Unformatted text preview: when τ < T) Inventory Level Order quantity, Q Slope=−λ Reorder point, R Lead time Order Order placed received 4QA3 F12 A. Gandomi Lead time Order Order placed received Time 22 ● Consider an item with an EOQ of 25, a demand rate of 500 units per year, and a lead time of six weeks. R = λ (τ − mT )
"τ $
where m = " $ ( the largest integer less than or equal to τ T )
#T % Source: Nahmias (2009) 4QA3 F12 A. Gandomi 23 ●
● The EOQ model with Iinite production rate is a variation of the basic EOQ model. Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate). 4QA3 F12 Source: Nahmias (2009) 24 P: production rate λ: demand rate Assume P > λ (i.e., no shortage) ⎛ྎ Q ⎞ྏ
⎛ྎ λ ⎞ྏ
H = Q − λT1 = Q − λ ⎜ྎ ⎟ྏ = Q ⎜ྎ1 − ⎟ྏ
⎝ྎ P ⎠ྏ
⎝ྎ P ⎠ྏ
λ
H
λ
λQ
Now, G (Q ) = K + h ⋅ = K + h(1 − ) ⇒
Q
2
Q
P2 4QA3 F12 2K λ
h' h' Q* H Inventory Level Inventory level with no demand Q* = Production Phase Demand Phase Time 25 A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The Iirm makes its own wheels at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Holding cost is $1 per wheel a tear. Setup cost for a production run of wheels is $45. The Iirm operates 240 days per year. Find the optimal run size, total cost, cycle time and run time. 4QA3 F12 A. Gandomi 26 ● Price per unit decreases as order quantity increases o All units discount: the discount is applied to ALL of the units in the...
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 Spring '14
 Operations Research, A., Initialisms, Gandomi

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