This needs to exist.

If I had time and money, I'd start a business. Specifically, a website. This website would be the Yelp of grocery stores.

Imagine this, only only live, with local prices, updated whenever a grocery store updates their prices via product database integration. Grocery stores would use it for promotions and attracting customers by showcasing their deals. Customers will use it to have something akin to this, only online and stored in an online profile wherein prices are seen in real-time and they can mix and match to save time and money.

For a monthly service charge, consumers would be granted additional features, among them a mobile application (that would open locations for them in Google Maps/Navigate) and access to a tool that allows them to put in their starting point address, cost of gas, gas mileage of their vehicle, and their shopping list, and find (for any given day) the least costly grocery shopping route. That's where the fun happens; the underpinnings of the website would be an optimization problem like that of the traveling salesman.

For a monthly service charge, businesses would be granted the tools to automatically push and synchronize changes in their prices to the online database. Furthermore, as consumers add usage data, businesses could be provided with statistical predictions of how many more customers would be drawn to their store after the adjustment of any item's price. This would give them a means to gauge the elasticity of demand and adjust their prices to maximize profit.

Why does this interest me?

• It involves numerical methods, ergo it is awesome.
• It addresses a fundamental human need: to forage for victuals.
• It optimizes the effort to fulfill said human need, reducing gasoline consumption and wasted resources, time being one of them. That would free up resources for other pursuits.
• It exposes and makes readily available information where previously the best way of getting that information was physically going to a store.
• It's something that I want, so I could use it myself.

That being said, why does this not exist yet?