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Unformatted text preview: thru m
obs
machines)
For each machine, there are n factorial order of
factorial
jobs. Jobs may also be processed on machines
in any order. (Almost 25billion possible
schedules)
schedules)
Johnson’s algorithm provides a efficient solution
to scheduling n jobs on two machines. 7 All
All Possible Schedules for
Two Jobs on Two Machines
Two Example 8.5
Job 1 2 3 4 5 Machine A 5 1 9 3 10 Machine B 2 6 7 8 4 8 Example
Example
Job 1 2 3 4 5 6 7 8 Machine A 5 7 3 0 2 5 4 7 Machine B 3 6 4 7 1 4 1 6 Results for Multiple Machines
The optimal solution for scheduling n jobs on
two machines is always a permutation schedule
(that is, jobs are done in the same order on both
machines). (This is the basis for Johnson’s
algorithm.)
algorithm.)
For three machines, a permutation schedule is
still optimal if we restrict attention to total flow
time only. Under rare circumstances, the two
machine algorithm can be used to solve the
three machine case.
When scheduling two jobs on m machines, the
problem can be solved by graphical means. 9 Assembly Line Balancing
Characteristics of the Assembly Line Balancing
Characteristics
problem.
A collection of n tasks must be completed on each
item
item
Tasks are assigned to stations. Tasks must be
sequenced properly, and certain tasks may not be
done at the same station.
The objective is to assign tasks to stations to
minimize the cycle time, C.
The general problem is difficult to solve optimally, but
effective heuristics are available. (the text discusses
one known as the ranked positional weight
technique.)
technique Schematic
Schematic of a
Typical Assembly Line
Typical 10 Reading
Reading
Textbook page 455 – 465. Selected Problems
3, 4, 5, 7, 10
3, 11...
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 Spring '14

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