Example 12.1 SportMart Excel Input Mean demand, mu = 350 Standard Deviation of D

Question

Example 12.1 SportMart Excel

Input

Mean demand, mu = 350

Standard Deviation of Demand, s = 100

Cost per unit, c = $100.00

Retail price, p = $250.00

Salvage Value, s = $80.00

Intermediate Calculations:

Cost of overstocking per unit, Co = $20.00

Cost of understocking per unit, Cu = $150.00

Expected overstock units (eqn 12.4) = 124

Expected understock units (eqn 12.5) = 6

Optimal Results:

Optimal Order quanity, O* (eqn 12.2) = 469

Optimal cycle service level, CSL* (eqn 12.1)= 0.88

Expected Profit (eqn 12.3) = $49,147

Expected profit at 350 $45,718

Using the Sportmart DemoPreview the documentView in a new window, the manager decided to conduct market research and, based on the additional information she obtained from the research, she believes that the standard deviation of demand can be reduced to 50 instead of 100. What is the impact of profitability? What happens to profitability if the standard deviation of demand increases to 150? What did you learn from this exercise? Note: This is not a “Solver” problem. Just change the Standard Deviation directly in Excel from 100 to 50 and then 150 to see the impact on profitability.

Explanation / Answer

Since some information such as referred equations numbers are missing in above problem, assuming it is single period inventroy model, calcualations are done as shown below:

Retail price per unit $ 250

Incase of Std Dev 150

Single period inventory model calculation shown below:

Since some information such as referred equations numbers are missing in above problem, assuming it is single period inventroy model, calcualations are done as shown below:

Retail price per unit $ 250

Cost per Unit $ 100 Salvage value $ 80 Cost of understocking per unit, Cu = $ 150 Cost of overstocking per unit, Co = $ 20 Expected overstock units (eqn 12.4) = 124 Expected understock units (eqn 12.5) = 6 Optimal Results: Optimal Order quanity, O* (eqn 12.2) = 469 Optimal cycle service level, CSL* (eqn 12.1) 0.88 Expected Profit (eqn 12.3) = 49147 Expected profit at 350 45718 Mean,m = 350 Std. Dev,s = 50 Using Single period inventory model , Z value at P =0.88 P <= Cu/(Co+Cu) = 0.88 Normal distribution, @ p = 0.88 Z = 1.175 Total quantity need = m + Z x s 409 Expected profit at at quntity 409 units $ 8850 Total profit @ 409 units $ 54568

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