Example L.L.Bean Expected Marginal Contribution of Each Additional 100 Parkas Additional Expected Marginal Expected Marginal Expected Marginal Hundreds Benefit Cost Contribution 11th 5,500×0.49=2,695 500×0.51=255 2,695-255=2,440 12th 5,500×0.29=1,595 500×0.71=355 1,595-355=1,240 13th 5,500×0.18=990 500×0.82=410 990-410=580 14th 5,500×0.08=440 500×0.92=460 440-460=-20 15th 5,500×0.04=220 500×0.96=480 220-480=-260 16th 5,500×0.02=110 500×0.98=490 110-490=-380 17th 5,500×0.01=55 500×0.99=495 55-495=-440 SEIEE AU406 11
+ - SEIEE AU406 11 Example L. L. Bean
Example L.L.Bean Expected↑ Profit at ▣The optimal order L.L.Bean quantity is 1,300 parkas ▣CSL is92% The fulfill rate is 99% R*Order Quantity fr=1×Prob(demand≤1,300)+∑(1,300/D)p D>1,300 =1×0.92+(1300/1400)×0.04+(1300/1500)× 0.02+(1300/1600)×0.01+(1300/1700)×0.01 =0.99 SEIEE AU406 12
+ - SEIEE AU406 12 The optimal order quantity is 1,300 parkas CSL is 92% The fulfill rate is 99% Example L. L. Bean
Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season Inputs: Co:Cost of overstocking by one unit,Co=c-s Cu:Cost of understocking by one unit,Cu=p-c CSL:Optimal cycle service level O*:Corresponding optimal order size CSL"is the probability that demand during the season will be at or below O. At the optimal cycle service level CSL*,the marginal contribution of purchasing an additional unit is zero SEIEE AU406 13
+ - SEIEE AU406 Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season 13 Inputs: At the optimal cycle service level CSL* , the marginal contribution of purchasing an additional unit is zero
Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season Expected benefit of purchasing extra unit =(1 -CSL")(p-c) Expected cost of purchasing extra unit =CSL(c-s) ▣ The expected marginal contribution of raising the order size from O*to O*1 is given by (1 -CSL')(p -c)-CSL'(c-s)(=0) ▣The optimal CSL*is cSL=Prob(Demand≤O）=P-C Cu 1 p-s Cu+Co 1 +(Co/Cu) SEIEE AU406 14
+ - SEIEE AU406 14 The expected marginal contribution of raising the order size from O* to O* + 1 is given by (=0) The optimal CSL* is Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season
Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season If demand during the season is normally distributed, with a mean of uand a standard deviation of o. The optimal order quantity is given by O*=F(CSL".u,)NORMINV(CSL',u, expected profit from ordering O units is given by Expo=(p-sur(O。）-(p-a(。） -O(c-s)F(O,u.)+O(p-c)[1-F(O.u.) SEIEE AU406 15
+ - SEIEE AU406 If demand during the season is normally distributed, with a mean of μ and a standard deviation of σ. The optimal order quantity is given by 15 Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season expected profit from ordering O units is given by