Country : Canada
Assignment Task

    

Task
1. A hotel has 100 rooms and two per-night fares: $150 and $250 for leisure and business customers, respectively. The probabilities of daily demands of each type of customers are available in Tables 1 and 2 (Note: both probabilities are assumed independent). The manager of the hotel wants to apply a policy of “nested bookings”. That is, a number of rooms are exclusively reserved for business customers. Once the number of leisure customers reaches a certain limit, any subsequent leisure booking is rejected. Of course, business bookings are always accepted (unless the hotel is at its full capacity). Leisure bookings are assumed to arrive first, i.e., when business bookings arrive leisure bookings have already been decided.
(a) Suppose currently the manager has reserved 15 rooms for business customers. Develop a simulation model to find the following measures of performance of this booking system:

  •  the expected number of leisure rooms used per night.
  •  the expected number of rejected leisure bookings per night.
  •  the expected number of business bookings.

(b) Develop a simulation model (can use the same as in part (a)) to find the optimal reservation siz (i.e., the number of rooms to be reserved for business which maximizes expected profit).

Demand Probability

  • 74 0.075
  • 75 0.011
  • 76 0.089
  • 77 0.034
  • 78 0.075
  • 79 0.028
  • 80 0.059
  • 81 0.021
  • 82 0.016
  • 83 0.091
  • 84 0.094
  • 85 0.051
  • 86 0.062
  • 87 0.037
  • 88 0.064
  • 89 0.067
  • 90 0.078
  • 91 0.048

Table 1: Leisure distribution
Demand Prob

  • 20 0.013
  • 21 0.076
  • 22 0.031
  • 23 0.062
  • 24 0.082
  • 25 0.011
  • 26 0.022
  • 27 0.102
  • 28 0.054
  • 29 0.023
  • 30 0.102
  • 31 0.082
  • 32 0.03
  • 33 0.094
  • 34 0.055
  • 35 0.05
  • 36 0.004
  • 37 0.107

 

Table 2: Business distribution
2. (a)
Allbest Airlines planes require repairing an average of 200 times per year and a single repairman takes one week to fix. Assuming the times between breakdowns and repairs are exponential, how many repairmen are needed to ensure that there is at least a 95% chance that 2 or fewer planes are being repaired? All repairmen work in a single plane until it is fixed. 
(b) From the time a request for data is submitted until the request is fulfilled, a database takes an average of 3 seconds. We find that the database is idle around 20% of the time. Answer the following questions, assuming that the database can be modeled as an M/M/1 system.
i. With these two values, compute ? and µ.
ii. What is the average service time per database query?
iii. What is the average number of queries in the system?
iv. What is the probability that 5 or more queries are present?
 

 

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  • Posted on : March 07th, 2020

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