Question 4: Different problem, same logic (Yield Management) Please complete the green cells!

You are contemplating to work as a sales channel for a hotel. The hotel has 210 identical rooms and is always fully booked at least one week in advance. A hotel room costs $105 a night.

Your private research has shown that this is a reasonable price, but comparable rooms in other hotels sell for $159 when booked within a week before the night of stay (clearly, short-term visitors, often business customers, have a higher willingness to pay).

You think that you can find a deal with the hotel. You will block rooms and resell them on your own website. You will pay $105 to the hotel for each room that block. When the hotel has sold all other rooms for $105 before the last week, you will offer your blocked rooms on your website for $159.

However, there is a catch: If you cannot sell a room that you blocked, then you have to pay the $105 nonetheless, i.e., you carry the risk of having a room left over, but ripe the gains of selling for a higher price.

1. what is overage cost Co?

2. what is underage cost Cu?

3. what is Critical fractile?

4. Taking this as the true distribution, you decide to block how many rooms?

5. Assum that the demand has a normal distribution with?=80 and ?=80 What would be the optimal order quantity?

what about worst-case?

Cost Parameters Overage cost Co: (What you loose if you have blocked one room too many.) Underage cost Cu: (What you miss out on if you have blocked one room too less.) Critical fractile Cu/(Cu+Co): So far, we ignored the demand. Fortunately, you also got info from a booking website that tells you about the demand for more expensive rooms within the last week prior to the stay. Demand for rooms priced