Operations Management 6 Problems

For the next 6 questions: no credit unless work is shown; give answers to at least 3 decimal places.

1. Undergraduate advising at a large university is available on a walk-in basis. All students first register at the check-in desk. Then each waits until an advisor is available. The process diagram is shown below. The check-in activity takes, on average, 3 minutes per student. On average there are 2 students waiting to check in. Advising takes an average of 20 minutes. On average, there are 10 students waiting to see an advisor. Lines can be long so some students leave before checking. Currently, 60 students per hour arrive for advising, however, 20% of them decide to leave before checking in. The process is stable.

Check-in Advising

c. (02 points) What is the average flow time of students in the process?a. (04 points) What is the average number of students talking with advisors?

b. (04 points) What is the average number of students in the process?

2. Kid Time Toy Company currently produces 4,800 Jane Austen action dolls per month. Dolls are processed through three operations. Dolls start in operation A, once completed they are moved to operation B, and then to operation C. Direct labor workers are paid $12/hour and work 8-hours per day, 20 days per month. Information about the number of workers, direct labor content and work-in-process (WIP) is given below. Assume the plant has been in operation for several months (i.e. ignore start-up conditions)

Operation Direct Labor Content Number of workers Average WIP (# of dolls)

(minutes per doll) at operation at operation

A 3.0 2 40

B 8.0 6 120

C 5.0 3 60

a. (03 points) What is the theoretical capacity in dolls per hour of each operation?

b. (02 points) What is the theoretical capacity of the process? Justify your answer.

c. (04 points) What is the capacity utilization of the process?

d. (02 points) What is the average flow time in minutes for a doll?

e. (03 points) What is the direct labor cost per doll?

3. In measuring and evaluating the quality of banking services, analysts have found that customers regard accuracy as one of the most important characteristics. First Chicago Bank tracks accuracy by counting the number of transactions rejected (i.e. have at least one error). Over a 5 week period, First Chicago collected samples of 1000 transactions for each of 5 weeks as baseline data and recorded the number of rejected transactions. The results are below.

Week Number of transactions rejected

1 11

2 08

3 12

4 06

5 13

Total = 50

a. (05 points) Find the 3-sigma control limits and centerline for a p-chart using the baseline data above.

b. (02 points) If the results for week 6 show 18 out of 1000 transactions were rejected, what would be your interpretation of this result? Would you take any actions or not and why?

c. (02 points) If the results for week 6 show 3 out of 1000 transactions were rejected, what would be your interpretation of this result? Would you take any actions or not and why?

4. The Bank of Banks in Banks, Georgia, is thinking about re?designing its drive?in window facility after getting complaints about long waits. It is estimated that customers arrive at an average rate of 24 per hour. The average transaction time is 4 minutes. Inter-arrival times and transactions times are exponentially distributed.

(a) (06 points) Currently, there are 2 tellers. Each teller has his/her own lane for cars to wait. Assume that demand is equally divided between the tellers and no lane changing is permitted. On average, how many minutes would a customer wait in line before being served?

(b) (06 points) Suppose the bank could locate both tellers inside the bank building and have both tellers work both lanes. The next available teller serves the customer who has been waiting the longest. On average, how many minutes would a customer wait in line before being served?

5. A computer company sells an average of 400 units per week of a popular model to distributors for

$1,250 per unit, giving it a profit margin of 20%. The company currently produces four-weeks supply

per batch, with a setup cost of $2,093.75 per batch. Assume that their cost of capital is 20% per year

and that there are 50 weeks per year.

(a) (05 points) Determine the total annual cost of production and inventory for their current policy.

(b) (05 points) Determine the total annual cost of production and inventory for an economic order

size policy.

6. Mass PC Inc produces a 4-week supply of its PC Pal model when stock on hand drops to 500 units. It

takes one week to produce a batch. Demand averages 400 units per week with a standard deviation of

125 units per week.

(a) (04 points) What cycle service level is Mass PC providing its customers?

(b) (06 points) Mass PC wants to consider improving its cycle service level to

90%, 95%, and 99%;what would be the resultant impact of each of these on their reorder policy?