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Doc APProvED

Doc APProvED: The Mathematical Complexity of Scheduling

Mohseni, Alex MD

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doi: 10.1097/01.EEM.0000441174.89005.22

    You probably have some understanding of the complexity involved in generating a quality schedule every month if you've ever been the scheduler for your site. I would hazard a guess, however, that most providers don't realize the true mathematical complexity of scheduling.

    Let me illustrate. The number of shift possibilities for just one day at a site with just four shifts per day and a pool of 10 doctors is 5,040 (10 x 9 x 8 x 7). The possibilities for four weeks is 4.6 x 10103, a number so large that it would take a computer evaluating one billion schedules per second more than 1087 years to evaluate every schedule possibility. Clearly, it's time to start paying your scheduler more. Or you can buy ShiftGen. (

    ShiftGen is the brainchild of Ram Duriseti, MD, a physician with a doctorate in computational algorithms from Stanford. ShiftGen is a schedule generation and management web application specifically designed to meet the needs of emergency medicine groups. Like its competitors, Tangier and ShiftAdmin, ShiftGen provides a centralized online site to create, publish, and edit your site's schedule.

    But where ShiftGen really excels (and in my view, beats the competition) is in its effective and robust shift analysis tools that give schedulers real-time feedback on the variance, complexity, and quality of the schedule being created or edited. Ram and his team also, and perhaps more importantly, have come up with a schedule auto-generation algorithm that can automatically create a quality schedule for you with the parameters you input. Given the computational impossibility of finding the global optimum schedule (see the math above), the algorithm uses heuristics to find “local optimums,” and these algorithms run off of the computational strength of scalable cloud-based computers (not your local desktop computer). Other companies also claim they can auto-generate a schedule, but their output is only as good as their algorithms, and these have historically not proven very successful.

    Given the significant impact of shift rhythms and patterns on quality of life and longevity of career, every group should take shift generation very seriously. Ram and his team have tackled this problem with a comprehensive and robust solution that represents the next generation of scheduling software at a price that beats most of the competition: free.

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    Doc APProvED is devoted to apps that can make the emergency physician's life easier, in and out of the ED. Tell us about your favorite apps by writing to Dr. Mohseni at

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