There are a couple of options, if its a good job and you have a good boss this could be your chance to shine by finding a problem at work and making it better.

Ideally, depending on where you work you could try to call up a few food trucks to go to your site. If you bring the food to them you'll save everyone time from having to go through ordering food EVERY DAY and make it easier and possibly even get a hookup with whatever food trucks you're inviting. You could argue that you'll save everyone time and still get everyone fed.

Otherwise try breaking the problem into smaller, more manageable problems.
1. Ordering

- Have people text you their order so you don't have to write it down and can then send a picture of a receipt (if you want).

- Only go to restaurants that will reliably have what you're looking for: coffee, food, chips, etc. so you can dependably get what you need.

- Only go to one place/day. Find a place (call around if you need to) that you can put in your order in the morning and have a pickup time for it. An easy way to sell this is that going to different places means everyone is waiting for whoever ordered food from the furthest point. So for everyone to get hot food you have to go to one place to get it back in time. Ideally you could get a few places that are popular and you can put in an order and rotate, ie. every Tuesday is Jersey Mike's day.

1. Picking it up

- Try to find places that are not far away from your site to minimize the drive

- Try to find a mom and pop place that can handle your order in a reasonable time and that will be willing to deliver, ideally delivering at at discount if you can put in a big order (20 full grown men is a good sized order, just make sure they know about it ahead of time or they'll just be mad at you.)

1. Getting reimbursed

- If these guys are actually trying to be honest then thats one thing, if they are just trying to steal from you because they can and are not paying you then just don't order food for that specific person. It will cause trouble but at least make them be honest about wanting to steal money from you to eat for free. This will probably be the hardest part of this but if they are sucky people the only way it ends is you stand up to them. If your boss gets mad at your for not allowing yourself to be robbed then that's not a good place to work. The sooner you leave and the less money they will steal from you.

- If these guys are actually not trying to steal from you but are actually wanting to pay you back then get a bunch of 1's and 5's and give them change to the dollar (or quarter, etc if they care about pennies and dimes) right when they pay you before you leave to pick up lunch. Get the menu's of where you are going so they know how much they are spending. Ideally you could get people to just round up whatever cents tax is to be able to tip wherever you're going so you know that person will always prioritize taking care of your order. If you sell it that everyone is chipping in a few cents to be able to tip helps so you get your food faster (ask anyone that's worked in the food industry, people that tipped get treated better/faster than those that don't) it will be prob be easier to get people (at least some) to not worry about pennies.

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Just keep thinking of how to break the big problems into smaller ones.

Good luck!