EIN%206336%282%29 - EIN6336 Backorders backordered(...

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Click to edit Master subtitle style  2/16/11 EIN 6336 EOQ Model with Shortages
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 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 
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 2/16/11 Backorders s T T 1 T 2 Q -  s
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 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
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 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
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 2/16/11 dTRC/dQ =  -(1/Q2)[DA + vr(Q-s)2/2 + b1Ds + b2s2/2] = 0 So that  Q2/2 = (1/vr)[DA + b1Ds + b2s2/2] + s2/2
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