In any hospital, operation theatres (OTs) are some of the most demanding units in terms of resources. Yet time and again, Indian audit studies put on record the idle theatre time, late starts and cancellations that are the consequence of over-running schedules. We address this by treating the allocation of surgeons to cases as a linear assignment problem and applying the Hungarian method to find a solution (Kuhn, 1955; Munkres, 1957). Our model is an orthopaedic and general surgery list of six cases for six surgeons, with the estimated procedure time in minutes serving as the cost we seek to minimise. Since Indian hospitals do not make surgeon-level time data available to the public, the cost matrix presented here is a simulation based on operational context from published OT audits in India. The paper walks through the entire process in detail, from row and column reduction and the covering-line test, to the θ adjustment and a final optimality check. The results show the optimal call for 460 surgeon-minutes all told. That figure is 22.9 per cent less than one would expect from a random assignment of 597 minutes, and 10.3 per cent under a fixed roster-order at 513 minutes. This unique solution has been borne out by a linear programming formulation run through Excel Solver, complete with dual values and cost ranging. In the discussion we consider how the approach can be applied to unbalanced lists and what limitations are inherent in a deterministic one-to-one model.

Keywords: operation theatre scheduling, assignment problem, Hungarian method, surgeon allocation, hospital operations, India