This assignment is based on the concepts of inventory models, queuing models, network models and simulation.

Question 1

A dealer supplies you the following information regarding a product dealt-in by him:

Annual demand = 10,000 units

Ordering cost = Rs. 1,000 per order

Holding cost = Rs. 400 per month

Price = Rs. 20 per unit

To store the product 10 square feet is required.

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

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

c)Calculate the reorder level of the products if lead time is 5 days.(3 marks)

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

e)If maximum storage capacity is 200 square feet, calculate the EOQ level. (2 marks)

f)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:

i)Order size

ii)50

iii)100

g)Calculate the EOQ if the total budget available to purchase the material is Rs. 10,000/-.

(2 marks)

(Total: 25 marks)

Question 2

A branch of a bank has only one typist. Since the typing work varies in length (number of pages to be typed), the typing rate is randomly distributed approximating a Poisson distribution with mean service rate of 8 letters per hour. The letters arrive at a rate of 5 per hour during the entire 8-hour workday. The typewriter is valued at Rs. 100 per hour.

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

b)What is the probability that the typist is idle?(2 marks)

c)How many hours do the typist idles per day?(2 marks)

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

e)On average how many letters are there at the typist in a day?(2 marks)

f)What is the average waiting time for letters? (2 marks)

g)What is the probability that there are 4 letters to be typed?(2 marks)

h)What is the probability that there are more than 8 letters to be typed?(2 marks)

i)What is the waiting time of a letter in the queue?(2 marks)

j)If the arrival rate of letters has 2per hour, how many typists are required to provide an equilibrium level of service?(5 marks)

(Total: 25 marks)

Question 3

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

Activity

Preceding activity

Normal Time (weeks)

Crash time (weeks)

Normal Cost (Rs.)

Crash cost (Rs.)

A

-

2

1

15000

20000

B

-

8

6

17000

20000

C

A

4

2

21000

25000

D

B

1

1

8000

8000

E

B

2

1

9000

14000

F

C, D

5

4

11000

15000

G

E

6

3

13000

16000

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)

Question 4

A bakery keeps stock of a popular brand of cake. Daily demand for last week is given below.

12

10

18

22

15

11

20

a) Randomly identify 10 values out of them in order to carry out a simulation. (Use the randomnumber table below). (10 marks)