Twelve tasks, with times and precedence requirements as shown in the following table, are tobe assigned to workstations using a cycle time of 1.5 minutes. Two heuristic rules will be tried:(1) greatest positional weight, and (2) most following tasks.In each case, the tiebreaker will be shortest processing time. TaskLength(minutes)ImmediatePredecessora 0.1 —b 0.2 ac 0.9 bd 0.6 ce 0.1 —f 0.2 d, eg 0.4 fh 0.1 gi 0.2 hj 0.7 ik 0.3 jl 0.2 k a. Draw the precedence diagram for this line.b. Assign tasks to stations under each of the two rules.c. Compute the percentage of idle time for each rule

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 111P
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Twelve tasks, with times and precedence requirements as shown in the following table, are to
be assigned to workstations using a cycle time of 1.5 minutes. Two heuristic rules will be tried:
(1) greatest positional weight, and (2) most following tasks.
In each case, the tiebreaker will be shortest processing time.

Task
Length
(minutes)
Immediate
Predecessor
a 0.1 —
b 0.2 a
c 0.9 b
d 0.6 c
e 0.1 —
f 0.2 d, e
g 0.4 f
h 0.1 g
i 0.2 h
j 0.7 i
k 0.3 j
l 0.2 k

a. Draw the precedence diagram for this line.
b. Assign tasks to stations under each of the two rules.
c. Compute the percentage of idle time for each rule

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