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Hospital departments face artificial demand variability when the demand for their care depends on the plans of other departments. This holds among others for ‘downstream’ departments like surgical wards and departments that treat patients without appointments (walk-in). Challenge: Variability in demand makes it hard for capacity planners to align capacity and demand at every moment. In addition, staffing levels typically need to be settled when the individual patients to care for are still unknown. Literature contains models to forecast artificial demand variability, but lacks implementation results. Method: This chapter describes the application of a forecast of demand for post-operative physiotherapy based on the surgical session roster. The forecast is used to determine staffing requirements on which the physiotherapists base their schedule. We test this approach in a case study at the Sint Maartenskliniek in the Netherlands, for physiotherapists who are part of the orthopaedic care chain. Results and Conclusion: Successful implementation of this methodology has shown positive effects for patients (12% more adherence to protocol), employees (twice the number of days were efficiently staffed), and the hospital (13% productivity increase). This demonstrates the potential of the methodology to help downstream hospital departments cope with artificial variability.

This book presents healthcare logistics solutions that have been successfully implemented at a variety of healthcare facilities. In each case, a major challenge is presented, along with the solution approach and implementation steps, followed by the impact on hospital operations. Problems encountered when implementing the results in practice are also discussed. Much of the work presented is drawn from the experiences of members of the Center for Healthcare Operations Improvement and Research (CHOIR) at Twente, along with the CHOIR spin-off company, Rhythm.

Enabling patients to walk in for their diagnostic examination without an appointment has considerable potential in terms of quality of care, patient service, and system efficiency. We present a model to evaluate the effect of implementing a combined walk-in and appointment system, offering appointments to all patients preferring or strictly requiring these, while enabling all other patients to walk in. In a combined system, appointments can be scheduled in periods with low walk-in demand to counterbalance the possible high variability in walk-in arrival rates. We develop a discrete event simulation model, combined with an intelligent algorithmic methodology for appointment schedule optimization, for evaluating the implementation of a combined walk-in and appointment system for diagnostic examinations. Our simulation model is reusable: its component-based structure and generic underlying logic enable it to automatically represent any type of diagnostic facility, for which it can then evaluate the effect of implementing a combined walk-in and appointment system. Applying this approach, we quantitatively investigate the impact of implementing a combined walk-in and appointment system for CT-scans, performing a case study at the Academic Medical Center (AMC) Amsterdam. Inspired by the results, the AMC CT-facility has implemented a combined walk-in and appointment system, thereby shortening patients' diagnostic trajectories, and decreasing the number of required hospital visits for many patients. (C) 2017 Elsevier B.V. All rights reserved

Around 40% of cured cancer patients in the European Union are treated with radiotherapy [2]. Delays in cancer treatment are associated with psychological distress and decreased cancer control. To this end, in the Netherlands standards for the access time for radiation treatment are set, which are currently not met in many Dutch oncological centers. The radiotherapy care process (i.e., preparation and treatment) consists of several consecutive stages, possibly related via time constraints. Inadequate capacity allocation may cause large delays, for example due to the capacity allocation of different stages not being aligned, or due to inadequate time division of single resources over different activities. The objective of this study is to increase compliance to access time standards without extending resource capacities, by developing a methodology for optimizing resource capacity allocation in the radiotherapy care process. For radiotherapy, time division of resources over different activities particularly applies to the doctors, who carry out consultations and scan contouring. Time slots for these activities are typically set for each doctor in a cyclic weekly scheme. We develop an integer linear programming (ILP) model to design a weekly doctors’ scheme that minimizes the expected access times of all patient types in the care process and that matches the number of consultation time slots with demand. In several experiments, the quality of the resulting doctors’ schemes is studied via a discrete event simulation model by evaluating the consequences of the schemes in a stochastic environment. Results from a case study in the Academic Medical Center (AMC) in Amsterdam show that the implementation of these schemes may result in a considerable access time reduction. The designed doctor’s schemes are being evaluated for implementation in the AMC.

The Academic Medical Center (AMC) in Amsterdam, The Netherlands, recently opened the ‘Children’s Muscle Center Amsterdam’ (CMCA). The CMCA diagnoses and treats children with neuromuscular diseases. The patients with such diseases require care from a variety of clinicians. Through the establishment of the CMCA, children and their parents will generally visit the hospital only once a year, while previously they used to visit on average six times a year. This is a major improvement, because the hospital visits are both physically and psychologically demanding for the patients. This paper describes how quantitative modelling supports the design and operations of the CMCA. First, an integer linear program is presented that selects which patients are to be invited for a treatment day and schedules the required combination of consultations, examinations and treatments on one day. Second, the integer linear program is used as input to a simulation study to estimate the capacity of the CMCA, expressed in terms of the distribution of the number patients that can be seen on one diagnosis day. Finally, a queueing model is formulated to predict the access time distributions based upon the simulation outcomes under various demand scenarios. Its contribution on the case under study is twofold. First, we design highly constrained appointment schedules for multiple patients that require service from multiple disciplines’ resources. Second, we study the effect of the trade-offs between scheduling constraints and access times. As such, the contribution of this case study paper is that it illustrates the value of applying Operations Research techniques in complex healthcare settings, by designing context-specific combinations of mathematical models, thereby improving delivery of the highly-constrained multidisciplinary care.

We present a methodology to design appointment systems for outpatient clinics and diagnostic facilities that offer both walk-in and scheduled service. The developed blueprint for the appointment schedule prescribes the number of appointments to plan per day and the moment on the day to schedule the appointments. The method consists of two models; one for the day process that governs scheduled and unscheduled arrivals on the day and one for the access process of scheduled arrivals. Appointment schedules that balance the waiting time at the facility for unscheduled patients and the access time for scheduled patients are calculated iteratively using the outcomes of the two models. Two methods to calculate appointment schedules, complete enumeration and a heuristic procedure, are compared in various numerical experiments. Furthermore, an appointment schedule for the CT-scan facility at the Academic Medical Center Amsterdam, The Netherlands, is developed to demonstrate the practical merits of the methodology. The method is of general nature and can therefore also be applied to scheduling problems in other sectors than health care. (C) 2014 Elsevier B.V. All rights reserved

We consider a master surgery scheduling (MSS) problem in which block operating room (OR) time is assigned to different surgical specialties. While many MSS approaches in the literature consider only the impact of the MSS on operating theater and operating staff, we enlarge the scope to downstream resources, such as the intensive care unit (ICU) and the general wards required by the patients once they leave the OR. We first propose a stochastic analytical approach, which calculates for a given MSS the exact demand distribution for the downstream resources. We then discuss measures to define downstream costs resulting from the MSS and propose exact and heuristic algorithms to minimize these costs.

In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an M|G|c|c system and an upper bound by an M|G|c-1|c-1 system, hence by simple Erlang loss expressions.The result is based on a product form modification for a special OT-ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.

Dit hoofdstuk beschrijft hoe het verbeteren van de capaciteitsplanning van klinische fysiotherapie na operaties kan leiden tot betere zorg voor patienten, een meer gelijkmatige verdeling van werklast en een verhoogde productiviteit van de behandelaren. De kern van capaciteitsplanning is het vinden van de juiste afstemming tussen de vraag naar zorg en in te zetten capaciteit. De vraag naar klinische zorg is variabel, doordat de benodigde zorg per specialisme en type ingreep verschilt, er niet op alle dagen in de week evenveel geopereerd wordt en er last minute wijzigingen in de operatieplanning optreden. Door de variabiliteit en onzekerheid in de vraag naar klinische zorg is het voor capaciteitsplanners moeilijk om een dienstrooster te maken waarmee het aanbod van fysiotherapeuten elke dag is afgestemd op de zorgvraag. Dit hoofdstuk presenteert een wiskundige methodiek waarmee de vraag naar klinische fysiotherapie meerdere maanden van tevoren voorspelbaar gemaakt kan worden en waarmee de afstemming tussen vraag en aanbod kan worden geoptimaliseerd. Succesvolle invoering van deze methodiek in de Sint Maartenskliniek toont positieve effecten voor de patient, medewerker en bedrijfsvoering.

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.

Workloads in nursing wards depend highly on patient arrivals and lengths of stay, both of which are inherently variable. Predicting these workloads and staffing nurses accordingly are essential for guaranteeing quality of care in a cost-effective manner. This paper introduces a stochastic method that uses hourly census predictions to derive efficient nurse staffing policies. The generic analytic approach minimizes staffing levels while satisfying so-called nurse-to-patient ratios. In particular, we explore the potential of flexible staffing policies that allow hospitals to dynamically respond to their fluctuating patient population by employing float nurses. The method is applied to a case study of the surgical inpatient clinic of the Academic Medical Center Amsterdam (AMC). This case study demonstrates the method's potential to evaluate the complex interaction between staffing requirements and several interrelated planning issues such as case mix, care unit partitioning and size, as well as surgical block planning. Inspired by the quantitative results, the AMC concluded that implementing this flexible nurse staffing methodology will be incorporated in the redesign of the inpatient care operations in the upcoming years.

This chapter aims to promote and illustrate the fruitful combination of classical Operations Research (OR) and Computer Simulation. First, a highly instructive example of parallel queues will be studied. This simple example already shows the necessary combination of OR (queueing) and simulation that appears to be of practical interest such as for call center optimization. Next, two more ’real life’ applications are regarded: - blood platelet production and inventory management at blood banks, and - train conflict resolution for railway junctions. Both applications show the useful combination of Simulation and optimization methods from OR, in particular Stochastic Dynamic Programming (SDP) and Markov decision theory (MDP), to obtain simple rules that are nearly optimal. The results are based on real life Dutch case studies and show that this combined OR-Simulation approach can be most useful for ’practical optimization’ and that it is still wide open for further application.

This paper presents a methodology to plan treatments for rehabilitation outpatients. These patients require a series of treatments by therapists from various disciplines. In current practice, when treatments are planned, a lack of coordination between the different disciplines, along with a failure to plan the entire treatment plan at once, often occurs. This situation jeopardizes both the quality of care and the logistical performance. The multidisciplinary nature of the rehabilitation process complicates planning and control. An integral treatment planning methodology, based on an integer linear programming (ILP) formulation, ensures continuity of the rehabilitation process while simultaneously controlling seven performance indicators including access times, combination appointments, and therapist utilization. We apply our approach to the rehabilitation outpatient clinic of the Academic Medical Center (AMC) in Amsterdam, the Netherlands. Based on the results of this case, we are convinced that our approach can be valuable for decision-making support in resource capacity planning and control at many rehabilitation outpatient clinics. The developed model will be part of the new hospital information system of the AMC.

During the upcoming decades, healthcare organizations face the challenge to deliver more patient care, of higher quality, and with less financial and human resources. The goal of this thesis is to help and guide healthcare professionals making their organizations future-proof. Building on techniques from Operations Research, a subfield of applied mathematics, and focusing on the management of operations, the research presented contributes to a better understanding and functioning of healthcare delivery. The outcomes support decision makers in realizing the best possible use of available resources. The work presented intends to make healthcare professionals more aware of the added value of taking an integral perspective on logistical decision making. First, the problems addressed emphasize the importance of integrality in terms of objectives: healthcare must be safe, effective, patient-centered, timely, efficient, and equitable. While the traditional belief is that quality and efficiency always confront each other, we demonstrate that they often can, and must, go hand in hand. Second, the research outcomes show the value of integrality in planning and control: performance is enhanced by aligning long-, medium-, and shortterm decision making and by realizing coordination and collaboration between the various care chain actors. The thesis is organized in six parts. Part I provides a general introduction. Part II provides an overview of the field of resource capacity planning and control in healthcare and a review of the state of the art in Operations Research. It sets up the conceptual framework within which several specific decision problems are studied in the following parts. Part III focuses on facilitating combination appointments during single outpatient visits, and Part IV on multidisciplinary treatments requiring a series of outpatient visits. Part V supports the design and operations of inpatient care services. Part VI builds a theoretical framework to model entire care pathways. In Part III–Part VI, a diversity of operations research techniques (often in combination) is applied: computer simulation, heuristics, Markov processes, mathematical programming, queueing theory, and stochastic Petri nets. Based on the obtained results, in the epilogue we claim that Operations Research can play a key role in addressing the tough logistical challenges healthcare organizations face.

This paper presents a methodology to plan treatments for rehabilitation outpatients. These patients require a series of treatments by therapists from various disciplines. In current practice, when treatments are planned, a lack of coordination between the different disciplines, along with a failure to plan the entire treatment plan at once, often occurs. This situation jeopardizes both the quality of care and the logistical performance. The multidisciplinary nature of the rehabilitation process complicates planning and control. An integral treatment planning methodology, based on an integer linear programming (ILP) formulation, ensures continuity of the rehabilitation process while simultaneously controlling seven performance indicators including access times, combination appointments, and therapist utilization. We apply our approach to the rehabilitation outpatient clinic of the Academic Medical Center (AMC) in Amsterdam, the Netherlands. Based on the results of this case, we are convinced that our approach can be valuable for decision-making support in resource capacity planning and control at many rehabilitation outpatient clinics. The developed model will be part of the new hospital information system of the AMC.

We provide a comprehensive overview of the typical decisions to be made in resource capacity planning and control in health care, and a structured review of relevant articles from the field of Operations Research and Management Sciences (OR/MS) for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making.

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theater and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule (MSS) and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (i.e., case mix, care unit size, care unit partitioning), tactical (i.e., allocation of operating room time, misplacement rules), and operational decisions (i.e., time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision support tool in a complete redesign of the inpatient care operations.

The shelf life of platelet concentrates (PCs) is a matter of days. Simultaneously, the demand is highly variable, shortages are not allowed, and producing too many results in outdating. Concurrently, younger PCs, implying an extended time till outdating (TTO), are preferred. Common PC inventory management relies on experience-based order-up-to rules. This study aimed at minimizing outdating and shortages, while extending the TTO through a theoretical approach. It focuses on PCs processed from whole blood donations.A combined approach of stochastic dynamic programming and simulation techniques (SDP/S), from the mathematical discipline operations research, has been implemented. This approach included the design of the dedicated software tool thrombocyte inventory management optimizer (TIMO). Based on the 2007 data, an optimal order-up-to rule was calculated. Outdating percentages and TTOs have been collected from August 2005 to July 2010. The resulting order-up-to rule has been applied and adjusted from summer 2007 onward.Over the study period, the results of the practical implementation showed significant improvements. The median weekly outdating percentage dropped to less than 1% and a gain in TTO of 0.48 day was reached. The results and the additional computer simulations brought confidence to the personnel to apply and adopt the "theoretical" approach and TIMO.Applying theory may help a blood bank to improve its PC inventory management and may help to identify to what extent practical limits can approach theoretical limits. The application of the theory has led to both a significant improvement and a more structured and less panic-driven PC inventory management.

Due to a limited ICU capacity patients can be rejected at both the Operating Theater (OT) and at the Intensive Care Unit (ICU) within hospitals. The corresponding ICU-rejection probability is an important service factor for hospitals. A simple expression for this probability is not available. With c the ICU capacity (number of ICU beds), this paper provides analytic support for: (i) An M|G|c|c-approximation. (ii) A secure M|G|c−1|c−1 upper bound. The upper bound can be of practical interest so as to dimension the size of an ICU to secure a sufficiently small rejection probability.

We introduce the categorized reference database ORchestra, which is available online at http://www.utwente.nl/choir/orchestra/.

Workload on nursing wards depends highly on patient arrivals and patient lengths of stay, which are both inherently variable. Predicting this workload and staffing nurses accordingly is essential for guaranteeing quality of care in a cost effective manner. This paper introduces a stochastic method that uses hourly census predictions to derive efficient nurse staffing policies. The generic analytic approach minimizes staffing levels while satisfying so-called nurse-to-patient ratios. In particular, we explore the potential of flexible staffing policies which allow hospitals to dynamically respond to their fluctuating patient population by employing float nurses. The method is applied to a case study of the surgical inpatient clinic of the Academic Medical Center (AMC) Amsterdam. This case study demonstrates the method's potential to study the complex interaction between staffing requirements and several interrelated planning issues such as case mix, care unit partitioning and size, and surgical block planning. Inspired by the numerical results, the AMC decided that this flexible nurse staffing methodology will be incorporated in the redesign of the inpatient care operations during the upcoming years.