Question

Given the following information, determine the optimal overbooking policy for Talia’s Beauty Salon. The salon’s capacity is 8 patrons. The historic number of no-shows for a typical day along with the probability of occurrence is shown in the table. The average profitability per patron is $100 and the cost of lost goodwill per patron due to overbooking is approximately $50.

Table Info

No shows 0,1,2,3    Probability 0.50, 0.30, 0.20

Answer 1

Cu = Cost of overage = Cost of overbooking one unit less than the no shows = $100
Co = Cost of overage = Cost of overbooking one unit more than the no shows = $50

So,

The newsvendor critical ratio = Cu / (Co + Cu) = 100 / (50+100) = 0.667

No shows (x)	P(x)	F(x)	Comparison with Critical ratio
0	0.50	0.50	< 0.667
1	0.30	0.80	> 0.667
2	0.20	1.00

Note that the cumulative probability F(x) crosses the critical ratio for x = 1.

So, the optimum overbooking policy is to overbook 1 patron.