Stable annual scheduling of medical residents using prioritized multiple training schedules to combat operational uncertainty

For educational purposes, medical residents often have to pass through many departments, which place different requirements on them. They are informed about the upcoming departments by an annual training schedule which keeps the individual departments’ service level as constant as possible. Due to poor planning and uncertain events, deviations in the schedule can occur. These deviations affect the service level in the departments, as well as the training progress and satisfaction of the residents. This article analyzes the impact of priorities on residents’ annual planning based on department assignments to combat uncertainty that might result in departmental changes. We present a novel two-stage formulation that combines residents’ tactical planning with duty and daily scheduling’s operational level. We determine an analytical bound for the problem that is superior to the LP bound. Additionally, we approximate a bound based on the solution approach using the objective value of the deterministic solution of an instance and the absences in each scenario. In a computational study, we analyze the performance of various bounds, our solution approach, and the effects of additional priorities in residents’ annual planning. We show that additional priorities can significantly reduce the number of unexpected department assignments. Finally, we derive a practical number of priorities from the results

Customized GRASP for rehabilitation therapy scheduling with appointment priorities and accounting for therapist satisfaction

Physical therapy in acute care hospitals plays an important role in the rehabilitation of patients. Nevertheless, the profession must deal with staff shortages caused by a lack of potential employees and absenteeism which are results of high physical and mental workloads. The therapist shortage negatively affects the total number of daily appointments the department can fulfill. For appointments that can be successfully scheduled, continuity of care with the same therapist cannot be guaranteed for individual patients. Lack of continuity of care negatively influences the therapist's satisfaction. Therapist preferences for individual appointments in general cannot always be guaranteed when designing schedules, which also hurts satisfaction. This paper develops a multi-criteria model for the daily therapy appointment-scheduling problem. The primary objective is to minimize the total sum of priority violations for unscheduled appointments. To improve therapist satisfaction, we consider therapist preferences including continuity of care as a secondary objective. Here, our integer programming formulation aims to minimize the total sum of preference violations for scheduled appointments. We are dealing with an operational planning problem with a daily planning horizon. The operational objective is to achieve therapist schedules in at most two hours. The therapists’ schedules together need to include several hundred appointments for a planning day. Due to intractability, the developed integer program cannot provide schedules for such problem sizes. Therefore, we develop a customized Greedy Randomized Adaptive Search Procedure (GRASP) with six innovative local search operations to improve an initially constructed solution. We test the heuristic algorithm on realistic data instances. The metaheuristic provides high-quality schedules for various problem sizes in short runtimes, i.e., within minutes. Comparisons with the optimal solutions for small problem instances show very good results of the GRASP with a similar number of scheduled appointments and good adherence to continuity of care and therapist preference requirements

Stable Annual Scheduling of Medical Residents Using Prioritized Multiple Training Schedules to Combat Operational Uncertainty

For educational purposes, medical residents often have to pass through many departments, which place different requirements on them. They are informed about the upcoming departments by an annual training schedule which keeps the individual departments’ service level as constant as possible. Due to poor planning and uncertain events, deviations in the schedule can occur. These deviations affect the service level in the departments, as well as the training progress and satisfaction of the residents. This article analyzes the impact of priorities on residents’ annual planning based on department assignments to combat uncertainty that might result in departmental changes. We present a novel two-stage formulation that combines residents’ tactical planning with duty and daily scheduling’s operational level. We determine an analytical bound for the problem that is superior to the LP bound. Additionally, we approximate a bound based on the solution approach using the objective value of the deterministic solution of an instance and the absences in each scenario. In a computational study, we analyze the performance of various bounds, our solution approach, and the effects of additional priorities in residents’ annual planning. We show that additional priorities can significantly reduce the number of unexpected department assignments. Finally, we derive a practical number of priorities from the results

Machine Learning–Supported Prediction of Dual Variables for the Cutting Stock Problem with an Application in Stabilized Column Generation

This article presents a prediction model of the optimal dual variables for the cutting stock problem. For this purpose, we first analyze the influence of different attributes on the optimal dual variables within an instance for the cutting stock problem. We apply and compare our predictions in a stabilization technique for column generation. In most studies, the parameters for stabilized column generation are determined by numerical tests, that is, the same problem is solved several times with different settings. We develop two learning algorithms that predict the best algorithm configuration based on the predicted optimal dual variables and thus omit the numerical study. Our extensive computational study shows the tradeoff between the learning algorithms using full and sparse instance information. We show that both algorithms can efficiently predict the optimal dual variables and dominate the common update mechanism in a generic stabilized column generation approach. Although the learning algorithm with full instance information is applicable when one has to solve the problem mainly for a fixed set of items, the algorithm with sparse instance information is applicable when there is more variability in the number of items between the different instances

A robust framework for task-related resident scheduling

We consider the training phase of physicians after finishing medical school. They specialize in a common field like ophthalmology or anesthesiology and are called residents. Technological progress in health care leads to increasing complexity in the requirements of physician training. As a consequence, those programs are often not only time-related but also task-related. Task-related means that residents should perform a given number of different interventions in their program. Typically, a resident will follow a rotation across different clinical departments, where the number of performed interventions per period may be estimated. Predicting the exact number of interventions is usually not possible. Accordingly, a resident might not be able to perform all of the required interventions during the planned rotation, resulting in an extension of the program. In this paper, a new model is presented that calculates the number of residents a hospital can reliably train on a strategic level. Our model also provides the corresponding training schedule. It considers minimum requirements of both time-related stays in specific departments as well as task-related interventions that have to be performed. The robustness of the model can be set by management to handle uncertainties in interventions. A Dantzig-Wolfe decomposition is used to accelerate the solution process and a new pattern generation approach that can construct multiple patterns out of one solution is developed. The termination of the column generation algorithm is accelerated significantly by this method. The model is evaluated using real-world data from a resident program for anesthesiology in a German university hospital. The results demonstrate that near-optimal solutions with an average optimality gap of below five percent can be achieved within computation times of few minutes. (C) 2019 Elsevier B.V. All rights reserved