Crafting an efficient schedule of college course offerings means solving a complex puzzle. And more colleges these days are turning to algorithms to help reduce the number of classes that are either overloaded or full of empty seats.

A study out last week of about 200 colleges found that many course schedules are “unbalanced,” with 45 percent of courses analyzed filled to less than 70 percent capacity and 23 percent of courses classified as “overloaded,” meaning more than 95 percent full.

That inefficiency is having an impact on retention, the study found. The greater the inefficiency of the course catalog, the lower the graduation rate at the institutions analyzed.

The study was done by a company that sells software to try to analyze the efficiency of course schedules, Ad Astra Information Systems, so it has an interest in showing the problem is large and that it matters. And the institutions included in the study were the company’s customers, and had already self-identified as struggling with the issue of schedule efficiency.

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