CS/APR 2006/MAT585

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UNIVERSITI TEKNOLOGI MARA

FINAL EXAMINATION

COURSE

INVENTORY CONTROL AND QUEUING THEORY

COURSE CODE

MAT585

EXAMINATION

APRIL 2006

TIME

3 HOURS

INSTRUCTIONS TO CANDIDATES

1.

This question paper consists of two (2) parts: PART A (5 Questions) PART B (5 Questions)

2.

Answer ALL questions.

3.

Candidates are not allowed to bring any material other than those allowed by the invigilator into the examination room.

4.

Start each new answer on a new page.

5.

Please check to make sure that this examination pack consists of: i) the Question Paper

ii) an Answer Booklet - provided by the Faculty

iii) a two-page Appendix (Formulae List)

iv) a one-page Appendix (Standard Normal Table)

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

This examination paper consists of 8 printed pages

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CS/APR 2006/MAT585

PART A (25 MARKS)

QUESTION 1

Discuss two purposes of inventory to an organization. For each purpose, give a relevant example to support your answer.

(3 marks)

QUESTION 2

Distinguish between the 'push' and 'pull' systems in JIT.

(6 marks)

QUESTION 3

The weekly demand for an item is 50 units. It is known that the holding cost per year is 20 percent of the unit price. A cost of RM40 will be charged on placing each order. That particular item costs the company RM150 per unit. Owning to high demand, the company's customers do not object to backordering and the backordering cost is RM5 per year. This company operates for 50 weeks a year.

a) Calculate the Economic Order Quantity.

(3 marks)

b) Determine the maximum quantity of backorder.

(2 marks)

c) How long does a customer have to wait in order to get the desired item? (2 marks)

QUESTION 4

A technician monitors a group of 4 machines that run an automated manufacturing facility. It takes an average of 10 minutes to adjust a machine that develops a problem. The machines run for an average of 60 minutes without requiring adjustment. Arrival and service times have been known to follow Poisson and exponential distribution respectively. a) Determine the probability that the system is empty.

(3 marks)

b) Calculate the average number of machines waiting for adjustment. (2 marks)

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CS/APR 2006/MAT585

QUESTION 5

Demand for a product is normally distributed with a mean of 10000 units a year and a standard deviation of 500 units. The price per unit is RM50. The ordering cost is known at RM20 per order and the holding cost is 20 percent of the unit price per year. Lead time is fixed at 2 weeks.

a) How many units should be ordered to minimize cost?

(2 marks)

b) Currently, an order is placed when there are 50 units left in the stock. What level of service does this result in?

(2 marks)

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CS/APR 2006/MAT585

PART B (75 MARKS)

QUESTION 1

a) Derive the formula for Economic Order Interval (EOI) for multiple items. (6 marks)

b) Save-mart is owned by En. Hakim. It is located near a residential area, where demands for most of the items it sells are very high. In order to make his customers satisfied, En. Hakim always makes sure that all highly demanded items are always in stock. But he knows that high inventory means high capital. Placing a joint order will help him minimize his annual cost. Given below are the items that he usually orders from the same vendor, along with the annual demand and the unit cost for each item. Item

Shallot

Garlic

Onion

Dried chilies

Potato

Salt

Annual Demand, Dj (kg)

12000

15000

10000

5000

10000

2000

Unit Cost, (RM/kg)

1.50

1.30

1.80

1.60

2.40

1.50

The ordering cost is RM20 per purchased order and RM0.50 per item. The holding cost is 10 percent per kg per year. Calculate

i)

the...