This grant provides funding for developing novel models and methods for planning, scheduling, staffing, and assignment (PSSA) problems that have multiple objectives and are unpredictable because of future uncertainty. Such problems arise frequently in the healthcare industry, which would be the focus application area. Examples of multiple, often competing, objectives are: patient safety and satisfaction, cost of service, continuity of care, educational goals of the residents, and staff satisfaction. Examples of uncertainty are patient workload and service times. Realistic mathematical models will be developed for such problems for healthcare professionals incorporating the unique features of this setting. A particular focus will be on medical resident scheduling. Computational methods will be developed for solving these models. In particular, heuristic methods will be developed for quickly identifying good candidate solutions for such problems. These methods will be tested on realistic data from the healthcare setting.

If successful, the results of this research will enable healthcare providers to improve work flow and to make utilize the skills of the provider's medical staff. Improved training schedules of medical school residents would be possible, while meeting their residency requirements. Patient satisfaction will improve as continuity of care is enhanced. The computational methods developed for solving problems arising in healthcare will also be useful for stochastic multi-objective integer programming models arising in a wide variety of application areas including production planning, supply chain management and vehicle.

Project Report

This grant resulted in the following three major modelign and methodological contributions. 1. Towards meeting the Accreditation Council for Continuing Medical Education (ACGME) requirements for surgical residents. This research demonstrated that in the current educatino and training mode it will be nearly impossible to meet the surgical medical continuity-of-care and case load requirements at the same time. In the continuity of care requirement, a resident is engaged during pre-surgical, surgery, and post-surgical patient consultation sessions. Two potential solutions are identified. First solution suggests that the surgical rotation length need to increase from one month to two months, and a borrow-back mechanism be instituted where a resident is "borrowed-back" from the next rotation to complete post-operative patient consultation sessions. The second solution suggests that an apprenticeship model of training residents be instituted, instead of the current model where residents are assigned their case-load through a scheduling mechanism. These recommendations were obtained after developing a detailed understanding of the problem, and extensive analysis and mathematical modeling using data collected from the electronic medical records at the Northwestern Memorial Hospital. Three research papers were published based on this research. One of these papers published in the leading journal (Annals of Surgery) in the field of surgery. The othe two papers published in leading applied journals in operations research and management science areas (Healthcare Management Science and Interfaces). The PhD student working on this project won a major student award (doing good with good OR) from the Institute for Operations Research and Management Science (INFORMS). 2. New Methods and Applications for Modeling Deterministic and Stochastic Multi-objective Optimization Problems This research developed a new family of models for multi-expert multi-objective/criteria decision making methodology that is suitable when a large number (say more than 4) of objectives are present in the decision making framework in a scientific and computationally tractable manner. A new concept of robust-Pareto optimality was introduced. Several modeling frameworks were developed. These frameworks allowed the function parameters and the decision makers' weights for the functions to be random. Reformulations of these models that allow the use of existing tools were given, and the practical usefulness of the concepts was illustrated using examples from agriculture planning, disaster management, and budget allocation to reduce inter-state disparity in diabetes care within US. Two reseearch papers were published based on this research. One publication was in the top methodology journal in the operations research area (Operation Research) and the other in leading healthcare management area (Healthcare Management Science). 3 New Models and Methods for the Healthcare Provider Staffing and Scheduling It is known that the patient volumes (demand on staff) in a hospital setting is highly variable. Howver, we need to provide safe patient care by maintaining a proper patient to staff ratio, e.g., patient to nurse ratio. In an healthcare environment where hospitals are under pressure to reduce costs, awe need to develop more effective tools that allow safe care while reducing costs incurred towards overtime. New stochastic and robust models were developed for staffing and scheduling problems under demand uncertainty. new methods were also developed to solve these models. The data used for this research was collected from different Northwestern Memorial Hospital patient care units (e.g., emergency medicine, hospital medicine, etc.). Discussions were held with the NMH administrators to elicit information the patient to volume ratio policies. First, a distributionally robust model was developed and studied to determine the number of nurses during a shift. Subsequently, an advanced two-stage stochastic optimization model was developed and studied to incorporate scheduling and staffing decisions in a single model. In the two-stage model he scheduling decisions take place six weeks in advance of the reaslization of patient demand, and the staffing levels are revised a week (or a day) prior to the actual service. The structural properties of the two-stage model were analyzed, and it was shown that the integrality requirement on the second stage variables can be dropped provided we add certain mixed-integer rounding inequalities to the model. This made the intractable models within reach of solving in a reasonable amount of computational time. Another twelve-fold improvement in solution time was achieved by introducing further algorithmic refinements. The research code was further parallelized to run on a computer with thirty two cores. Consequently, we managed to provide solutions to real-life problems in nearly twenty minutes of wall-clock time. Real=life results were achieved by developing demand forecasts using known forecasting techniques. It was shown that the approach approach will result in significant cost savings over the current practice. One paper has published in Asia Pacific Journal of Operations Research, and the second is under revision for the leading operations research journal (Operations Research). Reseach experience was also provided to a female undergraduate student by engaging her in the patient volume forecasting calculations.

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Northwestern University at Chicago
United States
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