Assignment 2

1. A producert purchases an item at the rate of Rs 10/- per piece from a manufacturer. The annual requirement is 2000 units of the item, while the cost per order is Rs 15/- and the holding cost is Rs 8/- per annum. There is a requirement of 5 square feet to store the item.

1. Calculate the economic order quantity (EOQ) of a product. (3 marks)

2. Calculate the cost of maintaining the inventory. (3 marks)

3. Calculate the reorder level of the products if lead time is 20 days. (3 marks)

4. If the stock out cost is Rs. 10/- per unit per month, calculate the EOQ level. (3 marks)

5. If maximum storage capacity is 300 square feet, calculate the EOQ level. (2 marks)

6. If a discount of 2% is offered for orders greater than 50 units but less than 100 units and 3% discount is offered for orders equal or greater than 100 units, calculate the inventory costs for the following scenarios:

1. Order size <=50

2. 50 < Order size < 100

3. 100 <= Order size (9 marks)

7. Calculate the EOQ if the total budget available to purchase the material is Rs. 1,000/-.

(2 marks)

(Total: 25 marks)

2. A person designing digital art works finds that the time spent on an art work follows Exponential distribution with mean 20 minutes. If the art works aredesigned in the order in which they come in and their arrival is approximately follows Poisson distribution with an average rate of 15 per 8-hour day.

1. What is the probability that the queuing system is empty? (4 marks)

2. What is the probability that the designer is idle? (2 marks)

3. How many hours do the designer idles per day? (2 marks)

4. What is the average length in the queue? (2 marks)

5. On average how many art works are there at the designer in a day? (2 marks)

6. What is the average waiting time for art works? (2 marks)

7. What is the probability that there are 4 art works to be designed? (2 marks)

8. What is the probability that there are more than 8 art works to be designed? (2 marks)

9. What is the waiting time of an art work in the queue? (2 marks)

10. If the arrival rate of art works has doubled per hour, how many designers are required to provide an equilibrium level of service? (5 marks)

(Total: 25 marks)

3. The following table gives data on time and cost of a project.

Activity	Preceding activity	Normal Time (days)	Crash time (days)	Normal Cost (Rs.)	Crash cost (Rs.)
A	-	2	1	10000	15000
B	-	8	5	15000	21000
C	A	4	3	20000	24000
D	B	1	1	7000	7000
E	B	2	1	8000	15000
F	C,D	5	3	10000	16000
G	E	6	2	12000	36000

a) Construct the network diagram for this project. (6 marks)

b) Find the critical path of the project. (1 mark)

c) Find the total project cost and duration. (2 marks)

d) To shorten the project by 3 weeks at the lowest possible cost, which task(s) should be shortened? (15 marks)

e) What would be the new cost after shortening of the project? (1 mark)

(Total: 25 marks)

4. A company manufactures 30 items per day. The demand of these items during the past 20 days are listed below.

35

28

24

29

27

21

30

35

35

29

23

32

30

26

17

25

26

40

31

28

1. Randomly identify 10 values out of them to carry out a simulation. (For the purpose of this examination, use the random number table given below and carry out the generation of random numbers starting from its top left hand corner value in vertical direction). (10 marks)

2. Describe how you selected the values. (5 marks)

3. Estimate the profit/ loss of the company for the next 10 days, if the profit per unit of sold products is Rs. 100/- and the loss per unit from unsold products at the end of the day is Rs. 30/-. (10 marks)

(Total: 25 Marks)