Unformatted text preview: constraints, not all the jobs are candidates for a position. For example, if a job has a successor, the job cannot be assigned to the last position. Hence, candidates for the last position are the ones without any successor. ● Which job to assign? 1. Eliminate all the jobs which are previously assigned, 2. Identify the candidates  jobs that have no successor or have successors all previously assigned, 3. 4QA3 F12 Among all the candidates, schedule the one with the minimum gi (lateness or tardiness). A. Gandomi 25 C
A B D
E Processing Due Lateness Job Time Date Candidate? if scheduled A
7
9
B
8
17
C
4
18
D
6
19
E
6
21
Completion time if scheduled
/
21
//
= 7+8+4+6+6=31 2/5
4QA3 F12 A. Gandomi 2117=4
32517=8
117=14
3118=13
2518=7
2119=2
3121=10 ü༏
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ü༏
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A B D C E
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26 ● The optimal solution for scheduling n jobs on two machines to minimize the makespan is always a permutation schedule (that is, jobs are done in the same order on both machines). This is the basis for Johnson’s rule. ● For n jobs on three machines problem, a permutation schedule is still optimal if we restrict attention to total 5low time only. Under rare circumstances, the Johnson’s rule can be used to solve the three machine case. ● When scheduling two jobs on m machines, the problem can be solved by graphical means. 4QA3 F12 A. Gandomi 27 Enter ●
● M2
M2 M1
M1 Exit A Conceptual View of
Every job 5irst visits Machine 1 and then Machine 2. A TwoMachine Flow Shop
Examples: o Machining and polishing, o Moulding and baking, o Repair and testing, o Typing and proo5ing (of chapters of a book), o Review and data entry (of claims), o Checkups by a nurse and a doctor (of patients). 4QA3 F12 A. Gandomi 28 ● We continue to assume that: o every machine can process one job at a time, o every job can be processed by one machine at a time and. ●
● Theorem: The optimal solution for scheduling n jobs on two machines is always a permutation schedule. A very efRicient algorithm for solving the two machine problem was discovered by Johnson (1954). Machine 1
Machine 2
4QA3 F12 Job 1 Job 2 Job 1 A. Gandomi Job 3 Job 2 Job 3 29 1. List time required to process each job at each machine. Set up a one dimensional matrix to represent desired sequence with # of slots equal to # of jobs. 2. Select smallest processing time at either machine. o If that time is on machine 1, put the job as near to beginning of sequence as possible. o If smallest time occurs on machine 2, put the job as near to the end of the sequence...
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 Spring '14

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