Question

The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 95 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 75 to 95 units, according to the following probability model:

                                                                           

Demand	75	80	85	90	95
Probability	0.05	0.20	0.20	0.20	0.35

This textbook costs the bookstore $82 and sells for $107. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $36.

a) Based on the given information, Vaidy's conditional profits table for the bookstore is:

		Demand
	75	80	85	90	95
Stock	p=0.05	p=0.20	p=0.20	p=0.20	p=0.35
75	1875	1875	1875	1875	1875
80	1645	2000	2000	2000	2000
85	1415	1770	2125	2125	2125
90
95

b) How many copies should the bookstore stock to achieve highest expected value?

c) The EMV of stocking this number of copies is

Answer 1

Based on the given data, we prepare the required table as shown below:

We solve the given problem by first finding Monetary value for various cases:

Case 1: Demand = 75, Purchase = 75

Case 2: Demand = 75, Purchase = 80

Case 3: Demand = 75, Purchase = 85.........and so on. We will have 25 cases for each combination of D = 75, 80, 85, 90, 95 and Purchase = 75, 80, 85, 90, 95. Accordingly, we get monetary values for each combination.

If Demand = Purchase, Profit = Demand * Cost of underage

If Demand is more than purchase, Profit = Demand * Cost of underage - (Purchase - Demand) * Cost of overage

If Demand is less than purchase, Profit = Demand * Cost of underage

Accordingly, the above solution in the form of formulas is shown below for better understanding and reference:

The row for 90 and 95 is updated.

The EMV is maximum for 85 no. of copies. To achieve the highest expected value, the bookstore stock should order 85 copies.

The EMV of stocking this number of copies is = 2018.50 as highlighted in green.