More than a year ago, Costco Wholesale (NASDAQ:COST) began preparing the ground for a massive change in its business. After a 16-year partnership with American Express (NYSE:AXP) that made AmEx the only credit card brand accepted at Costco, the warehouse giant decided to forge a new relationship with Citigroup (NYSE:C) and Visa (NYSE:V). The final switch occurred last week.

Under the new scheme, Visa cards will now be the only credit cards accepted at Costco. Meanwhile, Citi will now become the exclusive issuer of a Costco co-branded credit card, called the Costco Anywhere Visa card.

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Costco completed its credit card transition last Monday. Image source: The Motley Fool.

Costco executives have lauded the new arrangement as providing more benefits for cardholders (and Costco members more broadly). Meanwhile, American Express executives have been lambasted for losing the Costco business. However, American Express just might get the last laugh.

A turbulent transition

Despite spending more than a year preparing for the transition from American Express to Visa and Citigroup, the switchover this week has not gone smoothly. Using a Visa card in Costco doesn't seem to be an issue. However, many holders of the old AmEx TrueEarnings card (which has now been converted to the Costco Anywhere Visa card) have encountered trouble.

Some customers have had trouble activating their new credit cards. Some never received one at all. Others found that they were billed for charges they had already paid.

As a result, Citigroup received a staggering 1.5 million customer calls related to the Costco card between Monday and Wednesday of last week. Not surprisingly, call wait times spiraled out of control, further angering customers.

To some extent, these issues are not very surprising, considering the complexity of the operation. 11 million accounts had to be switched from AmEx to Citi, with accurate information on each cardholder's spending and payments. Meanwhile, Citi had to send a new card to every cardholder -- and each cardholder had to activate the new card.

Was Citi the right choice?

On the other hand, it's also possible that Citigroup didn't put enough resources into ensuring that the transition went smoothly. One customer-relations employee at Costco's corporate office said as much to a frustrated customer, according to Business Insider.

Citi was ranked as the second-worst credit card company in J.D. Power's most recent customer satisfaction survey. (American Express was the second-best.) Citi's failure to staff its call center appropriately for the transition fits right in with its spotty customer-service track record.

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American Express has a long reputation for excellent customer service. Image source: The Motley Fool.

It's too early to call the new Costco-Citigroup-Visa partnership a flop. However, given how many customers Costco has alienated in the past week -- many people have threatened to cancel their memberships, though most probably won't follow through -- it's reasonable to question whether switching credit card companies was shortsighted on Costco's part.

In arguing for Costco to renew its agreement with AmEx, American Express CEO Ken Chenault described his company as Costco's "trusted partner." Costco CEO Craig Jelinek retorted that AmEx was just a vendor, according to Bloomberg Businessweek. If another vendor was offering a lower price, Jelinek was perfectly happy to switch.

A few weeks ago, Chenault's perspective might have seemed quaint, or perhaps just conceited. Yet the rocky transition from American Express to Citigroup highlights the importance of having a reliable, customer-friendly credit card partner.

That's especially true for Costco, a company that has a deep relationship with its members and routinely ranks near the top of the retail industry in terms of customer satisfaction. Saving a little bit of money on swipe fees isn't worthwhile if it comes at the cost of alienating some customers.

Perhaps Citigroup will straighten things out quickly and find a way to regain Costco cardholders' trust, so that Costco's deal with Citi and Visa can ultimately live up to its full potential. But for now, it seems plausible that Ken Chenault was right -- and Costco may have undervalued the importance of having a reliable, customer-friendly credit card partner.

Adam Levine-Weinberg has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Costco Wholesale and Visa. The Motley Fool recommends American Express. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.