Scheduling the hospital-wide flow of elective patients

In this paper, we address the problem of planning the patient flow in hospitals subject to scarce medical resources with the objective of maximizing the contribution margin. We assume that we can classify a large enough percentage of elective patients according to their diagnosis-related group (DRG) and clinical pathway. The clinical pathway defines the procedures (such as different types of diagnostic activities and surgery) as well as the sequence in which they have to be applied to the patient. The decision is then on which day each procedure of each patient’s clinical pathway should be done, taking into account the sequence of procedures as well as scarce clinical resources, such that the contribution margin of all patients is maximized. We develop two mixed-integer programs (MIP) for this problem which are embedded in a static and a rolling horizon planning approach. Computational results on real-world data show that employing the MIPs leads to a significant improvement of the contribution margin compared to the contribution margin obtained by employing the planning approach currently practiced. Furthermore, we show that the time between admission and surgery is significantly reduced by applying our models

Driver Routing and Scheduling with Synchronization Constraints

This paper investigates a novel type of driver routing and scheduling problem motivated by a practical application in long-distance bus networks. A key difference from other crew scheduling problems is that drivers can be exchanged between buses en route. These exchanges may occur at arbitrary intermediate stops such that our problem requires additional synchronization constraints. We present a mathematical model for this problem that leverages a time-expanded multi-digraph and derive bounds for the total number of required drivers. Moreover, we develop a destructive-bound-enhanced matheuristic that converges to provably optimal solutions and apply it to a real-world case study for Flixbus, one of Europe's leading coach companies. We demonstrate that our matheuristic outperforms a standalone MIP implementation in terms of solution quality and computational time and improves current approaches used in practice by up to 56%. Our solution approach provides feasible solutions for all instances within seconds and solves instances with up to 390 locations and 70 requests optimally with an average computational time under 210 seconds. We further study the impact of driver exchanges on personnel costs and show that allowing for such exchanges leads to savings of up to 75%

Hospital-wide therapist scheduling and routing: exact and heuristic methods

In this paper, we address the problem of scheduling and routing physical therapists hospital-wide. At the beginning of a day, therapy jobs are known to a hospital's physical therapy scheduler who decides for each therapy job when, where and by which therapist a job is performed. If a therapist is assigned to a sequence which contains two consecutive jobs that must take place in different treatment rooms, then transfer times must be considered. We propose three approaches to solve the problem. First, an Integer Program (IP) simultaneously schedules therapies and routes therapists. Second, a cutting plane algorithm iteratively solves the therapy scheduling problem without routing constraints and adds cuts to exclude schedules which have no feasible routes. Since hospitals are interested in obtaining quick solutions, we also propose a heuristic algorithm, which schedules therapies sequentially by simultaneously checking routing and resource constraints. Using real-world data from a hospital, we compare the performance of the three approaches. Our computational analysis reveals that our IP formulation fails to solve test, which have more than~30 jobs, to optimality in an acceptable solution time. In contrast, the cutting plane algorithm can solve instances with more than 100 jobs optimally. The heuristic approach obtains good solutions for large real-world instances within fractions of a second

Machine learning approaches for early DRG classification and resource allocation

Recent research has highlighted the need for upstream planning in healthcare service delivery systems, patient scheduling, and resource allocation in the hospital inpatient setting. This study examines the value of upstream planning within hospital-wide resource allocation decisions based on machine learning (ML) and mixed-integer programming (MIP), focusing on prediction of diagnosis-related groups (DRGs) and the use of these predictions for allocating scarce hospital resources. DRGs are a payment scheme employed at patients’ discharge, where the DRG and length of stay determine the revenue that the hospital obtains. We show that early and accurate DRG classification using ML methods, incorporated into an MIP-based resource allocation model, can increase the hospital’s contribution margin, the number of admitted patients, and the utilization of resources such as operating rooms and beds. We test these methods on hospital data containing more than 16,000 inpatient records and demonstrate improved DRG classification accuracy as compared to the hospital’s current approach. The largest improvements were observed at and before admission, when information such as procedures and diagnoses is typically incomplete, but performance was improved even after a substantial portion of the patient’s length of stay, and under multiple scenarios making different assumptions about the available information. Using the improved DRG predictions within our resource allocation model improves contribution margin by 2.9% and the utilization of scarce resources such as operating rooms and beds from 66.3% to 67.3% and from 70.7% to 71.7%, respectively. This enables 9.0% more nonurgent elective patients to be admitted as compared to the baseline

A Data-Driven Approach for Baggage Handling Operations at Airports

Before each flight departs, baggage has to be loaded into containers, which are then forwarded to the airplane. Planning the loading process consists of setting the start times for the loading process and depletion of the baggage storage as well as assigning handling facilities and workers. Flight delays and uncertain arrival times of passengers at the check-in counters require plans that are adjusted dynamically every few minutes and, hence, an efficient planning procedure. We propose a model formulation and a solution procedure that utilize historical flight data to generate reliable plans in a rolling planning fashion, allowing problem parameters to be updated in each reoptimization. To increase the tractability of the problem, we employ a column generation–based heuristic in which new schedules and work profiles are generated in subproblems, which are solved as dynamic programs. In a computational study, we demonstrate the robust performance of the proposed procedure based on real-world data from a major European airport. The results show that (i) the procedure outperforms both a constructive heuristic that mimics human decision making and a meta heuristic (tabu search) and (ii) being able to dynamically (re)allocate baggage handlers leads to improved solutions with considerably fewer left bags

Efficient priority rules for the resource-constrained project scheduling problem

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel W 351 (350) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman