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Here's one study sort that answers your question

https://news.umich.edu/carbon-emissions-and-grocery-shopping...

In-store pickup using a internal combustion engined vehicle produced more emissions than any other option studied.

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Great, thanks. Here's the abstract. And for context, it's a collaboration with Ford Motor Co.

... We report and compare the greenhouse gas (GHG) emissions for a 36-item grocery basket transported along 72 unique paths from a centralized warehouse to the customer, including impacts of micro-fulfillment centers, refrigeration, vehicle automation, and last-mile transportation. Our base case is in-store shopping with last-mile transportation using an internal combustion engine (ICE) SUV (6.0 kg CO2e). The results indicate that emissions reductions could be achieved by e-commerce with micro-fulfillment centers (16-54%), customer vehicle electrification (18-42%), or grocery delivery (22-65%) compared to the base case. In-store shopping with an ICE pick-up truck has the highest emissions of all paths investigated (6.9 kg CO2e) while delivery using a sidewalk automated robot has the least (1.0 kg CO2e). Shopping frequency is an important factor for households to consider, e.g. halving shopping frequency can reduce GHG emissions by 44%. Trip chaining also offers an opportunity to reduce emissions with approximately 50% savings compared to the base case. Opportunities for grocers and households to reduce grocery supply chain carbon footprints are identified and discussed.

It's interesting that consumers driving EVs reduce the cost on the same scale as deliveries (presumably in an ICE vehicle).

They omit apples-to-apples comparisons (at least from the press release and abstract)

  * Consumer ICE vs. Delivery service ICE
  * Consumer EV vs Delivery service EV
  * Sidewalk delivery robot vs Bicycle or ebike
The last is a bit bizarre - comparing a 2-mile radius sidewalk mechanism to pickup trucks and delivery vans, but omitting the very popular 2-mile delivery method.
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Also this argument is easily refuted by the US Postal Service, which physically delivers individual pieces of paper in a few days, for pennies.
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Right but that’s a government service and it should be totally fine for them to deliver mail below cost using taxpayer money to make up the deficit.

Like every other government service - highways, defense, etc. They’re profitable to the system, but not per se.

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The US Post Office is funded by its own revenue, I'm pretty sure.
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It still enjoys many government mandated monopolistic advantages.

See: American Letter Mail Company.

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USPS is fueled by parcel deliveries, but also in large part by literal tons of junk mail on dead trees; spammers have paid Uncle Sam handsomely to spam every citizen's mailbox for decades, and it's the most lucrative thing USPS can do with our home mailboxes.
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The postal service is a quasi government entity that has operated (not to get too deep into the politics of it) for many years at a loss. It does compete with Amazon, as well as being used by Amazon, but it's very different as a business than Amazon.
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I got this when I told Gemini "post office loss retirement prepaid" because of other articles I have read that I cannot remember.

"In 2006, Congress passed the Postal Accountability and Enhancement Act (PAEA). This law forced the USPS to do something virtually no other government agency or private corporation has to do: prefund its retiree healthcare benefits 75 years into the future[0]. Essentially, they were legally required to fast-track billions of dollars into a fund to pay for the future retirement health benefits of current employees, and theoretically even future employees who hadn't been hired yet."

[0]: https://apwu.org/the-usps-fairness-act/

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There's also the externalities. Costco effectively supports car infested surburbia which lots of people blame for a great many problems.
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I would expect Amazon to be more efficient. Besides the round trips, there's operating the store, putting items on display, all that. As I said above, Amazon and Costco don't compete so directly though, like you aren't buying a pie from Amazon.
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Indeed true. Even more efficient is when people can wait a few days and let Amazon bundle your orders and deliver on a designated day.

That said people don’t typically get in a car to buy one thing -though obviously sometimes they do. On average though their trips will be for multiple things. I still think even without using designated delivery days Amazon deliveries are more efficient than individuals going out to buy things independently.

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I've always wondered why I don't see passed on savings for the "amazon day" thing. It's gotta be way better for their logistics to deliver bulk orders, or pick a standardized delivery day for each neighborhood or something. Why do they only offer a single dollar of credit for choosing it?
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I don’t know how much they are saving. On the one hand they save a stop (they aren’t saving a van as there are likely already vans delivering near by). on the other they have to hold on to stock longer waiting for things to all be ready. It costs money to store things
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I get 6% back instead of 5% with my Amazon card which is more than enough to incentivize me in many situations.
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I was zeroing out the amount purchased: The comparison is the customer picks up one item vs. Amazon delivers one item, or the customer picks up 12 or 20 things vs. Amazon delivers the same amount.

I'd still love to see data.

The problem with environmental impact is really a consequence of subsidized energy costs, including the externalization of environmental cost. If the consumer and Amazon paid the actual cost of fuel, they would make valid economic and environmental choices and we wouldn't need to figure it out like this.

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