Retail selling price, s = 190 Misrosoft selling price to retailer, c = 170 Salva

Question

Retail selling price, s = 190

Misrosoft selling price to retailer, c = 170

Salvage value, v = 90*(1-30%) = 133

Mean, = 100

Std deviation, = 42

a) Scenario: dispose of all of the unsold units of the Xbox one S at 30% off the retail price, at the end of the season.

Using the concept of Marginal Analysis,

Underage or shortage cost, Cu = s - c = 190 - 170 = 20

Overage or excess cost, Co = 170 - 133 = 37

To maximize profit, Optimal service level (stock-in probability) = Cu / (Cu+Co) = 20/(20+37) = 0.3509

z value = NORMSINV(0.3509) = -0.383

Optimal number of units of Xbox one S to purchase for the holiday season = + z = 100 - 0.383*42 = 84

Corresponding to z value as determined above, L(z) = 0.6193   (this value is taken from the standard normal table)

Expected lost sales, L(Q) = L(z) = 42*0.6193 = 26

Expected Sales S(Q) = 100 - 26 = 74

Expected inventory, V(Q) = Q - S(Q) = 84 - 74 = 10

Expected Profit =S(Q)*Cu - V(Q)*Co = 74*20 - 10*37 = $ 1,110

b) Scenario: Microsoft will buy back unsold units at a predetermined price of $160.00. However, Target would have to bear the costs of shipping unsold units back to Microsoft at $3.00 per unit

Using the concept of Marginal Analysis,

Underage or shortage cost, Cu = s - c = 190 - 170 = 20

Overage or excess cost, Co = 170 - 160 + 3 = 13

To maximize profit, Optimal service level (stock-in probability) = Cu / (Cu+Co) = 20/(20+13) = 0.6061

z value = NORMSINV(0.6061) = 0.2692

Optimal number of units of Xbox one S to purchase for the holiday season = + z = 100 + 0.2692*42 = 111

Corresponding to z value as determined above, L(z) = 0.2787   (this value is taken from the standard normal table)

Expected lost sales, L(Q) = L(z) = 42*0.2787 = 12

Expected Sales S(Q) = 100 - 12 = 88

Expected inventory, V(Q) = Q - S(Q) = 111 - 88 = 23

Expected Profit =S(Q)*Cu - V(Q)*Co = 88*20 - 23*13 = $ 1,461

Explanation / Answer

Target is trying to decide on how many units of Xbox one S to purchase for the holiday season. One unit of Xbox one S retails at $190.00. Microsoft, manufacturer and supplier of the Xbox one S to B&N sells a unit to Target for $170.00. Target will dispose of all of the unsold units of the Xbox one S at 30% off the retail price, at the end of the season. Target estimates that demand for this book during the holiday season is normally distributed with a mean of 100 and a standard deviation of 42.Microsoft is thinking of offering the following deal to Target. At the end of the season, Microsoft will buy back unsold units at a predetermined price of $160.00. However, Target would have to bear the costs of shipping unsold units back to Microsoft at $3.00 per unit.h. Write an overall conceptual analysis about all the expected profits in all the cases above?(i.e., comment on how different parties gain/lose in these different scenarios)

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