Workforce planning in medical imaging remains a complex problem characterized by heterogeneous employment contracts, multi-station rotation requirements, and regulatory compliance constraints. Existing scheduling practices in many non-profit health systems rely on manual, demand-agnostic approaches that produce systematic inefficiencies including coverage gaps, uncontrolled overtime, and paradoxical overstaffing. This study formulates an integer linear programming model to optimize technologist assignments in an X-ray modality of a non-profit regional hospital. The model operates over a seven-week, 1,176-hour planning horizon and minimizes a composite objective comprising fully loaded labor cost and a penalized coverage shortfall. A penalty coefficient parameterizes the cost-coverage trade-off, and its effect on staffing level, shortage rate, and total cost is characterized through systematic sensitivity analysis. The baseline manual schedule assigns 15 technologists across 15 rotation patterns, yielding an hourly shortage rate of 9.52%. The optimized solution assigns 17 technologists, reducing the shortage rate to 6.04%, a 36.55% reduction. Although seven-week labor cost increases from $147,346.71 to $166,937.47, the projected net annual financial benefit of $193,515.19 confirms the economic justification for the additional staffing. The model is implemented in Python using PuLP with the COIN-OR Branch-and-Cut solver. These findings establish that integer programming produces quantifiable and financially favorable improvements over manual scheduling, and the framework generalizes naturally to other imaging modalities and workforce planning contexts in healthcare.

Keywords

Operations Management, Mathematical Optimization, Healthcare, Mixed-Integer Linear Programming, Decision Support System.