A linear programming model for determining efficient combinations of 8-, 10-, and 12-hour shifts

I have formulated a linear programming model to determine changes in efficiency and productivity that would result from scheduling personnel to work combinations of 8-, 10-, and 12-hour shifts in a section of our pulmonary medicine department. My objective was to minimize the number of staff hours worked each day, subject to the constraints imposed by the levels of staffing required during each hour of the day. I found that a combination of 8-, 10- and 12-hour shifts could increase productivity 8.1% and reduce personnel requirements by one full-time equivalent. Salary expenses would decrease 7.5% if overtime were not paid for the extended hours of the 10- and 12-hour shifts. Two considerations in implementing the proposed schedule are the willingness of staff to work extended hours and the necessity of developing a format for communication between therapists who work discontinuous shifts.