Problem 1. Hotel California Hotel California is a luxury hotel which has just go
ID: 335867 • Letter: P
Question
Problem 1. Hotel California Hotel California is a luxury hotel which has just got a new manager, Rocky. Given its location and quality, the hotel always had enough people making advance reservations to fill up all the rooms available. The hotel charges $200 per room per night for reservations made in advance (Hint: think of this $200 as the purchasing cost in the Newsvendor model). Rocky had taken the OPRE3310 at UTD last semester and decided to implement some of those techniques in his current job. He implemented a policy of reserving some rooms for last-minute requests and charges these requests S300 per room per night (Hint: think of this $300 as the selling price in the Newsvendor model). The unsold reserved rooms are worth nothing at the end of the day (Hint: that is the salvage value is S0). Based on his estimation, the number of last minute customers is uniformly distributed with minimum of 1 and maximum of 10. a) How much is the cost of reserving too little by one? That is the underage cost, Cu b) How much is the cost of reserving too much by one? That is the overage cost, Co c) What is the optimal service level? d) How many rooms should be reserved for last-minute customers? Hint: what is Q*?Explanation / Answer
Answer to Problem 1 :
The underage cost , Cu
= Rate per room for last minute reservation – Rate per room for reservation made in advance
= $300 - $ 200
= $100
The overage cost , Co
= Rate per room for reservation made in advance – Rate per night for unsold rooms
= $ 200 – 0
= $200
Optimum service level
= Cu / ( Cu + Co )
= 100/ ( 100 + 200)
= 100/300
= 0.3333( or 33.33 % )
Number of last minute customers are uniformly distributed between 1 to 10 .
Therefore , number of rooms should be reserved for last minute customers
= Optimum service level x ( maximum demand – minimum demand ) + Minimum demand
= 0.3333 x ( 10 – 1 ) + 1
= 0.3333x9 + 1
= 2.9997 + 1
= 3.9997 ( 4 rounded to nearest whole number )
Answer to problem 2 :
Underage cost, Cu = Selling price / copy – Purchasing cost / copy = $ 0.5 - $.03 = $0.2
Salvage price for unsold copies = $ 0.15
Therefore, Overage cost . Co = Purchasing cost / copy – Salvage price/copy = $0.3 - $0.15 = $0.15
Optimum service level = Cu/ Cu + Co = 0.2 / ( 0.2 + 0.15) =0.2/0.35 = 0.5714 ( or 57.14% )
Demand for newspaper is uniformly distributed with minimum 10 and maximum 80
Number of newspapers should the bookstore order
= Optimum service level x ( Maximum demand – Minimum demand ) + Minimum demand
= 0.5714 x ( 80 – 10 ) + 10
= 0.5714 x 70 + 10
= 39.998 + 10
= 49.998 ( 50 rounded to nearest whole number )
If unsold copies are returned to print house for a full refund,
Savage price = $0.3
Therefore , revised overage cost , Co
= Purchasing cost / copy – Revised salvage price / copy
= $0.3 - $0.3
= 0
Optimum service level = Cu / ( Cu + Co ) = Cu/Cu = 1
Number of newspaper should the bookstore order
= Optimum service level x ( 80 – 10 ) + 10
= 1 x 70 + 10
= 80
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