Discrete Optimization
Minimizing the maximal ergonomic burden in intra-hospital patient transportation

https://doi.org/10.1016/j.ejor.2019.01.062Get rights and content

Highlights

  • An ergonomic patient routing problem is considered and solved by tabu search.

  • Tabu search can solve even large instances almost optimally in short time.

  • It can help hospitals to decrease physical stress and apply resources efficiently.

  • The trade-off between staff size and physical liability is analyzed.

  • The greater the staff, the lower the growth of stress caused by staff reduction.

Abstract

The transportation of patients within a hospital concerns three main groups. Firstly, the hospital managers, who must ensure an efficient transport system with sufficient porters so that delays of surgeries or examinations are (mostly) avoided. Secondly, the patients, for whom waiting times before and after appointments should not be too long. And thirdly, the porters, who carry out the physical transport of patients within the hospital. This last group faces high physical liability as well as risks of illnesses and injuries due to work-related musculoskeletal disorders. Despite these facts, the porters’ interests are often neglected in current research. This paper integrates the needs of all three aforementioned groups into a mathematical model, which is solved with the help of a tailored tabu search algorithm. Computational experiments reveal that the new procedure is able to find high-quality solutions in a very short time. Most often, the obtained solutions are even optimal. They also significantly improve upon those generated by a typical real-world planning approach. Furthermore, the trade-off between the interests of all three groups is analyzed.

Introduction

The rising demographic trend and subsequent increases in health care costs seen in industrial countries are placing ever more pressure on hospitals to be more efficient with their resources. Furthermore, accounting methods, like the Diagnosis Related Groups, require that hospitals do not keep patients longer than necessary (cf. Böcking, Ahrens, Kirch, & Milakovic, 2005) as well as manage their resources economically without decreasing the service quality. As a result of this cost pressure, physicians, nurses, and other health care workers find themselves under an increasing workload which leads to increased physical stress and ergonomic burden. This ultimately may result in long term health challenges for the staff members and, thus, further costs for the hospital and society as a whole (Lee, 1994).

Many hospital staff are exposed to physically demanding tasks such as, e.g., the unnatural postures held by surgeons, anesthetists, and theater nurses for several hours at a time during operations. This greatly increases the likelihood of work-related musculoskeletal disorders (MSDs). According to Watson (2010, p. 205), MSD is the most frequent work-related injury for nursing aides and orderlies. The occurrence of such injuries in this group of nursing personnel is higher than even for freight handlers and delivery truck drivers. The direct costs incurred by MSDs in Germany is estimated to be about 4.2 Billion Euro per year, making up around 10% of the total costs of all injuries and illnesses (cf. Bödeker, Friedel, Röttger, & Schröer, 2002). Similarly, the transport of patients within the hospital either by wheelchair or bed also represents physical burden to health care workers. About 8% of back injuries, 9% of back strains and sprains, and 20% of overexertion injuries sustained by industry workers are associated with pushing and pulling tasks (Health, 1981, Klein, Jensen, Sanderson, 1984). In large hospitals, it is not unusual for porters to walk up to 20km or even more in an eight-hour shift, partly pushing or pulling wheelchairs or beds with patients (Fröhlich von Elmbach, Boysen, Briskorn, & Mothes, 2015).

Despite these findings, efforts to optimize intra-hospital patient transportation usually focus on the economic implications of delayed or missed appointments, or on optimizing the patient’s convenience by reducing travel and waiting times. A third group also worthy of consideration are the hospital porters who are exposed to high levels of physical stress resulting from patient transportation. Minimizing their total travel time might serve as a proxy to reduce physical stress. However, many more factors impact the level of stress as will be shown later on. Besides, minimizing the sum of travel times does not consider the porter’s individual physical stress as this objective compensates for variations among them.

This paper treats the problem of scheduling intra-hospital patient transportation jobs of the pickup and delivery type with a focus on minimizing the maximal physical stress among the porters while keeping all appointments. To tackle this problem, we design a tabu search algorithm that is adapted to the problem by adding several established and new components. Its performance is examined in a comprehensive computational study on a broad range of randomly generated instances. The results clearly attest to the efficacy of our approach which is not only fast but also capable of optimally solving almost all investigated instances with up to 300 jobs. A further experiment shows that our approach is not only able to generate schedules which level the ergonomic burden of porters but also allows for reducing the work force without increasing the (maximal) physical stress compared to a typical real-world planning approach.

The remainder is structured as follows: Section 2 provides a literature review on the current state of related research. In Section 3, we develop a first approach towards the measurement and evaluation of porters’ physical stress in patient transportation. Then, in Section 4, we describe and formalize the resulting static patient transportation problem. Preliminary considerations for solving this problem heuristically are contained in Section 5. Afterwards, Section 6 elaborates on the details of the proposed tabu search algorithm. We report on the design of our comprehensive computational study and discuss the results in Section 7. Finally, Section 8 concludes the paper and describes future research needs.

Section snippets

Literature review of related research

Concerning the structure of the underlying optimization problem (cf. Section 4), the problem studied in this article belongs to the general class of vehicle routing problems, in particular, pickup and delivery and dial-a-ride, with time windows. However, as almost the complete research on those problems considers the routing of motorized vehicles and does not address ergonomic aspects, we do not give a lengthy description of those problem types but refer the reader to, e.g., Cordeau and Laporte

Quantifying physical liability

When incorporating ergonomic aspects into the optimization of health care operations, it is necessary to have a calculation scheme at hand that properly quantifies the ergonomic stress caused by activities such as pushing and pulling patient transportation vehicles. However, to the best of our knowledge, such a valid and widely accepted calculation scheme is not available to date. Therefore, in Section 3.1, we briefly describe the main factors affecting the physical liability of hospital

Problem definition

During their stay in a hospital, patients have to keep appointments like examinations or surgeries. To get to their appointments on time and back to their rooms afterwards, they are transported in non-motorized devices like beds and wheelchairs or escorted on foot, respectively, by so-called porters. Every porter transports one patient at a time on a direct way from the patient’s origin to their destination. Except for the emergency ward and the intensive care units – where usually a dedicated

Elements of a neighborhood search for EPTP

Due to the NP-hardness of EPTP and the dimension of real-world instances (about 300 jobs in an eight-hour shift of a large-sized hospital; cf. Fröhlich von Elmbach et al. (2015)), it seems to be reasonable to solve the overall problem by a neighborhood search. Since it is difficult to find feasible solutions (hard time windows) and the min-max objective is rather weak in discriminating between solutions, it is necessary to develop appropriate mechanisms to guide the search purposefully. In the

A tailored tabu search procedure for EPTP

We choose tabu search (TS) to tackle EPTP as it is a well-known and powerful neighborhood-based meta-heuristic in overcoming both infeasible and local optimal solutions. Building upon the basic elements (see Section 5) used in our search procedure, we now develop a tailored TS approach that is highly adapted to the specifications of EPTP.

In the literature, many heuristic algorithms for related problems from the fields of vehicle routing and machine scheduling can be found. However, most of

Computational experiments

To test our TS algorithm, we generate a set of test instances according to a full factorial design to cover relevant and realistic settings. The generation scheme is detailed in Section 7.1 and bases upon information from a large-sized hospital. Lower bounds on Emax are described in Section 7.2. In Sections 7.3 and 7.4, we present and discuss the results of our computational experiments in which we compare the performances of different TS variants, a typical real-world planning approach, and

Summary and conclusions

In contrast to most pickup and delivery problems in literature, patients in hospitals are usually not transported by motorized vehicles. Instead, humans carry out the physical transport. Efforts to optimize the intra-hospital transportation should therefore not only concentrate on timing, economic, or patient-related issues but also on ergonomic aspects. Induced by the increasing cost pressure in hospitals, establishing an efficient patient transport system with sufficient porters so that

Acknowledgment

We are indebted to Stefan Schwerdfeger and Christina Wille for valuable comments.

References (77)

  • N. Mladenović et al.

    Variable neighborhood search

    Computers & Operations Research

    (1997)
  • W.P. Nanry et al.

    Solving the pickup and delivery problem with time windows using reactive tabu search

    Transportation Research Part B: Methodological

    (2000)
  • National Institute for Occupational Safety and Health

    Work practices guide for manual lifting. Division of Biomedical and Behavioral Science

    DHHS publication (NIOSH)

    (1981)
  • A. Otto et al.

    Reducing ergonomic risks by job rotation scheduling

    OR Spectrum

    (2013)
  • E. Taillard et al.

    A tabu search heuristic for the vehicle routing problem with soft time windows

    Transportation Science

    (1997)
  • N.A. Wassan et al.

    A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries

    Journal of Combinatorial Optimization

    (2008)
  • D.S. Watson

    Perioperative safety

    (2010)
  • M.M. Ayoub et al.

    Effects of operator stance on pushing and pulling tasks

    AIIE Transactions

    (1974)
  • R. Battiti et al.

    The reactive tabu search

    ORSA Journal on Computing

    (1994)
  • A. Beaudry et al.

    Dynamic transportation of patients in hospitals

    OR Spectrum

    (2010)
  • H. Beaulieu et al.

    A mathematical programming approach for scheduling physicians in the emergency room

    Health Care Management Science

    (2000)
  • W. Böcking et al.

    First results of the introduction of DRGs in germany and overview of experience from other DRG countries

    Journal of Public Health

    (2005)
  • W. Bödeker et al.

    Kosten arbeitsbedingter Erkrankungen in Deutschland

    Forschungsbericht FB 946, Schriftenreihe der Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, Wirtschaftsverlag NW Verlag

    (2002)
  • S. Bourdais et al.

    HIBISCUS: a constraint programming application to staff scheduling in health care

  • O. Bräysy et al.

    Vehicle routing problem with time windows, Part i: Route construction and local search algorithms

    Transportation Science

    (2005)
  • M. Brütting et al.

    Muskel-Skelett-Belastungen beim Schieben und Ziehen von Krankenbetten und Rollstühlen

    Zentralblatt für Arbeitsmedizin, Arbeitsschutz und Ergonomie

    (2017)
  • B.J. Carnahan et al.

    Designing safe job rotation schedules using optimization and heuristic search

    Ergonomics

    (2000)
  • M.W. Carter et al.

    Scheduling emergency room physicians

    Health Care Management Science

    (2001)
  • J.F. Cordeau et al.

    The dial-a-ride problem: Models and algorithms

    Annals of Operations Research

    (2007)
  • Darcor Casters Limited (2014). Guide to workplace ergonomics....
  • M. Dell’Amico et al.

    Optimal scheduling of tasks on identical parallel processors

    ORSA Journal on Computing

    (1995)
  • EN 614-1

    Safety of machinery - ergonomic design principles, Part 1: Terminology and general principles

    European Committee for Standardization

    (2006)
  • A. Fröhlich von Elmbach et al.

    Scheduling pick-up and delivery jobs in a hospital to level ergonomic stress

    IIE Transactions on Healthcare Systems Engineering

    (2015)
  • T.D. Fry et al.

    Minimizing weighted absolute deviation in single machine scheduling

    IIE Transactions

    (1987)
  • M.R. Garey et al.

    One-processor scheduling with symmetric earliness and tardiness penalties

    Mathematics of Operations Research

    (1988)
  • F. Glover et al.

    Tabu search

    (1997)
  • T. Hanne et al.

    Bringing robustness to patient flow management through optimized patient transports in hospitals

    Interfaces

    (2009)
  • M. Haouari et al.

    Tight bounds for the identical parallel machine-scheduling problem

    International Transactions in Operational Research

    (2006)
  • View full text