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Unformatted text preview: Click to edit Master subtitle style 2/16/11 EIN 6336 EOQ Model with Shortages 2/16/11 Suppose shortages are permitted and are 100% backordered (customers will wait for demand satisfaction) Suppose the cost of a backorder is of the form b1 + b2t, where t is the time during which the item is stocked out b1 is a fixed cost for the shortage and b2 is a cost that increases with time Backorders 2/16/11 Backorders s T T 1 T 2 Q  s 2/16/11 T = Q/D since no demand is lost T1 = (Q – s)/D; T2 = s/D Backorders s T T 1 T 2 Q  s Area = (Q – s)2/2D Area = s2/2D 2/16/11 Average inventory level: (Q – s)2/2Q Average annual inventory cost: ◦ vr(Q – S)2/2Q Total backorder cost in a cycle: b1s + b2s2/2D Average annual cost of backorders: ◦ b1Ds/Q + b2s2/2Q Average annual cost (excluding Dv): ◦ TRC(Q, s) = DA/Q + vr(Q – S)2/2Q + b1Ds/Q + b2s2/2Q Backorders 2/16/11 dTRC/dQ = ◦(1/Q2)[DA + vr(Qs)2/2 + b1Ds + b2s2/2] = 0 ◦ So that  Q2/2 = (1/vr)[DA + b1Ds + b2s2/2] + s2/2...
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This note was uploaded on 02/15/2011 for the course EIN 6336 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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