIN CHENG

Keyword(s):

Flow Shop ◽

Probability Distributions ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Minimum Length ◽

Lower And Upper Bounds ◽

Minimal Set ◽

Processing Times ◽

Necessary And Sufficient ◽

Two Machines

The flow-shop minimum-length scheduling problem with n jobs processed on two machines is addressed where processing times are uncertain: only lower and upper bounds of the random processing times are given before scheduling, but their probability distributions are unknown. For such a problem, there may not exist a dominant schedule that remains optimal for all possible realizations of the processing times and so we look for a minimal set of schedules that are dominant. We obtain necessary and sufficient conditions for the case when it is possible to fix the order of two jobs in a minimal set of dominant schedules. The necessary and sufficient conditions are proven for the case when one schedule dominates all the others. We characterize also the case where there does not exist non-trivial schedule domination. All the conditions proven may be tested in polynomial time of n.

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Two Stage Flow Shop Scheduling Model Including Transportation Time with Equipotential Machines at Every Stage

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.l2740.1081219 ◽

2019 ◽

Vol 8 (12) ◽

pp. 5090-5094

Keyword(s):

Processing Time ◽

Parallel Machines ◽

Flow Shop ◽

Solution Algorithm ◽

Flow Shop Scheduling ◽

Two Stage ◽

Transportation Time ◽

Shop Scheduling ◽

Scheduling Model ◽

Two Machines

This study presents a solution algorithm for the problem of minimizing the makespan on equipotential parallel machines at every stage in two stage flow shop scheduling model. The processing time of all the jobs on all the two machines is given and the time for which parallel equipotential machines are available is also given. Transportation time for moving the jobs from first machine to second machine is also taken into consideration. A mathematical illustration is also given in support of the algorithm proposed

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Solving Permutation Flow Shop Scheduling Problems with Job Idle Time in between Two Machines

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.531-532.699 ◽

2012 ◽

Vol 531-532 ◽

pp. 699-702

Author(s):

A. Baskar ◽

Anthony M. Xavior

Keyword(s):

Flow Shop ◽

Flow Shop Scheduling ◽

Shop Floor ◽

Bench Mark ◽

Scheduling Problem ◽

Optimal Sequence ◽

Shop Scheduling ◽

Permutation Flow Shop Scheduling ◽

Permutation Flow Shop ◽

Two Machines

Finding an optimal sequence in terms of total completion time for processing ‘n’ jobs in ‘m’ processing centers in the shop floor is an important job for a shop floor supervisor. The problem is NP hard as the total number of sequences is (n!) for a permutation flow shop scheduling problem. Starting from Johnson’s Algorithm, many classical Heuristics were proposed in earlier days. After the invention of evolutionary algorithms and Meta Heuristics, finding an optimal sequence becomes comparatively easier. This paper deals with improving one such performance parameter, the make span, in a Permutation Flow Shop Scheduling problem in case of job idle times (though machines are available, jobs are not) observed in between two machines. The case of three machines, n jobs has been analyzed using the well known Taillard bench mark problems by coding in MATLAB R2008a and a new procedure has been proposed.

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