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Question

13) An insurance claims processing center has six work centers, any of which can be placed into any of six physical departmental locations. Call the centers 1, 2, 3, 4, 5, and 6, and the departments A, B, C, D, E, and F. The current set of assignments is A-3, B-1, C-6, D-2, E-4, and F-5.

The (symmetric) matrix of departmental distances, in meters is

The matrix of work flow (estimated trips per day) is among centers

The firm estimates that each trip costs approximately $4.

a. What is the cost of the current assignment?

b. Use trial-and-error to find one improved assignment.

c. What is that assignment, and what is its cost?

Answer: (a) The current assignment costs 14,000 meters, or $56,000. (b,c) The optimal solution is 10,450 meters, or $41,800, with A-3, B-5, C-4, D-1, E-6, and F-2. Students may find improved solutions other than the optimal solution.

14) An assembly line with 11 tasks is to be balanced. The longest task is 2.4 minutes, the shortest task is 0.4 minutes, and the sum of the task times is 18 minutes. The line will operate for 600 minutes per day.

a. Determine the minimum and maximum cycle times.

b. What range of output is theoretically possible for the line?

c. What is the minimum number of stations needed if the maximum output rate is to be sought?

d. What cycle time will provide an output rate of 200 units per day?

Answer: Minimum cycle time is 2.4 minutes. Maximum cycle time is 18 minutes. Maximum output is 600/2.4 = 250; minimum output is 600/18 = 33.3. For maximum output, 18/2.4 = 7.5 or 8 stations will be needed. To produce 200 units per day requires a 3-minute cycle time.

15) A facility is trying to set up an assembly line, and has identified the various tasks, and their relationship to each other, as shown in the following table. They wish to produce 600 units per day, working two 8-hour shifts.

a. Draw a network diagram of precedence relationships.

b. Compute the required cycle time per unit in seconds.

c. Compute the minimum number of workstations required to produce 600 units per day.

d. Balance this line using longest processing time.

e. What is the efficiency of the line obtained in part d?

Answer: (a) The precedence diagram appears below. (b) Required cycle time is 96 seconds. (c) 2.45 or 3 workstations are needed. (d) The computer output places tasks A-B-C-D in station 1, E-F in station 2, and G-H in station 3. (e) Efficiency is about 82 percent.