After months of testing and tweaking, the e-commerce start-up Jet.com opened its digital storefront on Tuesday, marking the official kickoff of the company's ambitious effort to battle Amazon and Wal-Mart for budget-conscious customers.

Jet is taking a new approach to pricing. Its algorithm doesn't simply look at the price of each individual item in your online shopping cart. It looks at all the items you want to buy, as well as your ZIP code, to determine which retailer or warehouse can ship that unique combination of items to you the cheapest. Shoppers can only buy things on Jet if they've signed up for a $49-per-year membership.

While there are plenty of nascent e-commerce businesses making lofty pledges to disrupt the shopping landscape, the retail industry and Silicon Valley are watching Jet particularly closely because of the brains and the money behind it. Jet's chief executive, Marc Lore, is the founder of Quidsi, an e-commerce business that was seeing soaring growth when it was bought by Amazon.com in 2011 for $545 million. That deal was struck after Amazon reportedly had waged an all-out price war with Quidsi's successful Diapers.com site.

Since Lore has had Amazon running scared once before, some analysts and investors believe he is especially well-positioned to compete with the e-commerce Goliath once again. (Amazon's chief executive, Jeffrey P. Bezos, owns The Washington Post.)

Jet is also astonishingly well-funded for a start-up: The $220 million it has raised in venture capital is among the largest seed or early-stage funding rounds in the past two decades.

Jet plans to spend $100 million on marketing this year to make sure you hear its name and consider shopping on its site. On launch day, its website featured a promotional video that stars Kumail Nanjiani, the actor who plays Dinesh on HBO's "Silicon Valley." The video opens with a dig at warehouse clubs such as Sam's Club or Costco.

"The old economics of saving money meant you had to buy items in bulk. And that's weird," Nanjiani says as a huge tub of mayonnaise is pictured on screen. "Because five pounds of mayonnaise is actually a fundamentally ridiculous thing to buy."

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This gets at the heart of how Jet is trying to distinguish itself in a crowded retail marketplace. Jet believes there are plenty of shoppers -- millennials, in particular -- who are very value-conscious and aren't having their needs met by the current shopping options. The bulk format of items in the warehouse clubs, Jet argues, is not great for people who live in small spaces or who don't have big families.

The site also offers additional ways to help you save, knocking additional pennies or dollars off your order if you pay with a debit card or waive the right to return an item.

Jet is also trying to set up a contrast between its $49 annual membership, which promises access to rock-bottom prices, and Amazon's $99 Prime membership. Lore makes the case that Amazon's offering essentially buys you convenience.

"I would say a large percentage of people in America can't afford to just do that. They don't have the luxury of spending $100 for faster shipping," Lore told The Washington Post back in April.

Jet will face big hurdles as it tries to turn us into a nation of "Jetheads," a term it hopes will catch on for loyal Jet shoppers. Amazon already brings in more than $40 billion a year in online sales and has tens of millions of shoppers signed up for Prime. Wal-Mart, the undisputed king of brick-and-mortar shopping in the U.S., is piloting its own membership shopping program known as Shipping Pass.

Last week provided a fresh example of just how fiercely these established players are fighting for your online shopping dollars, when Amazon announced a massive sale it called Prime Day, only to have Wal-Mart hit back with its own mega-sale. Jet is late to the party, and it will take serious effort to lure the shoppers who are already loyal to other outlets.

The chatter on social media Tuesday morning suggested that Jet is winning some early converts, but other commenters offered critiques of the site that encapsulate Jet's fundamental challenge: They have to figure out how to explain clearly how their complicated algorithm works and what its value proposition is.