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Unformatted text preview: holding cost
λ: annual demand rate c: unit purchase cost Q: order quantity Annual ordering cost = K . λ /Q Annual purchase cost = c . λ Annual carrying cost = h . (Q/2) Total cost = c. λ + K. λ/Q + h. Q/2 G(Q) Source: Nahmias (2009) 4QA3 F12 A. Gandomi 17 ● Deriving Optimal Order quantity Q*: G (Q ) = K λ
Q
+h
Q
2 d 2G (Q ) 2K λ
= 3 > 0 for Q > 0
2
dQ
Q dG(Q) − K λ h
2K λ
= 2 + = 0 ⇒ Q* =
h
dQ
Q
2 4QA3 F12 A. Gandomi 18 ● Some properties of the EOQ Solution: o Q* is increasing with both K and λ and decreasing with h, o c does not appear explicitly in Q*. However, it does affect the value of Q* indirectly, as h = I . c), o Holding cost and ordering cost are equal at the optimal point: hQ *
λ
=K *
2
Q
o G * 4QA3 F12 = G (Q * ) = 2 K λ h . A. Gandomi 19 A local distributor for a national tire company expects to sell approximately 9,600 steel belted radial tires of a certain size and tread design next year. Annual holding cost is $16 per tire and ordering cost is $75. The distributor operates 288 days a year. What is the EOQ? How many times per year does the store reorder? What is the length of an order cycle? What is the total annual cost if the EOQ quantity is ordered? 4QA3 F12 A. Gandomi 20 ● It can be shown that: ● G(Q) 1 ⎡ྎ Q* Q ⎤ྏ
= ⎢ྎ + * ⎥ྏ
*
G
2 ⎣ྏ Q Q ⎦ྏ For example, if we order Q = ½ Q* (i.e., 50% of the optimal quantity) then the resulting total cost only increases by 25%. 4QA3 F12 21 ● Reorder point is the level of inventory at which a new order should be placed to prevent shortages while also avoiding overstock. R = λ τ (...
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 Spring '14

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