Jump Bicycles on Thursday will launch San Francisco’s first stationless bike-sharing system, as well as the first system to offer electric-assisted bikes, under an exclusive 18-month permit that has at least two potential competitors seething.

In traditional bike-sharing operations such as the Bay Area’s Ford GoBike, bicycles must be locked in docking stations when not in use. Stationless or “dockless” bicycles can be parked anywhere because the lock is on the bike; it usually immobilizes the rear tire. Jump bikes are a little different because they must be locked to an object. Jump wants them locked to bike racks within the system’s operating area, which generally covers parts of the city’s east side. Users who disobey the rules can be locked out.

LimeBike, one of five other companies that applied to operate stationless bike-sharing in the city, is livid that the San Francisco Municipal Transportation Agency shut out other competitors for 18 months without telling them a single vendor would be chosen.

The process “resulted in the SFMTA permitting a single favored vendor which was expedited through the permit process rather than resulting in the best operator able to deliver the greatest service,” LimeBike Vice President Andrew Savage said in a letter to the agency.

Jamie Parks, the agency’s bicycle program manager, said it reviewed applications on a first-come, first-served basis and Jump was “the first to fulfill all the terms completely and to our satisfaction.” The permit allows Jump to roll out 250 e-bikes initially and 250 more after nine months if the city approves.

In most bike-sharing systems, users generally locate, unlock and pay for bikes with a mobile app, although some have other payment options. They are designed for short trips around town.

Jump will charge $2 for the first 30 minutes and 7 cents a minute thereafter for its vermillion electric-assisted bikes. Riders still pedal an e-bike, but an electric motor makes going up all but the steepest hills a breeze.

Jump buys e-bikes for about $1,000 each, which is roughly $400 more than it pays for standard bikes, said Ryan Rzepecki, its CEO. E-bikes also cost more to operate. They have about a 40-mile range and must be brought to a warehouse every two to three days to be recharged. Jump is based in Brooklyn and operates bike-sharing in 40 markets including San Mateo, which will get e-bikes this spring.

GoBike plans to add 250 electric-assisted bikes to its San Francisco fleet in April. GoBike charges by the ride, day or year. Its single-ride trips costs $3 for the first 30 minutes and $3 for each additional 15 minutes. Low-income residents can pay $5 a year.

Motivate, a Brooklyn company, is operating GoBike under a 10-year contract with the Bay Area Metropolitan Transportation Commission. The commission and each of the five participating cities (San Francisco, Oakland, San Jose, Berkeley and Emeryville) could get a cut of revenue if they exceed some rather high hurdles.

Jump has no contract or revenue-sharing agreement with the city. It will pay about $12,000 a year in fees for agency staff to monitor what the city is calling a pilot program, Parks said.

Other companies that submitted stationless applications include Limebike, Ofo, Spin, Mobike and Scoot. LimeBike, based in San Mateo, and Ofo, based in Beijing, have both asked the city to reopen its permitting process.

According to LimeBike, Jump submitted its application July 10 and got feedback a month later. It submitted its final application Nov. 14 and was approved Nov. 27. By comparison, LimeBike applied July 26 and didn’t get feedback for three months. It submitted its revised application Dec. 26, receiving no feedback.

“The SFMTA’s decision to award a sole-source contract to a non-SF Bay Area based company fails on all aspects of a transparent and fair review process, effectively eliminates all competition and limits the dockless bikesharing choices for San Franciscans,” its CEO, Toby Sun, said in a statement.

Ofo, in a statement, called the decision “disappointing and a direct assault on the people of San Francisco who deserve affordable, reliable and equitable transportation options.”

In a four-page memo outlining its permitting process, the agency said a stationless e-bike system like Jump will reach the neighborhoods and types of customer not served by Ford GoBike. It added that Jump bikes will lock to racks with an integrated U-lock, in contrast to freestanding stationless bikes, which “increase the operational burden of relocating improperly parked bikes” and pose a safety risk if they block a public right-of-way. “The pilot will be an opportunity for a thorough evaluation and monitoring of bikeshare expansion,” it added.

Derrick Ko, CEO of Spin, said he was happy to see the agency “allow a different form of mobility” by approving a stationless operation, but was surprised it is exclusive. His company, based in San Francisco, will continue talks with the agency because “San Francisco is an amazing city for biking.”

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender