Annual block scheduling for internal medicine residents with 4+1 templates

Jonathan F. Bard, Zhichao Shu, Douglas J. Morrice, Luci K. Leykum

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Internal Medicine residency programmes have traditionally been structured around monthly or 4-week blocks where a different rotation is assigned to each block over the year. A subset of those rotations carry the requirement of one or two half-day sessions of clinic duty per week. In the last several years, a growing number of Internal Medicine residency programmes have moved away from this traditional structure and have adopted an 'X+Y' template, where the resident spends X weeks on a rotation without clinic duty and then Y weeks mostly in clinic. This paper addresses the '4+1' annual block scheduling problem as adopted by the Department of Medicine at the University of Texas Health Science Center in San Antonio (UTHSC-SA). We believe it is the first attempt to investigate the problem formally; specifically, we develop a series of optimization models that can be used to construct individual block schedules for the academic year and to assign clinic sessions to the residents during their ambulatory week. (At UTHSC-SA, Internal Medicine residents are divided into five groups to match the 4+1 pattern, and scheduled so only one group at a time has clinic responsibilities each of the 52 weeks.) The objective is to balance the workload during the half-day clinic sessions and to ensure that each resident receives roughly the same training experiences over their programme. Once the blocks and groups are known, a second optimization problem is solved to determine individual clinic session assignments. The basic model takes the form of a mixed-integer program but was not solvable with commercial software. After decomposing it into two parts, we were able to find optimal solutions to the original problem. Complexity results are provided for the problems solved. Compared with current practice, our decomposition approach was seen to offer improved schedules with respect to the workload balance objective for each of the five resident groups.

Original languageEnglish (US)
Pages (from-to)911-927
Number of pages17
JournalJournal of the Operational Research Society
Issue number7
StatePublished - Jul 1 2016


  • 4 + 1 block scheduling
  • medical rotations
  • mixed-integer programming
  • resident scheduling
  • soft constraints

ASJC Scopus subject areas

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing


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