Early results of an experiment at The Gap provide hope that there might be a remedy for one of the most controversial labor practices in retailing, hospitality, health care, call centers, and many other service industries: schedules that require employees to work different shifts every week, often with only three days’ notice of next week’s schedule. These volatile schedules can wreak havoc with workers’ child-care arrangements, school classes, and other personal responsibilities. They can make it virtually impossible for part-timers to hold down multiple jobs, and widely fluctuating hours mean workers’ incomes also can fluctuate widely. But this situation could change. One element of an experiment at 28 retail stores in The Gap chain have already proven that one approach can make a big difference to workers and their managers: a smartphone app that allows workers to trade shifts.