# 13 newsvendor model performance measures for any

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13Newsvendor model performance measuresFor any order quantity we would like to evaluate the following performance measures:Expected lost sales The average number of units demand exceeds the order quantityExpected sales The average number of units sold.Expected left over inventoryThe average number of units left over at the end of the season.Expected profitExpected fill rate The fraction of demand that is satisfied immediatelyIn-stock probabilityProbability all demand is satisfied Stockout probabilityProbability some demand is lost
14Expected lost sales with Q= 3500Definition:e.g., if demand is 3800 and Q= 3500, then lost sales is 300 units.e.g., if demand is 3200 and Q= 3500, then lost sales is 0 units.Expected lost sales is the average over all possible demand outcomes.If demand is normally distributed:Step 1: normalize the order quantity to find its z-statistic.Step 2: Look up in the Standard Normal Loss Function Table the expected lost sales for a standard normal distribution with that z-statistic: L(0.26)=0.2824Step 3: Evaluate lost sales for the actual normal distribution:26.0118131923500Qz( )11810.2824334Expectedlost salesL z
15Measures that follow expected lost salesExpected sales = - Expected lost sales = 3192 – 334 = 2858Expected Left Over Inventory = Q - Expected Sales = 3500 – 2858 = 642\$702858\$20642\$187,221Expected profit Price-CostExpected salesCost-Salvage valueExpected left over inventory28581319289.6%Expected salesExpected salesExpected fill rate Expected demandExpected lost salesNote: the above equations hold for any demand distribution
16Service measures of performanceIn-stock probability = F(Q) = (z)Evaluate the z-statistic for the order quantity : Look up (z) in the Std. Normal Distribution Function Table, (0.26) = 60.26%Stockout probability = 1 – F(Q) =1 – In-stock probability= 1 –0.6026 = 39.74%Note: the in-stock probability is not the same as the fill rate26.0
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