Rocky Mountain Tire Center sells 11,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 50% of the purchase price of the tires per year. The purchase price is $21 per tire if fewer than 200 tires are ordered, $19 per tire if 200 or more, but fewer than 8,000 tires are ordered, and $15 per tire if 8,000 or more tires are ordered.
a. How many tires should Rocky Mountains tire order each time it places an order?
b. What is the total cost of this policy?
To be calculated:
(a) Economic order quantity (EOQ)
(b) Total cost
Given values:
Annual demand, D = 11,000 go-cart tires per year
Ordering cost, Co = $35
Holding cost, H = 50% of purchase price
Purchase price:
(Q < 200 tires), P = $21 per tire, Holding cost, H1 = 50% of $21 = $10.5
(200 = < Q < 8000 tires), P = $19 per tire, H2 = 50% of $19 = $9.5
(8000 tires = < Q), P = $15 per tire, H3 = 50% of $15 = $7.5
Solution:
(a) Economic order quantity is calculated as;
EOQ = SQRT (2*D*Co) / H
where,
D = Annual demand
Co = Ordering costs
H = Holding costs
1) For H1 = $10.5
EOQ = SQRT (2*D*Co) / H1
EOQ = SQRT (2 x 11000 x 35) / 10.5
EOQ = 83.571 or 84
EOQ = 84 units
2) For H2 = $9.5
EOQ = SQRT (2*D*Co) / H1
EOQ = SQRT (2 x 11000 x 35) / 9.5
EOQ = 92.368 or 92
EOQ = 92 units
3) For H3 = $7.5
EOQ = SQRT (2*D*Co) / H1
EOQ = SQRT (2 x 11000 x 35) / 7.5
EOQ = 116.999 or 117
EOQ = 117 units
Of the above three economic order quantities, only EOQ = 84 units (for holding cost = $10.5, P = $21) lies in the allowed range of (Q < 200 tires). Therefore,
Rocky Mountains should order 84 units each time it places an order.
(b) Total cost of the policy is calculated as;
Total cost = Purchase cost + Order cost + Holding cost
Total cost = (P x D) + (D/EOQ x Co) + (EOQ/2 x H)
where,
P = Purchase price
D = Annual demand
EOQ = Economic order quantity
Co = Ordering costs
H = Holding costs
Putting the given and calculated values in the above formula, we get;
Total cost = (P x D) + (D/EOQ x Co) + (EOQ/2 x H)
Total cost = ($21 x 11000) + (11000/84 x $35) + (84/2 x $10.5)
Total cost = $231,000 + $4,583.33 + $441
Total cost = $236,024.33
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