Given data, Retail selling price, S = $190 Microsoft selling price, C = $170 Mea

Question

Given data,

Retail selling price, S = $190

Microsoft selling price, C = $170

Mean, = 100

Standard deviation, = 42

Case 1:

Xbox will dispose the unsold units at seasons end:

Salvage value, v = 190 – 30% of 190 = 190-57 = 133

Calculate the following:

Underage cost, Cu = SP-C

                            = 190 - 170 = 20

Overage cost, Co = SP-Salvage value

                        =170 - 133 = 37

Calculate Optimal service level = Cu / (Co + Cu)

                                             = 20 / (20+37) = 0.3509

Calculate z value = NORMSINV*(0.3509) = -0.383

Number of units of Xbox should purchase, Q = + z

                                                               = 100 - 0.383*42

                                                                 = 84

Find L(z) corresponding to z from standard normal distribution table as 0.619

Expected lost sales, L(Q) = * L(z)

                                      = 42*0.619 = 26

Expected Sales S(Q) = 100 – expected lost sales

                                =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

Case 2:

Microsoft will buy back unsold units:

Buy back price, B = $160.00.

Costs of shipping unsold units = $3.00 per unit

Calculate the following:

Underage cost, Cu = S – C

                            = 190 - 170 = 20

Overage cost, Co = SP-Buy back price + shipping cost

                          =170 - 160 + 3 = 37

Calculate optimal service level = Cu / (Co + Cu)

                                            = 20 / (13+20) = 0.6061

Calculate z value = NORMSINV * (0.6061) = 0.2692

Number of units of Xbox should purchase, Q = + z

                                                         = 100 + 0.2692*42 = 111

Find L(z) corresponding to z from standard normal distribution table as 0.278

Expected lost sales, L(Q) = * L(z)

                                      = 42*0.2787 = 12

Expected Sales S(Q) = 100 – expected lost sales

                                  = 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

2. 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. f. Assume that Microsoft is able on average to earn $125 on each returned Xbox one S net the Microsoft’s handling costs (some units are destroyed while others are sold at a discount and others are sold at full price). Given the order quantity in part d what is Microsoft’s expected profit?

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