Question

Anna Sheen, upon graduating from a Boston-area university with a degree in journalism and operations research, returned to her hometown of Hamptonshire, Pennsylvania, to start a daily newspaper. The Hamptonshire Express emphasized local news, which Sheen believed was not adequately covered by big-city newspapers such as the The Philadelphia Inquirer, Pittsburgh Post-Gazette, and The New York Times.

Working in leased space that cost approximately $10 per day, Sheen wrote stories and articles daily around news and feature material that she gathered from around town, and then typeset the newspaper using desktop software. A local printer printed the newspapers overnight at a marginal cost of $0.20 per copy. Anna sold the copies the following morning from 6 a.m. to 10 a.m. from a newsstand at the intersection of Main Street and Center Street in the center of Hamptonshire. Newsstand rental was $30 per day. Express was sold to consumers for $1 per copy. Copies not sold by 10 a.m. were discarded.

Demand for newspapers was unpredictable; Sheen estimated demand daily before delivering the typeset paper to the printer. Based on data from similar entrepreneurial ventures and interviews with potential Hamptonshire customers, she estimated that daily demand for the Express was normally distributed with a mean of 500 and standard deviation of 100.

a. How many newspapers should Sheen stock (i.e., order from the printer)? What is the profit at this stocking quantity?

b. Verify that the value derived in part (a) is consistent with the optimal stocking quantity in the Newsvendor model using excel: Q*= µ + Normsinv(Cu/Cu+Co))σ

*Please show work

Answer 1

(a) Expected Demand = 500 = M. Standard deviation = s = 100. Marginal cost of production = 0.2 per copy and selling price per unit is 1.2. Any unsold copies are discarded. Hence the cost of understocking = Cu = 1.2 and Cost of Overstocking is Co = 0.2. The service level corresponding to optimal ordering is given by Cu / (Cu + Co) i.e. = 1.2/(1.2 + 0.2) = 85%. i.e the optimal order quantity will be equal to the mean demand plus k times the standard deviation where k is the value of the curve as per the normal table . Looking up the normal table we get k = 1.07.

Hence quantity = 500 + 100*1.07 = 607 units.

At this order quantity the Sales = 500 * 1.2 = $600. Cost = 607*0.2 + 10 + 30 = Cost of 607 units + Cost per day of leasing + Cost per day of rental = 161. Hence profit = Sales - Cost = 600 - 161 = $439.

(b) If we use excel to calculate 500 + Normsinv(0.85) we can verify the same = 607 units.