On a timetabling problem in the health care system

Abstract

This paper proposes a literature review and a mathematical goal program for the design of timetables for radiologists. The goal program converts the tedious monthly tasks of the head of the radiology department of a leading hospital to a simple goal optimization problem that abides to the regulations of the Ministry of Health and avoids conflicting issues that may arise among coworkers. The optimization problem which is designed for the tactical level can also be used at the strategic level (i.e., account for a long time horizon) to plan for longer term constraints such vacations, medical and study leaves, recruitment, retirement, etc. Despite its large size, the problem is herein solved using an off-the-shelf solver (CPLEX). Empirical tests on the design of timetables for the case study prove the efficiency of the obtained schedule and highlights the time gain and utility of the developed model. They reflect the practical aspects of timetabling and radiologists' availability. Specifically, not only does the model and its solution reduce the effort of the Department head in this design stage, but it also promotes social peace among the technicians and a sense of fairness / unbiasedness. In addition, the designed model can be used at the operational level as a rescheduling tool by those technicians wishing to trade their shifts, and as a sensitivity analysis tool by managers wishing to study the effect of some phenomena such as absenteeism, increasing or decreasing the workforce, and extending work hours on the welfare of patients.