A unified bi objective model for cost and preference optimization in smart hospital resource management

Modern hospital operations need more advanced optimization methods due to the factors such as the variation in patient demand, limited resources, and complicated workforce regulations. The initial research suggested a combined Linear and Mixed-Integer Linear Programming (LP/MILP) approach to the joint optimization of patient admissions, bed/OR utilization, and nurse scheduling. The model unified the operational costs and the staff preferences into a single weighted objective, thereby showing the very significant resource utilization and scheduling satisfaction improvements. We have extended the framework from its original version and in this extended work we are going to demonstrate how the nurse scheduling component is fashioned into an actual multi-objective optimization problem. Rather than addressing the problem via a single weighted aggregation, two opposing targets, minimizing overall operational cost and maximizing nurse preference satisfaction, are treated openly. Moreover, we introduce the Adaptive ε-Constraint method that allows us to take advantage of the division between coarse ε sweep and local refinement to produce a well-distributed approximation of the Pareto frontier. The progressive method not only addresses the clustering problem that has appeared in the naive ε sweeps but also creates a continuous and varied set of solutions that are not dominated by any other solution. With the extended model that utilizes synthetic but realistic nurse, demand, and preference data, a variety of feasible scheduling policies with obvious trade-offs between cost and employee satisfaction are provided. The Pareto frontier offers intermediate solutions which are able to achieve large increases in preference satisfaction at the expense of only negligible increments in operational costs when compared to the baseline cost-minimal and preference-maximal schedules. The findings emphasize the usefulness of multi-objective decision support in hospital practice and also prove that through the direct representation of staff preferences, it is possible to have even distributions of working time without losing the effectiveness of operations. On the whole, the extension demonstrates that the original "smart hospital" model is enriched and the decision-making process for the administrators is more flexible with the inclusion of multi-objective optimization, thus resulting in the enhancement of both efficiency and health of the staff.