Question

16.4 million international visitor arrivals in 2016. Each visitor stayed an average of 3.5 days. There are approximately 64,000 hotel rooms in country X and the average occupancy rate is 84%. It is estimated that 65% of visitors stay in a hotel . There are 366 days in 2016. Estimate the average number of guests per hotel room. Hint: Use Little’s Law.

Answer 1

16.4 million Visitors arrive per year

65% of them stay in hotel

So number of customer arrivals at hotels = 16.4 million visitors * 0.65 = 10.66 million Visitors / year

Arrival rate (per day) = 6.929 million arrivals per year / (366 days per year) =29125.68 customers per day

Average time a customer spends in the hotel = 3.5 days

In a stable system: Throughput = average departure rate = Arrival rate

Little’s law

WIP = Throughput * Lead Time

Where
WIP = average number of items in process = L

Throughput = average departure rate = Arrival rate

Lead Time = average time an item spends in the system

(Throughput is the departure rate and in a stable system it is the same as the arrival rate of Little’s original formula.)

Rewritten as ,

Average number of items in process = average departure rate * average time an item spends in the system

For this hotel case

Average number of customers in hotels = average departure rate * average time a customer spends in a hotel

=29125.68 customers per day * 3.5 days

= 101,939.89 customers

So on an average 101,939.89 customer’s stay in hotel rooms

The occupancy rate of hotels is 64000. So at any time only 64000* 0.85 = 54400 rooms are occupied

These 101,939.89 customers must be staying in those 54400 hotel rooms

The average number of customer per hotel room. = 101,939.89 / 54400 = 1.87 customer per room