Question

Hertz is an international car rental company with their regional offices in New England area having 2,500 cars. On average, eight cars per month require tire and oil change. The tire and oil change cost $850 each. There is also a $120 ordering cost, independent of the number of items ordered. Hertz in New England area has an annual holding cost rate of 30% on tires and oils. It takes two weeks to obtain the items after they are ordered. For each week that a car is out of service, Hertz loses $90 in profit. 1. What is the optimal order quantity? 2. What is the maximum number of backorders? 3. What is the time between orders (cycle time)? 4. What is total annual cost?

Answer 1

# cars	2500	cars
monthly demand, d	8	cars
Annual demand, D	96	cars
unit service cost, p	$        850
Ordering cost, Co	$        120
Annual holding cost, Cc	30%
=	$        255
Lead Time, L	2	weeks
unit backorder cost, Cb	$          90
1. Optimal order Quantity, EOQ=Q=sqrt(2*Co*D/Cc)*sqrt((Cc+Cb)/Cb)
Q	19	(rounding off)
2. Maximum No. of backorders, S= Q*(Cc/(Cc+Cb))
S	14	(rounding off)
3. No. Of orders/year=D/Q	5.2
time between orders (cycle time) = 12 / no of orders
	2.3	months
4. total annual cost = holding cost + ordering cost+ backordering cost
total annual cost = [Cc(Q-S)^2/2Q]+[D*Co/Q]+[S*2Cb/2Q]
	$ 847.00

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