Heuristic policies for mobile asset sharing within hospitals

Computers & Industrial Engineering 111 (2017) 352–363

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Heuristic policies for mobile asset sharing within hospitals Duygu Ersol, Nilgun Fescioglu-Unver ⇑ Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey

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Article history: Received 3 September 2015 Received in revised form 26 July 2017 Accepted 27 July 2017 Available online 28 July 2017 Keywords: Asset tracking Hospitals Real time locating systems Asset sharing policies

a b s t r a c t Hospitals that share their mobile assets among departments can use real time locating systems (RTLS) to track the assets. Caregivers use RTLS to locate the closest assets and request these assets from those departments. However caregivers state that they are reluctant to give permission to asset transfers, and if they need an asset right after authorizing the transfer to another department, they regret their decision. The aim of this study is to provide simple and easily applicable asset transfer policies to be integrated with RTLS and decrease the number of regrets. The policies introduced determine the departments to transfer an asset from and recommend a set of assets to caregivers. These policies use sorting and time series forecasting methods to transform the asset availability and demand data gathered from RTLS, into useful information. We use simulation method to test the performance of the policies in a medium sized hospital environment. Results show that using RTLS to transfer the closest assets significantly increases the number of regrets. The proposed policies decrease the number of regrets while keeping the time it takes an asset to reach a patient at a low level. Policies are robust to changes in demand rate and demand patterns. Integrating RTLS with decision support mechanisms significantly improves the value RTLS provides. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Lending a limited resource and needing to use it right after lending is a situation caregivers working in healthcare centers face with several times each day. Caregivers of healthcare centers which share mobile assets among multiple departments state that they are reluctant to let other departments transfer the assets, and they regret their asset transfer decision when this situation occurs. This paper proposes heuristic mobile asset sharing policies for hospitals with real time locating systems (RTLS) to reduce the number of times a caregiver needs an asset right after transferring it and therefore reduce the frequency of regret due to asset transfer. In a hospital with RTLS the locations of all assets are visible in real time. RTLS eliminates asset search time and reduces the time it takes for an asset to reach a patient (i.e. asset to patient time). RTLS systems are also capable of tracking detailed asset data such as demand frequency, usage duration, maintenance frequency, movement history etc. Several studies analyzed the benefits of RTLS in healthcare (Fisher & Monahan, 2012; Qu, Simpson, & Stanfield, 2011; Stubig et al., 2014). However the number of studies that enhance RTLS with decision support algorithms is limited.

⇑ Corresponding author. E-mail addresses: [email protected] (D. Ersol), [email protected] (N. Fescioglu-Unver). http://dx.doi.org/10.1016/j.cie.2017.07.038 0360-8352/Ó 2017 Elsevier Ltd. All rights reserved.

To the best of authors knowledge, there is no study in the literature that provides a solution to the asset transfer regret problem. In this research we introduce three heuristic mobile asset sharing policies for hospitals in order to reduce the number of times a department regrets accepting an asset transfer request, while keeping the asset to patient time at a low level. The complexity of the methods these policies use range from sorting to time series forecasting. These policies determine which departments to transfer the asset from and recommend a set of assets to the caregiver who needs to transfer that asset. We use simulation method to test the policies for different demand rate and demand pattern conditions. We measure the performance of the policies using asset to patient time and number of regrets performance metrics, and compare the policies with each other, with the case where the hospital does not have RTLS and with the case where RTLS is used without an asset selection decision support mechanism. Results show that the proposed policies decrease the number of regrets significantly. In addition the policies are robust to changes in demand rate and pattern, and continue performing good under different conditions. This research improves the literature by introducing asset sharing policies which provide a solution to the asset transfer regret problem in hospitals. This paper is organized as follows: In Section 2, we present RTLS usage in industry and healthcare, and related studies. Section 3 introduces the asset sharing policies. Sections 4 and 5 present the policy test bed. The experimental results

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and demand rate/pattern sensitivity analysis are presented and discussed in Section 6. Finally Section 7 summarizes the overall findings and presents the conclusions.

2. Background Real time locating systems (RTLS) enable real time wireless tracking of objects and people. RTLS applications has a wide range from production to service and healthcare systems. In manufacturing industry RTLS is used for tracking the mobile assets, monitoring the work in process and scheduling the production (FesciogluUnver, Choi, Sheen, & Kumara, 2015; Zhang, Huang, Sun, & Yang, 2014). Transportation industry use real time location information to track cargo, and improve cargo loading and processing (Hsu, Shih, & Wang, 2009; Wei & Leung, 2011). RTLS is enabled by technologies such as WiFi, infrared, Zigbee, bluetooth and RFID (Boulos & Berry, 2012). Hospitals and healthcare systems frequently use RFID based RTLS systems (Wamba, Anand, & Carter, 2013; Yao, Chu, & Li, 2012). In healthcare sector RTLS is used for tracking patients, personnel and assets. Patient tracking can be used to automate the patient-flow process in order to reduce wait times (Stubig et al., 2014) or to provide additional safety for elderly or Alzheimer’s patients (Bowen, Craighead, Wingrave, & Kearns, 2010). Personnel tracking enables locating critical personnel in a short time and monitoring compliance with hand hygiene standards (Boyce, 2011). Asset tracking prevents asset theft and enables locating the shared assets easily. RTLS also discourages the caregivers who sometimes ‘hide’ or ‘hoard’ the assets they need so that they can find it easily when they need it (Boulos & Berry, 2012). Fisher and Monahan (2012) reports the results of a survey with 23 US hospitals and states that best usage of RTLS in hospitals is for asset tracking with whole hospital deployment. RTLS can give information about the location of an asset (the department it is currently located in and/or the exact coordinates of the asset). The state of the asset (‘busy’, ‘available’, ‘under maintenance’ etc.) can also be tracked with the integration of additional software and/or hardware layers. Attaching an additional button operated state signaling tag enables users to indicate the assets’ current state (busy or available). Integrating RTLS with additional software layers can enable users to directly change the state of an asset through the system (i.e. when the nurse selects an asset on the RTLS system, s/he puts a ‘busy’ mark to the asset’s view in the RTLS system. When nurse finishes using the asset - s/he changes the state back to ‘available’.). In addition three different ways to gather information about the asset state are suggested: location based, interaction based and usage based (Mareco, 2016). For example maintenance state can be easily tracked by location-based technologies which basically identify the current location of the asset. If the asset is currently in a location where maintenance operations are handled, then the asset is considered in maintenance state. Usage-based state tracking requires additional sensory information, for example for an IV pump, sensory data which shows if the pump is actually active, can be used to track usage. There are limited number of studies which quantify the benefits of RTLS in healthcare. Qu et al. (2011) proposed a Markov chain model and demonstrated on the defibrillator equipment how RTLS reduces equipment shrinkage and asset search time in hospitals. Efe, Raghavan, and Choubey (2009) used simulation to compare two utilization based asset selection policies (random vs. minimum utilization) with respect to the number of asset moves and emergency rentals. None of the existing studies in the literature consider the asset transfer regret problem in hospitals. A conceptually similar asset sharing problem exists in the retail sector in mul-

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tiple retailer systems where a group of retailers sell the same product to the same customer group. Retailers need to determine their transhipment policies - which retailer to ask for a product transhipment when they run out of the product and whether to accept or reject the request when they are the requested retailer. Retailers aim to maximize their profits while making these decisions. Research shows that using heuristic transhipment policies which consider the salvage price, demand probability and product availability of retailers perform close to optimal in these types of problems (Comez-Dolgan & Fescioglu-Unver, 2014). Studies which improve the value of RTLS through decision support algorithms are also limited. Saygin (2007) developed inventory control models that rely on RFID data for time perishable items. Kim, Tang, Kumara, Yee, and Tew (2008) improved delivery chain performance in a shipping yard by integrating RTLS with heuristic algorithms. Both of these studies (Kim et al., 2008; Saygin, 2007) test the performance of the algorithms through discrete event simulation. In his patent study, Choubey (2009) proposed a genetic algorithm for integration with hospital RTLS in order to determine how many assets to transfer from which department when a department needs several units of a particular asset. Discrete event simulation is frequently used for performance analysis in healthcare (Gunal & Pidd, 2010). Studies range from modeling a single department (i.e. emergency department) (Wang, Li, Tussey, & Ross, 2012) to ambulance operations. Aboueljinane, Sahin, and Jemai (2013) presents an extensive review on simulation studies on emergency medical services and ambulance deployment. The goals of these studies include reducing the response time, service time, waiting time etc. Although simulation is frequently used in healthcare the number of studies which cover the complete hospital are very limited because of its complexity (Gunal & Pidd, 2010).

3. Asset sharing policies This section introduces three asset sharing policies for integration with RTLS in hospitals. These policies determine the departments to ask for an asset transfer and recommend a set of assets to the caregivers. They transform the data provided by RTLS into useful information for asset selection. In an asset transfer process, there are two parties - requesting caregiver and requested department. When a caregiver needs a specific asset, she can locate all assets of that type through RTLS. If there is an asset of that type available within her department, she selects that asset. If there are no available assets of that type within the department, she selects one from the list RTLS provides. The requesting caregiver makes her asset selection decision based on two pieces of information: availability (is the asset currently available or in use/maintenance) and distance to the caregiver. Requesting caregivers frequently select the available asset within shortest distance (the closest asset) and make an asset transfer request to the department that holds the asset. Requested department may accept or reject the asset transfer request. Requested department makes the asset transfer accept-reject decision based on caregiver opinions and limited real time information. If the requested department accepts the transfer, the asset is transferred to the requesting caregiver. Requested department may reject the asset transfer request based on the anticipation that the department may need the same asset in a very short time. In that case requesting caregiver selects another asset and asks for a transfer. The requesting caregiver may have to request an asset transfer for several times, until she finds an accepting department. Rejecting an asset transfer request results in increased overall asset transfer time to patient. Requested department may accept the

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transfer regardless of the demand expectations. In that case, when the requested department needs that asset, they need to search for an asset and transfer it, which will increase the asset to patient time for that department. In addition, if the asset transfer has occurred a short time ago, requested department regrets the transfer accept decision. The length of this ‘short time’ duration may vary for each condition depending on factors such as the average utilization duration length of that asset type, the number of assets of the requested type available within the hospital, the workload of the requested department nurses when they need the transferred asset and the emergency of the current situation. RTLS are capable of collecting real time data about assets. This data is usually transformed into asset usage and transfer information for reporting purposes. Asset usage information reveals how long each asset has been used, asset transfer information shows how frequent each asset is transferred between departments. RTLS provide real time asset visibility, therefore eliminate asset search time but the caregivers still have the option to decline an asset transfer. We propose using historical asset location and availability data to give more informed asset selection decisions. We introduce three heuristic policies to support requesting caregiver’s asset selection decision. These policies work integrated with RTLS, use the data coming from RTLS sensors and provide a list of assets to the requesting caregiver through RTLS monitors. Requesting caregiver randomly selects one asset from this list and asks for an asset transfer. These policies enforce requested department to always accept the asset transfer request. All of these policies initially make a list of the available assets and the departments they are located. If the asset needed is available within the requesting caregiver’s department the policies recommend that asset. If there are no available assets of that type in the department, the asset sharing policies recommend a list of assets as follows. Policy - Min probi : Request from the department i which has the lowest probability of needing that asset type within this hour. If there are several departments that have the same probability, present a list to the requesting caregiver. Policy - Max numi : Request from the department i which has the highest number of available assets of requested type on hand at the moment of request. If there are several departments that have the same maximum number of assets, present a list to the requesting caregiver. Policy - MaxMin nmpri : Request from the department i which has the highest number of available assets of requested type on hand at the moment of request. If there are several departments that have the same maximum number of assets, present the one with the lowest probability of needing that asset within this hour. If there are more than one departments with the same maximum number of assets and same lowest probability, present a list to the requesting caregiver. This policy is a combination of Policy Min probi and Policy Max numi . Policy Max numi summarizes the momentary asset availability data. Policies Min probi and MaxMin nmpri collect historical asset movement and availability data from RTLS. They use this data to make a forecast of asset demand for each asset type and each department. The demand forecast is made on an hourly basis. At the beginning of each hour the expected demand of that hour is computed (i.e. the demand forecast of 4:00PM-4:59PM interval is calculated at 4:00:00PM. This forecast value is used in the policies for all requests made from 4:00PM till the end of 4:59PM.). All of these policies use sorting techniques. When there are several assets that are equivalently suitable for the given policy (multiple assets having the best rank after sorting), the nurse can choose one

randomly from the presented list. We compare the performance of these policies with each other and with the following cases: Min disti : Request from the department i which is within the shortest distance (distance measured in terms of the walking path length following the aisles of the hospital). If there are several departments within the same minimum distance, present a list to the requesting caregiver. This case represents the current usage of RTLS. No RTLS: Request from a department i randomly. In this case requesting caregiver has no information about which department i has the asset of that type available at that moment. If the requested department does not have an available asset of that type, the asset search continues and requesting caregiver chooses another department to request from. This policy represents the case when the hospital does not have RTLS. We use two performance criteria to compare these policies: Asset to patient time: The time it takes for an asset to reach a patient. Time measurement starts when the requesting caregiver initiates an asset search. For systems with RTLS, time measurement starts when the caregiver makes a request through the system. When the requesting caregiver selects the asset, first the department’s healthcare support personnel is allocated, next he goes to the requested department and brings the asset to requesting caregiver. If there are no available assets at that time, the caregiver waits until an asset is available in the system. Time measurement ends when the asset transfer is complete. For the case with no-RTLS, time includes requesting caregiver’s searching for an available asset. Number of regrets: When a demand for a certain asset type occurs, if an asset of that type is not available in the department and if the department has transferred that asset to another department a short time ago, the department regrets this transfer. The department now has to make an asset request to other departments and the new asset transfer process increases the workload and asset to patient time for that department. Number of regrets performance criteria counts the number of times a department has to transfer in an asset that it has given away a short time ago. We tested 10 min, 15 min and 20 min as ‘short time’ period lengths. With these policies, we propose using the data provided by RTLS to make more informed asset transfer decisions. Policies Min probi and MaxMin nmpri use time series forecasting methods to predict the asset demand. Section 4 describes the time series forecasting method. In order to measure the performance of these policies we use a simulation model as a test bed. Section 5 presents the test bed model. 4. Asset demand forecasting In this section we investigate the patient arrival pattern analysis and volume forecasting studies in the literature, and introduce our forecasting models for the test bed model. 4.1. Test bed model patient arrival patterns Hospital demand pattern analysis and forecasting studies in the literature focus on patient arrivals and volumes in specific departments. There are no studies on the hourly demand rates for a specific asset type in the literature. However patient arrival rate is correlated with asset demand. Studies categorize hospital departments as inpatient clinics, outpatient clinics and emergency care.

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Rising, Baron, and Averill (1973) analyzed daily arrival patterns for an outpatient clinic to schedule patient appointments during the periods when walk in demand is low. Cote, Robison, Pham, and Leeret (2012) analyzed inpatient clinics’ patient arrival patterns to provide methods that decrease the environmental services (i.e. bed cleaning) response times. Morzuch and Allen (2006) presented the patient arrival patterns for an emergency department in their arrival forecasting study. Asefzadeh (1997) analyzed the patient flow in a pediatric clinic. In order to develop a realistic test bed, we contacted a medium sized hospital, took this hospital as our reference and obtained expert opinions about daily patient arrival rates. We did not have access to detailed hourly patient arrival rates so we adapted the arrival patterns in literature to the reference hospital and generated sample hourly arrival patterns for the model. We used the patterns (Asefzadeh, 1997; Cote et al., 2012; Morzuch & Allen, 2006; Rising et al., 1973) presented to generate arrival patterns for our test bed model. Using this approach enables us to make a proof of concept and compare the performance of the policies. Fig. 1 shows the adapted arrival pattern for one of the outpatient clinics of the test bed model and the arrival pattern taken from literature (Rising et al., 1973) which was used as the basis for adaptation. For this adaptation we follow these steps: First compute the average of the hourly patient arrival rates of the base pattern (the pattern from literature). Next divide each hourly arrival rate to this average hourly arrival rate to compute a proportion. Finally use these proportions to calculate the hourly arrival rates for the test bed. A sample calculation is as follows: For the base pattern the average hourly arrival rate is computed as 13:58 (including the hours with zero patient arrival). The reference hospital’s experts report an average hourly arrival rate of 2:29 (an average of 55 patients each day). For the first operating hour (between 08:00am and 09:00 am) the arrival rate in the base pattern is 32. Next computing 2:29
ð32=13:58Þ gives us an arrival rate of 5:4 for the first hour of the test bed model. Similarly we generate all the inpatient/outpatient departments’, and the pediatric and emergency departments’ patient arrival schedules for the test bed. In the test bed model, we assume that the hourly patient arrivals have a Poisson distribution with the average hourly arrival rate (Poisson distribution’s k parameter) equal to the adapted

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patient arrival schedule’s corresponding hourly rate. Every hour patients arrive departments in accordance with Poisson distribution such that the time between arrivals has exponential distribution. Information about demand for each asset type at each department is computable from expert opinions on the percentage of patients needing a specific asset type in each department. For each patient arrival, we generate asset demands according to the proportions provided by the field experts (department nurses). Therefore the demand for each asset type at a given department increase and decrease at the same time - following that department’s patient arrival pattern. 4.2. Test bed model demand forecasting There are several forecasting methods used for patient arrival prediction in the literature. These methods include time series regression, exponential smoothing (Champion et al., 2007), autoregressive integrated moving average (Champion et al., 2007; Jones, Joy, & Pearson, 2002; Milner, 1997; Tandberg & Qualls, 1994), and artificial neural networks. Jones et al. (2008) evaluate several forecasting methods for emergency departments. Linear regression can also predict daily patient volume when based on calendar factors (Batal, Tench, McMillian, Adams, & Mehler, 2001; Holleman, Bowling, & Gathy, 1996; Rotstein et al., 1997). We use seasonal autoregressive integrated moving average (SARIMA) time series forecasting method to predict the hourly asset demand. Model development is completed in three stages: identification, estimation and verification. For model development, we collected hourly patient arrival data from the test bed for 10 simulation days, making a total of 240 data points. In order to generate this data we created hourly arrivals in the simulation model. Hourly arrival rates are obtained by distributing the daily arrival rate into hours using the procedure described in Section 4.1(the hourly arrival pattern repeats itself in 24 h - every day). We counted the number of actual arrivals for 24 h of 10 simulation days which made a total of 240 data points. We reserved 70 data points for verification and used the rest for model identification and parameter estimation. While developing the forecast models, we acted as if we have no prior information about the hourly arrival distribution and how the data was generated, and followed the model development steps. During identification stage we exam-

Fig. 1. Arrival pattern adaptation for an outpatient clinic.

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ined the ACF (autocorrelation function) and PACF (partial autocorrelation function) graphs to determine the degree of differencing, autoregressive and moving average terms. After generating alternative models we determined the parameter values and investigated the p-values for statistical significance of the parameters. In the verification stage we examined the RMSE (root mean square error) and MAE (mean absolute error) values of the models. Using this procedure, we developed a separate model for each department. Seasonal ARIMA models can be represented with the ðp; d; qÞðP; D; Q Þm notation, where m represents number of time periods per season and P; D and Q represent the autoregressive, differencing, and moving average terms for the seasonal part respectively. We selected ð1; 0; 0Þð0; 1; 1Þ24 model for the emergency department and ð0; 0; 0Þð0; 1; 1Þ24 model for the other departments. At the end of each hour, models forecast next hour’s patient arrival count for each department. Once the forecast for the number of patients is available, the demand estimates for each asset at each department is computable. The asset sharing policies Min probi and MaxMin nmpri use the hourly asset demand estimates as input. 5. Simulation test bed We used simulation method to test the performance of the asset sharing policies. In order to build the testbed we investigated the reference hospital, completed detailed surveys and collected data. Our aim was to measure and compare the performances of the policies in a realistic test bed environment rather than creating an exact model of the reference hospital. 5.1. Asset type and coverage selection The reference hospital resided on a single building with four floors. It consisted of 25 departments with a total of 100 beds. The hospital shared the mobile assets among departments and did not have RTLS implemented. Nurses complained about spending a significant amount of time for searching assets. The search time varied between 5 min and 30 min for different departments and asset types. In addition in some cases they were not able to transfer the assets because the requested department did not authorize the transfer due to their own demand expectations. Tracking all mobile assets within a hospital is possible but it increases the implementation cost of RTLS. Therefore we conducted interviews and surveys with the nurses and hospital management to determine which mobile assets to track and which departments to cover if they were to implement RTLS. The survey results showed that the nurses frequently used 38 different types of asset. Among these asset types, 28 were rarely searched for, or the price of the asset was lower than the price of the RTLS tag, or the asset was not compatible with the tag (it was not ergonomic to use the asset with the tag attached). Next we conducted another survey to determine which departments to cover and evaluated the priority of tracking each asset type for each department. Survey results showed that all the remaining asset types were transferred among several departments and several floors of the hospital, and tracking each of these assets had high priority for at least one department (Demircan & Fescioglu-Unver, 2016). Hence this information made covering the complete hospital necessary. The complete list of assets selected and the total number of these assets are provided in Table 1. 5.2. Simulation model After determining the asset types to track, we conducted detailed interviews with nurses to obtain expert opinions about

Table 1 Total number of assets for each type. Asset type Echocardiography ACT device Bilirubin meter Tee probe

Total count

Asset type

Total count

2 3 2 2

EKG Nebulizer Wheelchair

8 20 18

demand frequency and usage duration for each asset in each department. Some of the assets (Monitor, IV Pump and syringe pump) were used on patients for very long durations like a week, a month or more. We eliminated these assets from our model as we could not obtain detailed usage duration information. We conducted time studies to collect EKG and Echocardiography devices’ usage duration data and fitted appropriate statistical distributions. For usage times of other devices where only expert opinions were available, we used triangular and uniform distribution (Banks, Carson, Nelson, & Nicol, 2010; Law, 2007). The reference hospital’s nurses provided us expert opinions on daily patient arrival rates and the asset demand per arrival. However we needed hourly asset demand data to test our policies. We created hourly patient arrival rates for different clinics, by distributing the total daily patient arrival rates into hourly arrival rates using the patterns from the literature. Section 4.1 describes the data adaptation procedure in detail. In order to simplify the model we made the following assumptions: hourly arrival rates had Poisson distribution, there is no elevator waiting time, there is only one healthcare support personnel (HSP) per department, the healthcare support personnel is only responsible from asset transfer, only the healthcare support personnel transport the assets (caregivers – i.e. nurses – do not carry assets between departments), caregivers do not reject any asset transfer request. Nurses provided information about the asset search times. Distances between departments were directly measured from the hospital plan. Using these information, we initially built the No RTLS case simulation model. In the No RTLS case, there is no asset tracking system. The nurses search for an asset by calling other departments until they find a department with an available asset. The simulation model is built using Arena 13.9. We completed the verification and validation analysis of the simulation model as follows: In the verification stage we traced the model logic for different events and actions, evaluated the reasonableness of the outputs given different input parameter values and under extreme conditions, and finally presented the model flow and assumptions to department nurses. In the validation stage we used quantitative indicators. We computed the average utilization rates of different asset types using the expert opinions about demand frequency and usage duration, compared these values with the simulation outputs, and verified the model. Department nurses also evaluated the results according to their experience and the model showed high face validity. Since we could not obtain number of regrets and asset to patient time data from the hospital (because of the privacy limitations), we cannot present this model as an exact representation of this hospital. However the model was found accurate enough to test the policies proposed in this study. We used Welch procedure and determined the warm up period length as 2 days. The run length was 32 days, leaving a total of 30 days of output data collection period for each run, We made 30 replications for each model. After completing the No RTLS model, the next step was integrating the asset sharing policies to the simulation model. The simulated process is described in detail in Fig. 2. When an asset demand occurs, the nurse enters information about this demand to the asset tracking system and looks for an available asset. Sys-

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Fig. 2. Simulation process flowchart.

tem provides a list of suitable assets (according to the asset selection policy). When the nurse selects an available asset, the system puts an ‘on hold’ tag on the asset. Depending on the location of the asset, either the healthcare support personnel or the nurse brings the asset to the patient. Once the asset usage is complete, system removes the ‘on hold’ tag from the asset and the asset is left at the location where it was used. There is no asset search time for the cases with RTLS and assets are selected according to the specified asset sharing policy. The policies Min probi and MaxMin nmpri require demand forecasts as input. We developed the forecast models as described in Section 4.2. Next we coded the forecast models and the asset sharing policies in Visual Basic and integrated with the Arena simulation model.

department needs to request an asset from another department, and it has transferred that asset to another department within the last 15 min, the number of regrets count for that day increases by one. Section 6.1 compares the policies under base demand conditions. Sections 6.2 and 6.3 measure the sensitivity of the policies to increasing demand rates and changes in demand pattern, respectively. We compare policies with each other using paired t-test. In all pairwise comparison tables a negative interval indicates that the left method has a smaller number of regrets value (or shorter asset to patient time) than the top method, and vice versa for a positive interval. 6.1. Heuristic policy performance tests

6. Results and discussion In this section we compare the performance of the proposed asset sharing policies with each other, with the case when the hospital does not use RTLS (No RTLS) and with the current usage of RTLS (Min disti ). Next we investigate the sensitivity of the policies to increasing demand rates and different demand patterns. The policies are compared using the asset to patient time and the number of regrets performance metrics. These metrics are introduced in Section 3. Asset to patient time metric gives the average of all asset to patient times of all asset requests during the simulation run, measured in terms of minutes. Number of regrets metric gives the average daily number of regrets. The number of regrets is counted in a daily basis and taking the average of these daily regret counts during the 30 days of simulation run computes the number of regrets performance metric. By the definition in Section 3, a department regrets an asset transfer if the department needs an asset which is not currently available in that department, and it has transferred that asset ‘a short time’ ago. In order to determine the length of the ‘short time’ duration, we inspected the asset usage durations, and tested different lengths of ‘short time’ periods. Completing different runs with 10 min, 15 min and 20 min of ‘short time’ periods showed that the value of the number of regrets metric increases with longer duration but the order of the policies from best performing to least performing remains the same. The policy comparisons in this section use 15 min as the length of this duration. If a

In this section we compare the asset sharing policies under the base demand conditions. In base demand conditions, the average daily patient arrival rates (hence the daily asset demand rates) of the departments are equal to that of the reference hospital, but the average hourly rates change in accordance with the specified arrival pattern from literature. Departments which belong to the same category (inpatient or outpatient) share the arrival pattern of that category. Section 4.1 describes the arrival pattern adaptation procedure in detail. Table 2 shows the average utilization rates for each asset type under base demand conditions. The utilization rates are computed over 24 h of maximum usage time, as inpatient and emergency departments continue creating asset demand for 24 h. Low utilization rates show that the number of resources for each asset type is sufficient for the demand rates of the hospital. Under these demand conditions we can also expect a low number of regrets as low utilization rates indicate that there may be a number of resources available at the time of demand.

Table 2 Asset utilization rates. Asset type Echocardiography ACT device Bilirubin meter Tee probe

Ave. util. rate (%)

Asset type

Ave. util. rate (%)

10:29  0:15 2:02  0:04 0:97  0:02 3:50  0:15

EKG Nebulizer Wheelchair

3:13  0:02 6:83  0:04 4:86  0:04

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Fig. 3 displays the asset to patient time and number of regrets for all asset sharing policies. Results show that the No RTLS case has the longest asset to patient time as the caregivers have to search for an asset. For all other cases, assets are located by RTLS (no asset search). Asset to patient time includes searching for an asset (only for No RTLS case), allocating a healthcare support personnel (HSP), and HSP walking to and from the requested department. Min disti has the shortest asset to patient time with an average of 1.86 min. Among the asset sharing policies proposed, MaxMin nmpr i has the shortest asset to patient time, followed by Max numi and Min probi . For the number of regrets performance metric, MaxMin nmpri is the best performing policy and Min disti is the least performing policy. No RTLS case also outperforms Min dist i . Min dist i has an average of 9.96 daily regrets whereas the case with No RTLS results in an average of 6.01 daily regrets. This difference can be explained as follows: In No RTLS case if the asset is not available in the demanding department, it is requested from a random department. Whereas Min disti policy always requests from the closest department. Therefore if a couple of close departments frequently need the same type of assets, they will end up requesting that asset from each other continuously. This type of coupling between departments increases the total number of regrets significantly. In order to investigate the asset to patient time and number of regrets differences between policies in detail, we compared the policies with each other using paired t-test. Tables 3 and 4 show the pairwise comparison of policies for asset to patient time and number of regrets performance measures, respectively. For both tables, to achieve a %95 overall confidence level, we made each comparison with %99.5 confidence level in accordance with Bonferroni inequality (Law & Kelton, 1990). In Table 3, a negative interval indicates that the left method has a shorter asset to patient time than the top method. Similarly in Table 4, a negative interval indicates that the left method has a smaller number of regrets value than the top method, and vice versa for a positive interval. Table 3 shows that asset to patient time difference between the MaxMin nmpri policy and the current RTLS usage case Min disti is between 0.09 min (5.4 s) and 0.21 min (12.6 s). MaxMin nmpri achieves this performance without considering the distance between departments. Min disti transfers the asset from the closest department, regardless of the conditions (expected demand, number of available assets) of that department. For asset to patient time performance metric, policies from best performing to least can be listed as: Min disti , MaxMin nmpri , Max numi , Min probi , and No RTLS. Table 4 compares the average daily number of regrets for different policies. The difference between the best performing policy

MaxMin nmpri and least performing policy Min disti is around 7 regrets daily. When Min disti policy is used, the requested departments may have to transfer their single and most needed asset to other departments, which results in an overall increased number of transfers and number of regrets. Increased number of transfers is also an explanation to why these two policies have a very close asset to patient time. When MaxMin nmpri policy is used, there is a higher chance of finding an available asset within the requesting department. Therefore, although a single transfer made by MaxMin nmpri policy may take more time, making a smaller number of transfers results in a close asset to patient time to the Min disti policy. For number of regrets performance metric, the order of policies from best performing to least performing is: MaxMin nmpri , Min numi , No RTLS, Min probi , and Min disti . Another interesting point is the performance of the Min probi policy with respect to the No RTLS case for the number of regrets metric. Table 4 shows that No RTLS case has a slightly better performance than Min probi policy. This shows that under base demand conditions, considering the demand probability alone, does not decrease the number of regrets, in fact making a random selection is a better approach. Max numi policy performs better than both Min probi and the No RTLS case. When Max numi policy is used, the caregiver randomly selects an asset from the list of departments which has the same maximum number of assets on hand. When MaxMin nmpri policy is used, the recommendation is based on both number of available assets and demand probability. Combining demand probability and availability information provides the best performance which shows that demand probability is important but not sufficient for a performance improvement under base demand conditions. Asset to patient time measurement includes the time needed to allocate a healthcare support personnel. We assumed that there is a single HSP at each department, and this HSP is responsible from all asset transfers of that department. If the HSP is not available at the time of demand, the caregivers first have to wait for the HSP to become available, and then the asset transfer occurs. In order to examine the asset to patient time without the HSP allocation time, we relaxed the ‘one HSP per department’ assumption and tested the policies with unlimited HSP. Unlimited HSP assumption is equivalent to assuming that the requesting caregiver completes the asset transfer by going to and coming from the transferring department. Fig. 4 shows the performance of the policies with unlimited HSP. Tables 5 and 6 show the pairwise comparison of policies for asset to patient time and number of regrets with unlimited HSP assumption. Table 5 shows that when the caregivers do not wait for an HSP to become available, the asset to patient time for Min disti and

Fig. 3. Asset to patient time and number of regrets for all asset sharing policies.

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D. Ersol, N. Fescioglu-Unver / Computers & Industrial Engineering 111 (2017) 352–363 Table 3 Pairwise comparison of policies for asset to patient time. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½5:88 ½5:50 ½5:57 ½5:73

 5:72  5:32  5:41  5:57

Min disti

Min probi

Max numi

MaxMin nmpr i

½5:72 5:88

½5:32 5:50 ½0:46  0:32

½5:41 5:57 ½0:37  0:25 ½0:01 0:15

½5:57 5:73 ½0:21  0:09 ½0:16 0:32 ½0:09 0:23

½0:32 0:46 ½0:25 0:37 ½0:09 0:21

½0:15  0:01 ½0:32  0:16

½0:23  0:09

Table 4 Pairwise comparison of policies for number of regrets. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½3:46 4:44 ½0:51 1:43 ½2:74  1:88 ½3:80  3:02

Min dist i

Min probi

Max numi

MaxMin nmpr i

½4:44  3:46

½1:43  0:51 ½2:52 3:46

½1:88 2:74 ½5:82 6:70 ½2:87 3:69

½3:02 3:80 ½6:96 7:76 ½4:00 4:74 ½0:77 1:43

½3:46  2:52 ½6:70  5:82 ½7:76  6:96

½3:69  2:87 ½4:74  4:00

½1:43  0:77

Fig. 4. Asset to patient time and number of regrets for all asset sharing policies with unlimited HSP.

Table 5 Pairwise comparison of policies for asset to patient time with unlimited HSP. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½5:57 ½5:27 ½5:40 ½5:57

 5:50  5:19  5:31  5:48

Min dist i

Min probi

Max numi

MaxMin nmpr i

½5:50 5:57

½5:19 5:27 ½0:34  0:27

½5:31 5:40 ½0:21  0:14 ½0:09 0:16

½5:48 5:57 ½0:05 0:03 ½0:26 0:34 ½0:13 0:21

½0:27 0:34 ½0:14  0:21 ½0:03 0:05

½0:16  0:09 ½0:34  0:26

½0:21  0:13

Min disti

Min probi

Max numi

MaxMin nmpr i

½4:93  3:76

½1:42  0:54 ½2:80 3:94

½1:22 2:19 ½5:45 6:65 ½2:22 3:15

½2:99 3:79 ½7:20 8:27 ½3:99 4:75 ½1:26 2:11

Table 6 Pairwise comparison of policies for number of regrets with unlimited HSP. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½3:76 4:93 ½0:54 1:42 ½2:19  1:22 ½3:79  2:99

½3:94  2:80 ½6:65  5:45 ½8:27  7:20

MaxMin nmpri policies become very close and the confidence interval of the difference includes zero, which means that we cannot say that these two policies perform differently. When there was one HSP per department, Min disti policy showed slightly better performance (see Table 3). Fig. 4 shows that both policies improved their asset to patient time but the improvement amount for MaxMin nmpri policy was bigger. Removing the HSP limit enabled MaxMin nmpri policy reach the asset to patient time performance of the Min dist i policy.

½3:15  2:22 ½4:75  3:99

½2:11  1:26

Table 6 shows that the order of the policies with respect to number of regrets performance metric does not change when the limit on number of healthcare support personnel is removed. The analysis with base demand rate conditions shows that using RTLS to locate the closest assets (Min disti policy) increases the daily number of regrets. The suggested policies Min probi , Max numi , and MaxMin nmpr i lead to a lower number of regrets and slightly higher asset to patient times. Among these, MaxMin nmpri is the best performing policy for both asset to patient time

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and number of regrets metrics. When the limit on number of HSP is removed, MaxMin nmpri achives an asset to patient time that is not different from the Min disti case.

demands becomes more important. With the four folds increase in demand rates the order of policies from best to least performing in number of regrets metric becomes: MaxMin nmpr i , Max numi , Min probi , No RTLS, Min disti .

6.2. Sensitivity of heuristic policies to changes in demand rate 6.3. Sensitivity of heuristic policies to changes in arrival pattern Under base demand conditions, the assets have low utilization rates (see Table 2) and there are sufficient number of assets to handle an increase in demand rates. In this section we test how the policies will perform in case of an increase in demand. We assume there is no limit on number of HSPs (i.e. the requesting caregiver will transport the asset). For each department, the base demand condition’s hourly demand rates are increased by two, three and four times. The policies Min probi and MaxMin nmpri use demand forecasts to make asset recommendations. Changes in the demand rates necessitate generating new forecast models for all departments. We ran the simulation model with the new demand rates for 10 simulation days, collected data and created new forecast models using the procedure described in Section 4.2. Fig. 5 shows that asset to patient time increase with increasing demand rates. When demand rates increase, the possibility that a requesting caregiver will not be able to find the asset within her department increases. This will lead into an increased number of transfers and asset to patient times. In addition, when demand rates increase requesting caregivers may have to wait for an asset to become available if all assets of the same type are in use at the time of request. These factors cause an increase in the asset to patient time for all policies. When the demand rates increase by factors two and three, the asset to patient time difference between MaxMin nmpri and Min disti policies become as low as [0.23 0.06] and [0.45 0.03] minutes respectively. When demand is increased four times, we can not say these two policies perform differently. Increasing demand rates also decreased the asset to patient time difference between Min probi and Max numi policies. Fig. 6 demonstrates how increasing demand rates increase the number of regrets for all policies. Number of transfer requests increase along with the demand and caregivers more frequently need the assets that were transferred to other departments a short time ago. With the increasing demand, the number of regrets criteria performance difference between the policies increase. MaxMin nmpri policy more clearly demonstrates its advantage with high demand rates. As demand rates increase, Min probi policy outperforms No RTLS which basically randomly selects an asset. This result is expected as with the increasing demand rates, the difference between department demands increase and estimating the

Section 4.1 categorized the hospital departments as inpatient, outpatient, emergency according to the patient arrival patterns. The departments in the inpatient category shared the same arrival pattern and similarly the departments in the outpatient category shared a single arrival pattern. In other words, although the average daily patient arrival rates of the departments from the same category are different from each other, the demand is distributed among hours of the day according to the same pattern, i.e. the demand in these departments increase and decrease simultaneously. In this section we examine how the policies would perform if the departments in the same category have different arrival patterns. We created different arrival patterns for each department by modifying the existing arrival pattern of the category. Fig. 7 illustrates how different arrival patterns were created for several departments of inpatient category by shifting the peak demand time period. For each department, the average daily arrival rate is kept the same with the reference hospital’s corresponding department. After creating the new arrival patterns, we ran the simulation model for 10 simulation days, collected data and created new forecast models. Fig. 8, Tables 7 and 8 compare the policies. We assumed unlimited HSP (requesting caregivers carry the assets themselves) during the simulation runs. Fig. 8(a) shows the asset to patient time and Fig. 8(b) shows the number of regrets metrics under the new demand conditions and provides a side by side view with Fig. 4 for an easier comparison of the policies under different demand patterns with same average daily demand rate and unlimited HSP. Fig. 8 shows that all policies perform better when the departments have different demand patterns. This is an expected result as when the departments have different patterns and peak demand times, the total asset demand will be better distributed along the day which will result in an increased number of available assets at a given time. When the number of available assets increase, the number of times a requesting department has to wait for an asset to become available decrease, and the probability of finding an available asset within one’s own department increase. These lead to improved number of regrets and asset to patient time metrics for all policies. Asset to patient time is slightly improved for all policies (see Fig. 8(a)). Table 7 displays the pairwise comparison of polices in

Fig. 5. Asset to patient time wrt. demand rate.

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361

Fig. 6. Number of regrets wrt. demand rate.

Fig. 7. Arrival pattern modification.

terms of asset to patient time with a %95 overall confidence level. Results show the order of the polices from best performing to least is preserved. Min disti and MaxMin nmpri are still the best performing policies followed by Max numi , Min probi and No RTLS. Fig. 8(b) shows that performance of all policies improved for the number of regrets metric. It is important to note that the largest percentage improvement is in Min probi policy. When departments in the same category have the same demand pattern, the demand probability in these departments increase/decrease simultaneously. Section 6.2 showed that for small demand rates, using Min probi policy does not provide a benefit over No RTLS (random asset selection) when the departments share the same demand pattern. However when the demand patterns change, estimating the demand of separate departments provides more information and Min probi outperforms the No RTLS case. Table 8 compares the number of regrets metric for policies pairwise with a %95 overall confidence level. Results show that the order of the policies from best performing to least is: MaxMin nmpri , Max numi , Min probi , No RTLS and Min disti . 6.4. Discussion of results In this study we introduce three mobile asset sharing policies for hospitals to be integrated with real time locating systems.

Our goal is to decrease the number of times a caregiver needs an asset right after transferring it to another department (number of regrets), while keeping the time it takes an asset to reach a patient (asset to patient time) at a low level. The policies introduced (Max numi , Min probi and MaxMin nmpri ) use asset availability and asset demand probability data which can easily be collected by the RTLS systems. We use simulation method to compare the performance of these policies with the current usage of RTLS (selecting the closest asset - Min disti ) and with the case when the hospital does not use RTLS (No RTLS). RTLS reduces asset to patient time significantly by eliminating asset search time. Caregivers intuitively expect allocating the closest asset - Min disti - to result in the lowest asset to patient times. However, results show that asset to patient time for Min disti and MaxMin nmpri are very close and under high demand conditions the policies do not perform differently. Min dist i policy does not consider the condition (number of available assets and demand expectations) of other departments while making an asset recommendation. Transferring the single asset of a department that might need that asset in a short time results in an additional asset transfer which increases the overall asset to patient time. For the number of daily regrets metric Min disti is the worst performing policy in all scenarios. All policies introduced in this study and No RTLS case - which randomly selects an asset - outperform

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Fig. 8. Asset to patient time and number of regrets when departments have different demand patterns.

Table 7 Pairwise comparison of policies for asset to patient time when departments have different demand patterns. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½5:55 ½5:33 ½5:42 ½5:53

 5:47  5:25  5:34  5:45

Min disti

Min probi

Max numi

MaxMin nmpri

½5:47 5:55

½5:25 5:33 ½0:25  0:19

½5:34 5:42 ½0:16  0:10 ½0:06 0:13

½5:45 5:53 ½0:04 0:01 ½0:17 0:24 ½0:08 0:15

½0:19 0:25 ½0:10  0:16 ½0:01 0:04

½0:13  0:06 ½0:24  0:17

½0:15  0:08

Table 8 Pairwise comparison of policies for number of regrets when departments have different demand patterns. Policy/policy No RTLS Min dist i Min probi Max numi MaxMin nmpr i

No RTLS ½2:39 3:26 ½0:69  0:1 ½1:37  0:73 ½2:00  1:43

Min dist i

Min probi

Max numi

MaxMin nmpri

½3:26  2:39

½0:10 0:69 ½2:81 3:63

½0:73 1:37 ½3:45 4:30 ½0:37 0:94

½1:43 2:00 ½4:14 4:94 ½1:08 1:56 ½0:39 0:93

½3:63  2:81 ½4:30  3:45 ½4:14  4:94

Min disti . These results shows that using RTLS ‘as is’ (without decision support rules) prevents us from using RTLS to its full potential. MaxMin nmpri is the best performing policy for this metric. The performance difference between MaxMin nmpri and Min disti increase with the growth in demand rates. Min probi policy’s performance improves as demand rates increase and when different departments show different demand patterns. Max numi is a generally good performing policy which is relatively easier to implement as it does not require forecast

½0:94  0:37 ½1:56  1:08

½0:93  0:39

models. In cases where demand probability data is not available, using Max numi policy can decrease the number of regrets without increasing the asset to patient time to a great extend. MaxMin nmpri combines probability and availability information and achieves the best results for both metrics. Overall, the analysis shows us that making use of the information that can be gathered by RTLS, significantly improves the value RTLS provides.

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7. Conclusion Most hospitals share their mobile assets among different departments. Caregivers admit that they hesitate giving permission to asset transfers to other departments thinking their department might need that asset in a very short time. This study proposes a solution to this problem by introducing three asset sharing policies to be integrated with RTLS. Results show that the policy which considers demand probability and asset availability information together, reduces the number of asset transfer regrets significantly while keeping the time it takes an asset to reach a patient at the same level as using RTLS to locate the closest asset. These policies improve the performance of RTLS and are especially built using easy to implement mathematical methods. The complexity of the methods the policies use range from sorting to time series forecasting. Although implementation of the demand forecasting policies (Min probi and MaxMin nmpri ) requires expertise in this area, results show that using the Max numi policy which is basically a sorting algorithm - still provides performance improvement over using RTLS as is. The policies introduced in this paper are developed for healthcare RTLS but they can also be used in other industries which share mobile assets. For example in manufacturing industry tracking the service/repair tools and transportation assets such as forklifts with RTLS and sharing them according to these policies will improve the performance of the complete system. This study is not without limitations. We used ARIMA time series forecasting method for the Min probi and MaxMin nmpri policies. Using other forecasting methods may improve the forecast accuracy and the performance of the policies that use these inputs. In addition, real life implementations might consider self-adapting forecasting models that will change their parameters automatically when there is a change in demand patterns. The test bed environment was generated by taking a medium sized hospital with limited patient arrival data as a reference. Having a bigger hospital with complete data would show the effects of the policies more clearly. Acknowledgments The authors are grateful to Private TOBB ETU Hospital management team and personnel for their support throughout this work. References Aboueljinane, L., Sahin, E., & Jemai, Z. (2013). A review on simulation models applied to emergency medical service operations. Computers & Industrial Engineering, 66(4), 734–750. Asefzadeh, S. (1997). Patient flow analysis in a children’s clinic. International Journal for Quality in Health Care, 9(2), 143–147. Banks, J., Carson, J., Nelson, B., & Nicol, D. (2010). Discrete event system simulation. Pearson, Upper Saddle River. Batal, H., Tench, J., McMillian, S., Adams, J., & Mehler, P. S. (2001). Predicting patient visits to an urgent care clinic using calendar variables. Academic Emergency Medicine, 8(1), 48–53. Boulos, M. N. K., & Berry, G. (2012). Real-time locating systems (rtls) in healthcare: A condensed primer. International Journal of Health Geographics, 11(25). Bowen, M. E., Craighead, J., Wingrave, C. A., & Kearns, W. D. (2010). Real-time locating systems (rtls) to improve fall detection. Gerontechnology, 9(4), 464–471. Boyce, J. M. (2011). Measuring healthcare worker hand hygiene activity current practices and emerging technologies. Infection Control, 32(10), 1016–1028. Champion, R., Kinsman, L. D., Lee, G. A., Masman, K. A., May, E. A., Mills, T. M., et al. (2007). Forecasting emergency department presentations. Australian Health Review, 31(1), 83–90.

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