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Unformatted text preview: l amount of demand that has has not been satisﬁed:
• All backordered demand is eventually ﬁlled, i.e., there are no lost
sales. • Inventory level = Onhand inventory  Backorder. • Inventory position = Onorder inventory + Inventory level. • Order upto level = S
• the maximum inventory position we allow. • sometimes called the base stock level. What determines the inventory level?
• Short answer:
• • Inventory level at the end of a period
= S  demand over (l+1) periods. Explanation via an example
• with S = 6, l = 3, and 2 units onhand, 2 on the way at the start of
period 1
x3
x1
1 2 x4 x2 1 D1
2 D2 D3 D4
? Meet the Service Target
• Decide S to make instock probability ≥ α • Demand D over l+1 period
• • Standard normal
distribution Probability (D<S) is
!
! • µ=(l+1)λ, σ=sqrt((l+1)λ) p= S (l + 1)
p
(l + 1) !
square root law So the order upto quantity S is
S = (l + 1) + 1 (↵ ) p (l + 1) Choose the Service Target
1.Based on experience if no quantitative measures are available.
2.Quantitative Method
• “Too muchtoo little” challenge:
• If S is too high, then there are holding costs, Co = h
• • If S is too low, then there are backorders, Cu = b
• • h equal the holding cost per unit per period
b equal the penalty per unit backordered Optimal instock probability
• Instock probability = critical ratio Cu
b
↵=
=
Co + Cu
h+b Part 4: News Vendor Model A review of News Vender problem
• Proﬁt function
• demand of news paper: D • order quantity: q • order price: c • selling price: p • salvage value: s
⇡ (q ) = pE(mi...
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This document was uploaded on 01/28/2014.
 Fall '14

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