- JetAirways flight from Philadelphia to Boston has 150 seats. The high fare on the
flight is $780 and the restricted/low fare is $500. There is ample demand for the low
fare class but high fare demand is uncertain. Demand for the high fare is poisson
with mean 50. Further, the customers buy low fare tickets well in advance of high
fare customers.
a. What is the optimal protection level for the high fare tickets?
b. What is the expected revenue (in thousands) from high fare passengers when a
booking limit of 60 is selected for the low fare tickets?
c. The JetAirways Customers’ Bill of rights states that “Customers who are
involuntarily denied boarding shall receive $1,200 in addition to a ticket
refund.” The RM department notices that the number of no-shows is Poisson
distributed with mean of 7.5. What is the maximum number of reservations in
excess of plane capacity that the airline should accept?
2. Jim is a CFO of a mid-sized construction company. One of his key tasks is to ensure
that the company has sufficient cash to pay its daily and hourly workers who are hired
whenever need arises. The company operates all 365 days a year and Jim estimates
that on any day his payroll is poisson with mean $ 25. Jim manages his cash reserves
using the order-up-to model: each morning he places an order for cash with the bank
and the armored vehicle arrives 2 days later with the money.
a. Suppose Jim is interested in ensuring that the company immediately satisfies
all employee salary requirements with a 95% probability. What is the
corresponding order-up-to level?
b. Suppose Jim uses the order-up-to level of $15. One of these days the armored
car is robbed. What is the probability that more than $20 is stolen?
- Supreme Cola is a supplier of fountain equipment to restaurants, bars and cafeterias.
The fountain equipment is manufactured at their York PA plant site. A national
distribution center (DC) for the fountain equipment is also maintained adjacent to the
plant. Supreme has one common platform design to which they add various features
and accessories to create 10 different product options. The lead time for
manufacturing and delivering a batch of products to the distribution center is 2 weeks.
They review inventory and order weekly. For product ACola, demand is poisson
with mean 25.
a. What order upto level should Supreme choose to achieve at least a 99.25% instock
probability?
b. What is the probability that Supreme will have more than 40 units on order of that product at the start of any given week?
- Radio Shack sells the same 32GB flash drive on their e-commerce site which has a single distribution center. Daily demand at their e-commerce DC is forecasted to be poisson with a mean of 5 units. The lead time to receive a replenishment at the distribution center from their supplier is 2 days. Assuming they operate 7 days a week, what base stock level should they choose for the DC if they want to achieve a 99.3% in-stock probability?
4. Inn at Penn has 200 rooms. For regular-fare customers, rooms are priced at $300 per
night while the rooms are priced at $700 per night for the high-paying customers who
generally arrive at the last minute. The demand for such high fare customers is
distributed normally with mean 60 and standard deviation 50. Assume that there is
ample demand for regular-fare customers.
a. What should the protection level for the high fare be to maximize expected
profit?
b.Suppose that Inn at Penn operates with the protection level of 50 rooms for
high fare customers. On average, how many high-fare customers are turned
away because of lack of rooms?
c. Suppose again that the Inn at Penn operates with the protection level of 45
rooms for high fare customers. What is the probability that there are at least 5
rooms left unoccupied?
