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Help Me Prove My Boss Wrong

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Okay bear with me, I work for a company that delivers food. One of my jobs as a manager is to achieve the lowest average delivery time across all orders each week. Before I became the manager, my boss who used to do my job used to be able to achieve an average delivery time of around 40 minutes each week. This was years ago when we did less orders and had less drivers. Once I became the manager most weeks our average delivery times is in the high 40s. Even on our best weeks with very little order issues or order delays I can only get our average delivery time around 43 to 45 minutes. My boss often wants to know why I can’t consistently achieve the low 40s that he was able to achieve in the past. I explain that I believe that the number of issues grow exponential as we add more drivers, more restaurants and more orders. The increased issues mean a higher average time. He disagrees and explains that he believes the issues are relative and even though there are more problematic orders we also have more orders that aren't problematic therefore it should balance itself out. I have never been good at math but his point just doesn't make sense and I believe math can solve our disagreement but I need somebody that is actually good at math to crunch some numbers. Any takers?

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This is not an answer to your direct question, but a couple of my own.

What factors have you looked at in determining the change of average delivery time? Have the average distances to customer changed? Have the average speed limits changed? Are there changes to what is done while delivering (e.g. do drivers now fill their own gas tanks while out on deliveries?) Has traffic increased? Are deliveries made during lunch time? Are orders larger, possibly requiring longer times to get things off the truck? Any changes to the time it takes customers to accept orders?

In general, I'm not sure the answer to the ultimate question (why aren't you as fast as me?) can be found with the math problem you have proposed. 

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Another question can be : Will planning a route with numerous customers assigned to the route maximize delivery time as opposed to fewer customers on the same route. In essence can better route planning to get as many customers on the same trip decrease average delivery times.

Rather than try to prove your boss wrong, it may be more beneficial to seek ways other alternatives to decrease average delivery times. Look into the factors carefully that cause delays, those could even include metro transit systems as buses can slow things down depending on  how the bus stops are designed. Also talk to each driver and see if they have recommendations on which routes to take and the problems they face when running those routes.

Though to be clear I would imagine some of these factors you may well already be looking into. It is always a better approach to admit an issue, look into what is causing the issue and presenting viable solutions to the issue.

Edited by Mordred

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How are you measuring time of delivery?

Are you using cars? Bikes? Electric bikes?

Do you have GPS installed in these devices?

How many orders is delivered at once?

Are there used applications which tell what route to drive to couple points the most optimal way?

Famous "Travelling salesman problem" https://en.wikipedia.org/wiki/Travelling_salesman_problem

Sometimes it's better to invest in bikes/electric bikes, as they can pass through the city even if there is traffic jam.

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