Practice Midterm

(I) Provide short answers to the following: (5*5=25 marks) 1. A local hardware store keeps 13 weeks of supply of Seven-inch-Hammers. On an average, the store has 500 such hammers. The net profit from selling a hammer is $3. What is the annual profit the store earns from these hammers?

$6000

2. In the EOQ formula, we do not have revenue terms. Why?

3. 180 people leave Disneyland every 5 minutes. On an average 7200 people are inside Disneyland at any time. How long, on an average does a person spend in Disneyland?

200 minutes

4. Consider a process that consists of three intermediate steps. These steps involve machines A, B and C (in that order). Every job in the process has to

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go through each intermediate step. Consider steady state and assume heavy traffic arrivals.

A 40 per/Hr

B 20 per/Hr

C 60 per/Hr

(a)What is the cycle time of this process?

3 minutes

(b) Suppose that the process is flexible and you can reorder the sequence of the steps (for instance, the order need not be A-B-C anymore, but each job has to still go thru the 3 steps). Further, a re-ordering costs $300, but in the long run, a decrease in cycle time saves you $100,000 per minute of decrease. What is your recommendation and why? nothing

5. What is the main the trade-off involved in selecting the number of periods in a simple moving average forecast?

Not included

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(II) A bank installs an ATM and observes that the customers arrive at a rate of 15 per hour and the arrivals follow a Poisson distribution. The ATM has a fixed non random service time of 3 minutes per customer. Assume steady state. (5 * 5 = 25 marks). 1. Calculate the average time spent by a customer in this system.

Plug into the formula.

2. On a particular day, it so happens that 200 customers arrived between 12.00 noon and 1.00pm. On that day, what is the probability that no customers will arrive from 1.00 pm to 1.15 pm?

Exp(-15*15/60)

3. What % of time is the ATM idle? 25%

4. Over time, the ATM machine becomes slower. If the ATM machine slows down and requires 5 minutes per customer, what happens to the utilizatilion?

100%

5. When this ATM machine breaks down, the bank resorts to a teller system. The teller takes 1 minute to serve half his customers and 5 minutes for the other half. Who is more idle, the teller or the ATM?

25%

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(III)

Consider the following project: (25 marks)

Activity Immediate Predecessors A B C A D A, B E B F C, D G D, E H F, G I E J C

Optimistic Time 2 3 1 1 2 1 1 1 2 1

Most Likely Time 3 6 3 2 4 1 1 3 5 3

Pessimistic Time 4 9 5 3 6 1 1 5 8 11

Cost to crash Per week 9000 8000 8000 11000 7000 12000 9000 11000 13500 12000

1. What is the expected completion time of the project? (5 marks)

15

2. What is the slack on activity E? (5 marks)

zero

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3. What is the probability that the project will be completed within in 15 weeks? (5 marks)

0.5

4. Suppose you are allowed to crash jobs by no more than 1 week each, develop a rational schedule to lower the expected completion time to 12 weeks. (10 marks)

Crash b e I

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(IV) The annual demand for black pens is 1000 units. Every order incurs a fixed amount of $5 per order. The annual holding cost of a pen is $1.25. The delivery lead time is 5 days. The wholesale price of a pen is $12.5. (5 *5=25 marks) 1. What is the optimal ordering policy?

Order 89.4 when inventory hits 13.7

2. How many orders should be placed?

1000/89

3. What is the total cost incurred by following the optimal policy?

12611.81

4. What is the W.I.P.?

89/2

5. What happens to the order quantity and the re-order point when a. The fixed order cost increases by 10%? Q increases. b. The wholesale price decreases by $2.5? nothing

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