Scheduling jobs, with exponentially distributed processing times, on two machines of a flow shop

1973 ◽  
Vol 20 (1) ◽  
pp. 69-81 ◽  
Author(s):  
Andrew A. Cunningham ◽  
Sujit K. Dutta
Keyword(s):  
Flow Shop ◽  
Distributed Processing ◽  
Processing Times ◽  
Two Machines

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

2009 ◽  
Vol 26 (06) ◽  
pp. 715-734 ◽  
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.

Partial job order for solving the two-machine flow-shop minimum-length problem with uncertain processing times

2009 ◽  
Vol 42 (4) ◽  
pp. 1517-1522
Author(s):  
Natalia M. Matsveichuk ◽  
Yuri N. Sotskov ◽  
Frank Werner
Keyword(s):  
Flow Shop ◽  
Minimum Length ◽  
Processing Times

scholarly journals Multi-Objective Optimal Model for Task Scheduling and Allocation in a Two Machines Robotic Cell Considering Breakdowns

2020 ◽  
Keyword(s):  
Optimal Allocation ◽  
Solution Procedure ◽  
Optimal Solutions ◽  
Operational Cost ◽  
Optimal Model ◽  
Robotic Cell ◽  
Swarm Optimization ◽  
Multi Objective ◽  
Processing Times ◽  
Two Machines

This paper aimed to demonstrate a metaheuristic as a solution procedure to schedule a two-machine, identical parts robotic cell under breakdown. The proposed previous model enabled one to determine optimal allocation of operations to the machines and corresponding processing times of each machine. For the proposed mathematical model to minimize cycle time and operational cost, multi-objective particle swarm optimization (MOPSO) algorithm was provided. Through some numerical examples, the optimal solutions were compared with the previous results. MOPSO algorithm could find the solutions for problems embeds up to 50 operations in a rationale time.

Sign in / Sign up

Export Citation Format

Share Document