Lee Hnetinka founded WunWun last year and hopes to expand to other cities.
WunWun reports that Trader Joe's is among the most popular place that users order from. Typically, orders peak on Sunday nights and during thunderstorms.
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With the likes of Google and Amazon making deliveries, and recently Uber announcing a test for consumer delivery services in Washington, it remains to be seen which players will emerge as leaders in the on-demand delivery sector.
Sucharita Mulpuru, principal analyst at Forrester Research, said that while there is massive venture funding pouring into the space, the biggest challenge is figuring out the economics of how to make logistics practical.
According to her research, it can cost between $10 and $20 to deliver a package, yet on average people don't want to pay more than $3 to $5.
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"People typically want free over fast. If you can do both, great, but I don't see how we're going to get to economies of scale anytime soon," she said.
Mulpuru said that whichever company is willing to lose the most money will ultimately have the potential to win. Between the complexities of inventory management and high delivery costs, Malpuru predicted it could take a decade or more for any player to become profitable.
—By CNBC's Uptin Saiidi.