By Paul Ziobro 

Target Corp.'s website went down Sunday morning, overwhelmed by shoppers clamoring for the retailer's latest design partnership.

The discount chain took its site offline for about 20 minutes due to a rush of shoppers looking for its 250-piece collection of Lilly Pulitzer bathing suits, shift dresses and jumpsuits selling for a fraction of the price of the Palm Beach designer's luxury clothing.

At other times during the morning, Target paced visits to the site, leaving many shoppers unable to access the site or its shopping app. The company also delayed the online launch by two hours.

"When the traffic got heavier, we made the website inaccessible," Target spokesman Joshua Thomas said. "We realize there is an extreme amount of excitement around this collaboration, and we apologize for any disappointment this may have caused our guests."

Target planned to have the sale up fully live at 3 a.m. Central Time, but delayed it until 5 a.m. because of high traffic, Mr. Thomas said. The number of visits was similar to the Black Friday sales around Thanksgiving. Three hours into the sale, the entire selection was nearly sold out online.

The online sale started before shoppers could buy the items at Target stores, which open at 8 a.m. Some people lined up hours before stores opened.

The episode was a less serious echo of the launch of Target's Missoni collection in 2011, when the website crashed and couldn't be restored for several hours. It shows Target is still able to generate hits after some less buzzy collaborations with upscale brands. But it also reveals that the company still has some kinks to work out in its online operations at a time when it is relying heavily on them to beat back competition from Amazon.com Inc.

The Missoni snafu came shortly after Target retook control of its web operations from former partner Amazon, and it highlighted shortcomings of the chain's online infrastructure.

Shortly afterward, Target shook up its online leadership. Executives have since touted improvements to the website to handle massive traffic, including sales around Black Friday that generated record online results for the site.

Once the site was restored, shoppers were able to pick up some of fast dwindling items.

Target has been building significant buzz for the Palm Beach-inspired Lilly Pulitzer line, setting up a temporary shop in New York's Bryant Park and running a juice bar, offering free manicures and setting up pingpong tables.

Write to Paul Ziobro at Paul.Ziobro@wsj.com

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