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In order to estimate the number of gasoline station, I will break down it to 2 components: number of gas station = total of gas consumption per day / total gas pump of each gas station per day

To estimate total gas consumption, I will have 3 assumptions:

1/ Total population of Paris is 2 million

2/ Age range % population: 0 -> 18 years old: 20%, 18 -> 60 years old: 60%, > 60 years old: 20%

3/ Gas consumption per person per day for each age range:

    + 0 -> 18 years old and > 60 years old is 0 due to driving capability

    + 18 -> 60 years old is 1 litre per day

Total gas consumption calculation:

    + Total population of 18 -> 60 years old is 2,000,000 * 60% = 1,200,000 people

    + Total population of 0 -> 18 years old is 2,000,000 * 20% = 400,000 people

    + Total population of 0 -> 60 years old is 2,000,000 * 20% = 400,000 people

    + Total consumption of gas in Paris per day is 400,000*0 + 1,200,000 * 1 + 400,000*0 = 1,200,000 litre

To estimate total productivity of each gas station, I will have 3 assumptions:

1/ Productivity per working day:

     + 8:00 -> 16:00: 60% capacity (high traffic)

     + 6:00 -> 8:00 and 16:00 -> 22:00: 40% capacity (low traffic)

     + 22:00 -> 24:00 and 0:00 -> 6:00: 10% capacity (low and no traffic at mid night)

2/ Number of gas pump per gas station is 5

3/ Speed per gas pump is 1 litre/ 10 second

Total productivity per gas station calculation:

Speed per gas station: speed per gas pump * number of gas pump per gas station = 5 * 1 = 5 litre/ 10 second

Total working hour with high traffic time range: 8 * 60% = 4.8 hours

Total working hour with low traffic time range: 8* 40% = 3.2 hours

Total working hour with low and no traffic at mid night time range: 8*12.5% = 1 hour

Total working hour per day: 4.8 + 3.2 + 1 = 9 hour

Total productivity per gas station per day: 9 * 5 * 6 * 60 = 45 * 3600 = 16,200 litre

Total number of gas station at Paris: 1,200,000/ 16,200 = 74 gas stations

To solve this problem I would start by making 2 key assumptions:

1. France is similar to the United States in demographics and fuel consumption.
2. The population of Paris is 3 million.

Then, I would estimate the number of people serviced by 1 gas station in my community (in the US), using this information I would calculate an estimate for the number of gas stations in Paris.  

I live on a major road in Hartford, CT that feeds into several smaller (mostly residential streets and closes. There are 4 gas stations along this stretch and the estimated population of the neighbouhood it services is 20,000. Consequently, 1 gas station services 5000 (20,000/4) people.

Given the assumed similarity between France and the United States, The number of gas station in paris is 600 (3,000,000/5000).

Hello,

This is a fantastic idea! 

My answer is based on the following 2 facts.

1. A 'gas station' is anything with >= 1 public gas supply pump.
2. The analysis is for Paris Metro area.

As for my answer - I believe there are 100 gas stations within the metro area.

Workings:

1. This is a demand problem as we can assume that if demand was not being met, there would be more gas stations opened. 
2. Popn = 2.2m Paris Metro
3. % who can afford cars is 50%
4. % who actually own a car is 1/6 = 16% = 176K~
5. Avg car tank = 50L
6. Avg Trip Km = 5
7. Avg # Trips per week = 3
8. Avg fuel per Km = 1
9. Fuel used per week = 15L
10. Therfore a car fills up every 3 weeks= ~ 50K cars per week use gas stations.
11. Gas stations work 15 hours per day
12. Avg Pump # is 3
13. Pump flow is 30L per minute
14. Utilization is 30% 
15. Avg fuel supply per day = 15 x 60 x 3 x 30 x .3 = 24,000L
16. Total Avg station weekly supply = 24K x 7 = 168KL
17. Total Fuel demand of paris = 50k cars x 50L tank = 2.5m L
18. Therfore to meet this demand, there must be X number of stations
19. X = 2.5m L Demand / 24,000L avg station supply = 100~ Stations

https://www.preplounge.com/en/management-consulting-cases/interviewer-led-mckinsey-style/intermediate/gas-station-19

Will this work?:)

part1)

• Paris population 2.2M, assume 3 people per household, 0.73M hoseholds
• About 83% household own cars in France
• 0.73*83%=0.6M cars

part2)

• 2 cars are being filled up at the same time at each gas station
• each car blocks a pump for 6 minutes, 60/6*2=20 cars
• 1 gas station services 20 cars per hour
• gas station hours from 8am to 10pm, so 14 hours each day
• 14*20=280 cars per day
• 280*7 days per week=1960 cars per week
• Assume each car need to fill once a week
• 0.6M/1960 cars=310 gas stations

Can you please define Paris?

Hi everyone!

It's time to draw the winner!

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[What we did was we assigned a number to each answer and drew the winner with an automatic number generator: (1 Raghed; 2 Phan Thien Phuoc; 3 Enuma; 4 Anonymous A; 5 Andrey; 6 Tania).]

Great job to everyone and thank you all for participating in our first Consulting Q&A Quiz! 

Our PrepLounge team also gave it a try and this is what we came up with...

What do you think?

Good luck for the rest of your case prep!

Astrid

PrepLounge Community Management

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Hi Tom!

Thank you for your feedback to our answer :) Of course in our calculation tree, the reasoning is missing. In an actual interview, we would have to explain and justify it as the following:

Here is the logic behind the 78 vehicles/pump:

And this is how we came to 9 liters/vehicle:

What do you think?

You can also check out the full case study and solution to get all the details. 

Best,

Astrid

PrepLounge Community Management

Follow us on: Facebook | Instagram | LinkedIn | twitter 

Hi..

Sorry for the late answer. Would be great if you guys could share some feedback on my approach.

Here goes,

Paris' energy consumption (surface transport) for 2006 :-

Gasoline  : 68208 Tera Joules. (Calorific value of gasoline : 33.7 MegaJoule/litre)

Diesel : 138096 Tera Joules.  (Calorific value of gasoline : 36.9 MegaJoule/litre)

Hence, annual consumption for 2006 equates to

Gasoline : 2024 million litres 

Diesel :  3742 million litres

Considering the fact that France's oil consumption figures have reduced from 1.9million bbl/day in 2006 to 1.6million bbl/day, in 2017 owing partly to the advent of the affordable electric vehicles and pervasion of the same, let us consider 85% capacity in 2017 compared to that of 2006. 

Hence, annual consumption figures of Paris for 2017 are 

Gasoline : 1720 million litres 

Diesel :  3181 million litres

Now, considering an even distribution of consumtion over the year, the average daily consumption comes to

Gasoline : 4.71 million litres

Diesel : 8.72 million litres

Now, let the average filling station in Paris cater to both gasoline & diesel consumers. On an average underground fuel tanks at filling stations have a capacity of 30~40kilolitres. The capacity is so selected to cater to an average of 3-day demand at the filling stations. There should be separate tanks for gasoline & diesel.

Let us consider one 30kilolitre tank with an average of 3 days capacity for diesel in a filling station. This gives us a daily consumption of 10kilolitres per filling station for diesel.

Therefore, a maximum of (8.72million litres(diesel) / 10kilolitres = ) 872 filling stations are there in Paris. 

Similar calculation considering gasoline would give a figure of 471 filling stations. However, as diesel consumption is almost twice that of gasoline consumption, and owing to the fact that filling stations would prefer using similar capacity underground tanks owing to space constraints, economic & technical reasons, it seems that quite a few filling stations would be 'diesel only'.   

Hence, let us go with a figure of 872 for this case.

Thanks,

Rr.