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Question

Station Task Time (hours) Time left (hours) Ready tasks (#followers)
A(6),B(4)
1 A 4. B(4),C(4),D(2)
C 2. 2. B(4),D(2)
2 B 6. 2. D(2),E(2),F(2)
3 D 6. 2. E(2),F(2)
4 E 3. 5. F(2)
F 3. 2. G(1)
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.

10) There are three work centers (A, B, and C) behind the financial aid counter at a nearby university. They can each fit into any of three office spaces (1, 2, and 3) off the corridor behind the desk. There is no student contact in these areas, only workers. The distance 1-2 is 20 feet, 2-3 is 30 feet, and 1-3 is 50 feet. The matrix of work (trips per day) at the three centers is in the following table. Remember that each trip must be a round-trip (from 1 to 2 and back, for example).


A B C
A -- 20 0
B 45 -- 25
C 60 0 --

a. How many possible assignments are there? List them.

b. Calculate the total distance traveled in each of these assignments.

c. Which assignment minimizes distance traveled?

Answer: (a) There are 3! = 6 assignments, listed in the table below. (b) The cost, in feet, of each assignment appears in the table below. (c) The lowest cost assignment is A-2, B-1, C-3.


A B C Cost
1 2 3 10,100
1 3 2 10,400
2 1 3 8,700
2 3 1 8,800
3 1 2 11,100
3 2 1 10,900

11) Hemo-tech, Inc., a biomedical technology and research laboratory, produces a standard blood filtering device on an assembly line basis. Six basic tasks are performed along an assembly line. The time to perform each task and the tasks that must immediately precede each task are in the table below. Twenty pumps per 450-minute day must be produced by the assembly line.

Answer

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