A firm operates a flow shop building kitchen cabinetry for recreational vehicles. The major activities of this process are listed below

Task Duration (hours) Predecessor 1 Predecessor 2 Predecessor 4
A 4 --
B 6 --
C 2 A
D 6 A
E 3 B C
F 3 B C
G 5 D E F
H 1 G

a. Draw the appropriate network for this project.
b. What would the cycle time be if the goal is to produce 20 units per month (the plant operates
160 hours per month)?
c. What is the theoretical minimum number of workstations needed?
d. Balance with the most following tasks heuristic. What tasks are assigned to which stations?
e. What is the efficiency of the line obtained in part d?

Station Task Time (hours) Time left (hours) Ready tasks (#followers)
A6.,B4.
1 A 4. 4. B4.,C4.,D2.
C 2. 2. B4.,D2.
2 B 6. 2. D2.,E2.,F2.
3 D 6. 2. E2.,F2.
4 E 3. 5. F2.
F 3. 2. G1.
5 G 5. 3. H(0)
H 1. 2.
Summary Statistics
Cycle time 8 hours
Time allocated (cycle time ∗ #) 40 hours/cycle
Time needed (sum of task times) 30 hours/unit
Idle time (allocated-needed) 10 hours/cycle
Efficiency (needed/allocated) 75%
Balance Delay (1-efficiency) 25%
Min (theoretical) # of stations 4

(b) The cycle time is 160/20 = 8 hours; (c) This line requires at least 30/8 = 3.75 or 4 stations; (d) A and C are in Station 1; B is in Station 2; D is in Station 3; E and F occupy Station 4; and G and H are in Station 5. (e) Efficiency is 30/40 = .75 or 75 percent.