A toy store in Kenwood Mall plans to sell one new model of the popular toys in t

Question

A toy store in Kenwood Mall plans to sell one new model of the popular toys in the upcoming holiday season. The store pays $20 for each unit to its supplier and sells to customers for $40 each. Any leftover inventory will be disposed at salvage value of $5 per unit. The store estimates the demand forecast to be the following:

1. Now, we assume the store can precisely estimate the actual demand after observing sales on “Black Friday”. On the other hand, the supplier allows retailers to place rush orders during the season, charging 50% premium for each unit included in the second (rush) order. All replenishment orders will be delivered to stores via second day air of UPS. For simplicity, we suppose the retailer does not run out of inventory before the second order arrives. Considering this whole new scenario, how many units must be ordered in the initial order (Q1)? How much should be ordered for the rush order (Q2)?

Explanation / Answer

Cu=50%*20 = 10 (the extra cost for including one unit in the second order)

Co=C-S=15P*=10/(10+15)=0.4

Thus optimal Q1 for initial order=200 units

Scenario 1: the actual demand=100. Q2=D-Q1=0. So we need to order 0 units for the second rush order.

Scenario 2: the actual demand=200, we need to order 0 units in the second rush order.

Scenario 3: the actual demand=300, we need to order Q2=D-Q1 = 100 units in the second rush order.

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