Clarifying Questions:

1. Is it an aggregator model using existing bike providers or starting a new one?

2. Are we supposed to optimize the bike sharing for a specific goal? e.g. maximize use of bicycle, acceptable wait time etc?

Top Equation:

# Bicycles required = # people requiring bicycle in peak time / # people served per bicycle at any time with acceptable wait time

Now lets solve this one by one:

1. To solve the first part of the puzzle, we need to make certain assumptions:

Population of a big city 5M

Target users who would use the bicycle sharing

1. Visitors/ travelers (1% * 30% )

2. Daily Commuters taking public transport (10% * 30%)

3. Shoppers (2% * 20%)

4. Students - school/ college (20%*30%)

#2 and #3 would show opposite characteristics over weekdays and weekends. e.g. commuters would be 10% over weekdays but shoppers would be 10% over weekends

# people requiring bicycle per min in peak time = # population require bicycle / peak duration in min

5M*0.01*.3 + 5M*.1*.3 + 5*.02*.2 + 5*.2*.3 = .5M

2. To solve the second part of the puzzle, we need to look at the demand patterns:

Lets say that demand is evenly sparsed in the peak time and the peak duration is between 7-9am in the morning where most commuters and students travel

So peak duration is 2 hrs = 120 mins

Average distance a person can/ will travel on a bicycle = 1 Mi

Average time a person can/ will use a bicycle in peak time = 10 min including traffic time

People a bike can serve per min = 1/10

Acceptable wait time = 2 min (assumption as people may prefer to walk instead of using bike to be in office/ school in time)

People one bike can serve in 120 min = 12

# people served per bicycle at any time with acceptable wait time = 1/5

Now lets feed this into our top equation to get the estimate of bikes required:

# Bicycles required = .5M/.2 = 2.5M

Since we have our estimate at hand, lets double check whether this number seems reasonable.

Bike Required is coming out to be half the size of the population, so we need to go back and correct our assumptions.

Our estimation of the second equation seems correct but the population set requiring bike seems way off.

Couple of additional factors that come to my mind:

1. We have considered the full city population while we could narrow it down to a specific area that we like to target but lets not talk about that for a min

2. Our population number is still the people who prefer to use bicycle for their mode of transportation but we haven’t considered how many of those would be interested in bike sharing service. Lets say this number is 10%

3. Even for the population that is interested in using bike sharing population, our penetration may be slow and lets say we can only take 10% of the market of interested people as there may be other players

So reworking that equation with #2 and #3

# people requiring bicycle per min in peak time = .5M * .1 * .1 = 5K

So revised estimate for # Bicycles required = 5K/.2 = 25K

This number would be reasonable to serve a large city and to penetrate deep into the market. However, company might want to target a smaller area to test their operations out and can actually reduce the bike requirement to an acceptable number.