Question

   Question No.1

ABC Company makes bicycles. It produces 500 bicycles. It buys the tires for bicycles from a supplier at a cost of 15 RO per tire.

The company inventory carrying cost is estimated to be 20% of cost and the ordering cost is 45 RO per order.

(a) Determine the economic order quantity (EOQ).

(b) How many orders will be placed per year using the EOQ?

(c) What is the length of an order cycle?

(d) What is the total annual cost if the EOQ quantity is ordered?


Question No.2:

The computer lab at BUC has a help desk to help the students working on computer spreadsheet assignments. The students patiently from a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 21 students per hour, with the service rate being described by an Exponential distribution. Calculate the following operating characteristics of the service system.

1. Rate of arrivals

2. Rate of service

3. The average utilization of the help desk server

4. The average number of students in the system

5. The average number of students waiting in queue

6. The average time a student spends waiting in line

7. The average time a student spends in the system

8. The probability of having more than 4 students in the system

Question No.3:

Solve the following assignment Problem by complete enumeration method.

Jobs/workers	1	2	3
A	110	90	70
B	50	60	80
C	100	130	110

  



  

Answer 1

	We know the following formula for Optimum /Economic Ordering Quantity or EOQ
	EOQ = Sq Root of [(2*Ordering cost*Annual usage)/Carrying cost per unit]
	Given Annual production=D=	500
	Ordering cost/order=O=	45
	Units cost	15
	Carrying cost @20% of unit cost=H=	3
	So EOQ= Sq Rt [2*500*45]/3
a	EOQ =122.47 or 122 (rounded off)
b	No of orders using EOQ=D/EOQ=500/122.47=	4.08
c	Length of an order cycle=365/4=	91.25	days
d	Total Annual cost using EOQ
	cost of material =500*15=	$           7,500.00
	Cost of ordering @45=45*D/EOQ	$                183.7
	Average Inventory =EOQ/2
	Cost of annual holding=3*EOQ/2=	$                183.7
	Total Annual cost using EOQ	$           7,867.42