Patient admission planning using Approximate Dynam

Authors: Peter J H Hulshof Martijn R K Mes Richard J Boucherie Erwin W Hans

Publish Date: 2015/04/18

Volume: 28, Issue: 1-2, Pages: 30-61

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Abstract

Tactical planning in hospitals involves elective patient admission planning and the allocation of hospital resource capacities We propose a method to develop a tactical resource allocation and patient admission plan that takes stochastic elements into consideration thereby providing robust plans Our method is developed in an Approximate Dynamic Programming ADP framework and copes with multiple resources multiple time periods and multiple patient groups with uncertain treatment paths and an uncertain number of arrivals in each time period As such the method enables integrated decision making for a network of hospital departments and resources Computational results indicate that the ADP approach provides an accurate approximation of the value functions and that it is suitable for large problem instances at hospitals in which the ADP approach performs significantly better than two other heuristic approaches Our ADP algorithm is generic as various cost functions and basis functions can be used in various hospital settingsThis paper concerns tactical planning in a hospital setting which involves the allocation of resource capacities and the development of patient admission plans Hulshof et al 2012 More concretely tactical plans distribute a doctor’s time resource capacity over various activities and control the number of patients that should be treated at each care stage eg surgery One of the main objectives of tactical planning in healthcare is to achieve equitable access and treatment duration for patients Hulshof et al 2013In tactical planning the term care process is used for a set of consecutive care stages followed by patients through a hospital This is the complete path of a patient group through the hospital such as for example a visit to an outpatient clinic a visit to an Xray and a revisit to the outpatient clinic Patients are on a waiting list at each care stage in their care process and the time spent on this waiting list is termed access time If access times are controlled this contributes to the quality of care for the patient The term care process is not to be confused with “clinical pathways” which is described by Every et al 2000 as “management plans that display goals for patients and provide the sequence and timing of actions necessary to achieve these goals with optimal efficiency” As care processes are defined by multiple steps that link departments and resources together in an integrated network fluctuations in patient arrivals and resource capacity availability at a single department or resource may affect other departments and resources in the network For patients this results in varying access times for each stage in a care process and for hospitals this results in varying resource utilizations and service levels To mitigate and address these variations reallocation of hospital resources incorporating the perspective of the entire care chain Cardoen and Demeulemeester 2008 Hall 2006 Porter and Teisberg 2007 seems necessary Hulshof et al 2013The tactical planning problem in healthcare is stochastic in nature Randomness exists in for example the number of emergency patient arrivals and the number of patient transitions after being treated at a particular stage of their care process Several papers have focused on tactical planning problems that span multiple departments and resources in healthcare Garg et al 2010 Kapadia et al 1985 Nunes et al 2009 and other industries Graves 1986 Hulshof et al 2012 2013 reviewed the literature and conclude that the available approaches for tactical planning are myopic are developed to establish longer term cyclical tactical plans or cannot provide tactical planning solutions for practical largesized instances The authors develop a deterministic method for tactical planning over multiple departments and resources within a mathematical programming frameworkIn this paper we develop a stochastic approach for the tactical planning problem in healthcare by modeling it as a Dynamic Programming problem DP Due to the properties of the tactical planning problem with discrete time periods and transitions that depend on the decision being made DP is a suitable modeling approach As problem sizes increase solving a DP is typically intractable due to the ‘curse of dimensionality’ To overcome this problem an alternative solution approach for reallife sized instances of the tactical planning problem is needed The field of Approximate Dynamic Programming ADP provides a suitable framework to develop such an alternative approach and we use this framework to develop an innovative solution approach ADP uses approximations simulations and decompositions to reduce the dimensions of a large problem thereby significantly reducing the required calculation time A comprehensive explanation and overview of the various techniques within the ADP framework are given in Powell 2011 The application of ADP is relatively new in healthcare it has been used in ambulance planning Maxwell et al 2010 Schmid 2012 and patient scheduling Patrick et al 2008 Other applications in a wider spectrum of industries include resource capacity planning Erdelyi and Topaloglu 2010 Schütz and Kolisch 2012 inventory control Simao and Powell 2009 and transportation Topaloglu and Powell 2006With this paper and the proposed model we aim to contribute to the existing literature in two ways First we develop a theoretical contribution to tactical resource and admission planning in healthcare in the field of Operations Research and Management Science OR/MS We develop an approach to develop tactical plans that take randomness in patient arrivals and patient transitions to other stages into account These plans are developed for multiple resources and multiple patient groups with various care processes and integrate decision making for a network of hospital departments and resources The model is designed with a finite horizon which allows all input to be time dependent This enables us to incorporate anticipated or forecasted fluctuations between time periods in patient arrivals eg due to seasonality and resource capacities eg due to vacation or conference visits in developing the tactical plans The model can also be used in ‘realtime’ If during actual implementation of the tactical plan deviations from forecasts make reallocation of resource capacity necessary the developed model can be used to determine an adjusted tactical plan The model can be extended to include different cost structures constraints and additional stochastic elements Second the solution approach is innovative as it combines various methods and techniques within the ADPframework and the field of mathematical programming Also the application of ADP is new in tactical resource capacity and patient admission planning and relatively new in healthcare in general where it has mainly been applied in ambulance planning Maxwell et al 2010 Schmid 2012 and patient scheduling Patrick et al 2008The main contribution of this paper is a methodology to create reallife tactical plans that takes randomness into account In addition we use an innovative combination of methods and techniques within the ADPframework and the field of mathematical programming This combination of techniques is relatively new in the area of healthcare This paper is organized as follows Section 2 discusses the mathematical problem formulation and describes the exact Dynamic Programming DP solution approach for small instances Section 3 introduces the ADP approaches necessary to develop tactical plans for reallife sized instances Section 4 discusses computational results and Sect 5 describes how the model can be used to develop or adjust tactical plans in healthcare Section 6 concludes this paperThis section introduces the reader to the problem the notation and the patient dynamics in care processes The tactical planning problem formulation introduced in Hulshof et al 2013 is extended in this section to include stochastic aspects such as random patient arrivals and patient transitions between queues

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