A decision integration strategy for short-term demand forecasting and ordering for red blood cell components
AA decision integration strategy for short-term demand forecasting andordering for red blood cell components
Na Li , Fei Chiang , Douglas G. Down , Nancy M. Heddle , Department of Computing and Software, McMaster University, Hamilton, Ontario L8S 4L8, Canada McMaster Centre for Transfusion Research, Department of Medicine, McMaster University, Hamilton,Ontario L8S 4L8, Canada Centre for Innovation, Canadian Blood Services, Ottawa, Ontario K1G 4J5, Canada
Abstract
Blood transfusion is one of the most crucial and commonly administered therapeutics worldwide. Theneed for more accurate and efficient ways to manage blood demand and supply is an increasing concern.Building a technology-based, robust blood demand and supply chain that can achieve the goals of reducingordering frequency, inventory level, wastage and shortage, while maintaining the safety of blood usage,is essential in modern healthcare systems. In this study, we summarize the key challenges in currentdemand and supply management for red blood cells (RBCs). We combine ideas from statistical timeseries modeling, machine learning, and operations research in developing an ordering decision strategy forRBCs, through integrating a hybrid demand forecasting model using clinical predictors and a data-drivenmulti-period inventory problem considering inventory and reorder constraints. We have applied theintegrated ordering strategy to the blood inventory management system in Hamilton, Ontario using a largeclinical database from 2008 to 2018. The proposed hybrid demand forecasting model provides robust andaccurate predictions, and identifies important clinical predictors for short-term RBC demand forecasting.Compared with the actual historical data, our integrated ordering strategy reduces the inventory level by40% and decreases the ordering frequency by 60%, with low incidence of shortages and wastage due toexpiration. If implemented successfully, our proposed strategy can achieve significant cost savings forhealthcare systems and blood suppliers. The proposed ordering strategy is generalizable to other bloodproducts or even other perishable products.
Keywords : Demand forecasting; inventory management; data-driven; blood demand and supply chain;red blood cell components.Contact: Na Li. Email: [email protected] work has been submitted to Operations Research for Health Care for publication in August 2020.1 a r X i v : . [ s t a t . A P ] A ug Introduction
Blood transfusion is one of the most crucial and commonly administered therapeutics worldwide. Theneed for more accurate and efficient ways to manage blood demand and supply is an increasing concernin many countries, including Canada. Building a technology-based, robust blood product demand andsupply system that can achieve the goals of reducing wastage and shortage, while maintaining the safetyof the blood system, is essential in modern health care systems.Canadian Blood Services (CBS) is the national blood supplier in Canada (excluding Qu´ebec ). Asshown in Figure 1, the current blood supply chain network in Canada is a centralized regional networkconsisting of two levels: regional CBS distribution centres and hospital blood banks. For example, thereis one CBS regional blood distribution centre in Brampton, Ontario that covers the demands from themajority of hospitals in Ontario. There are nine regional CBS blood distribution centres across Canada [1].Each regional centre sets priorities to meet the demands of its own network; if there is excess supply,CBS decides centrally where the products are to be reallocated. D i s t r i bu t e R e qu e s t p r o du c t s Canadian Blood Services (CBS)
Extracting, Storing and Distributing Products
Donor CollectionHospital 1 I ss u e p r o du c t s P h y s i c i a n D i a g n o s i s Regional CBS Blood Centre Level • Responsibility : Blood product production, storage and distribution • Supply : CBS blood donor collection • Demand : Hospital blood bank orders
Hospital Blood Bank Level • Responsibility : Blood storage, cross-matching, placing orders to CBS, receiving products from CBS, issuing products to patients, managing inventory • Supply : Blood from regional CBS distribution centre • Demand : Physician orders
Hospital 2
Hospital K-1 Hospital K I ss u e p r o du c t s P h y s i c i a n D i a g n o s i s I ss u e p r o du c t s P h y s i c i a n D i a g n o s i s I ss u e p r o du c t s P h y s i c i a n D i a g n o s i s Fig 1.
Two-level supply chain with one regional blood centre and multiple hospitalsCurrently, CBS has no information on recipient demographics and clinical utilization of the bloodproducts distributed to hospitals. As a result, it has been very challenging for CBS to predict futuredemand and plan donor collection. For example, through this collaboration we discovered that decisionmakers at CBS have noticed a significant reduction in red blood cell (RBC) transfusions over recentyears. They hypothesize this reduction could be caused by changes occurring in local hospitals, such asincreased engagement on RBC clinical transfusion guidelines or improved surgical techniques. However,without clinical data, any such hypothesis cannot be investigated. In addition, the impact of clinicalchanges on the RBC demand cannot be evaluated. It is essential to maintain robust blood demand andsupply management not only at the regional blood centre and individual hospital levels, but also as a Quebec has its own blood supplier, H´ema-Qu´ebec, that supplies blood and other biological products of human origin tohospitals in the province. . It may also lead to extra costsfor reallocating units close to expiry. Moreover, studies [2–5] have shown that duration of RBC storagecan affect functional integrity and quality standards which could impact patient outcomes. Results ofrandomized trials suggest that there is no benefit to transfusing very fresh blood compared to blood storedfor a longer duration (i.e. less than 10 days since blood donation compared with 24 days or more [6]);however, it has been suggested that the clinical impact of blood storage over its 42-day shelf life may notbe linear. More specifically, the risk of a specific outcome (i.e. mortality) by days of storage could be aconvex curve [7]. Through controlling inventory levels in hospital blood banks, it is possible to restrictthe age of transfused blood into a reasonable range that may correlate with better patient outcomes.Furthermore, from the national blood supplier’s point of view, when hospital blood banks hold a largeamount of inventory, it prevents CBS from understanding the real demand and restricts the ability ofCBS to adjust for demand variability. As a result, both hospital blood banks and CBS cannot operate thedemand and supply chain efficiently. With the availability of a large amount of clinical data and advancedanalytical methodologies, there are opportunities to increase the accuracy of blood demand forecastingand improve the efficiency of the entire demand and supply chain.Fresh blood components include RBC, platelets, and plasma. The RBC component experiences thehighest demand among all the fresh components. It is prepared by removing plasma from a whole blooddonation and is used to treat hemorrhages and to restore tissue oxygenation [8]. The demand for RBCcomponents determines the plan for blood collection and production. In this study, we aim to tackle thedemand forecasting and inventory management challenges for RBC components.We study a large clinical database with over 1.2 million blood transfusions for nearly 100,000 patientsin Hamilton, Ontario from 2008 to 2018. We perform a thorough investigation of RBC utilization withassociated trends, and formulate a hybrid model for short-term RBC demand forecasting using clinicalindicators. The demand forecasting model is then used to develop an integrated ordering strategy. Theproposed integrated methodology achieves three goals: i) a more accurate forecasting method that reflectsthe actual RBC demand at hospital blood banks, which increases the transparency between CBS andhospital blood banks; ii) a leaner and fresher inventory at hospital blood banks, which may correlate withbetter patient outcomes; iii) a simpler ordering strategy that requires less frequent orders on scheduled Throughout this paper, the terms “wastage” and “waste” are all referring to the blood products wasted due to expiration.
This section describes the daily routine of blood product ordering and inventory management in atypical hospital blood bank. There are four hospital blood banks in Hamilton, Ontario operated by oneTransfusion Medicine (TM) laboratory team consisting of four faculty members and three technicalspecialists spread across Hamilton General Hospital, Juravinski Hospital, McMaster University MedicalCentre (MUMC) , and St. Joseph’s (STJ) Healthcare Hamilton. These laboratories manage and store The TM laboratory at MUMC is the hub site for performing all remote testing for the West Lincoln Memorial Hospitalsatellite site. MUMC is a children’s hospital that has a small number of adult and pediatric outpatient clinics. This backgrounddescription is based on the information collected at MUMC prior to the COVID-19 pandemic. Visits to other blood banks werecancelled for safety considerations during the pandemic situation. The hospital blood bank at MUMC has relatively smallerdemands compared with other blood banks in Hamilton, Ontario. However, all hospital blood banks in Hamilton, Ontario aremanaged by the same Transfusion Medicine laboratory team.
Hospital blood bank daily routine:
The TM labs are responsible for ordering, storing, managing andissuing all fresh blood components including RBCs, platelet components, frozen plasma components,frozen cryoprecipitate and other experimental blood components such as COVID-19 convalescent plasma.At MUMC, every Monday to Saturday at approximately 4 pm, a technical specialist in the lab performsa routine physical count for each product in their inventory, compares the physical counts with thepre-defined inventory targets and sends an order to CBS (Brampton) through fax. The order deliveryfrom the CBS distribution centre usually arrives between 8:30 am and 10 am on the next day. CBSprovides a paper-copy summary list of the delivered products with the shipment. The technical specialistcompares this summary list with the order form they faxed to ensure they received all the products theyrequested. (Feedback from the hospital blood bank indicates that only occasionally their orders arereplaced, cancelled or delayed. However, due to the fact that there are no electronic data entries to tracethe orders, a statistical summary of such information is not possible.) On the CBS side, a specific personmanually transfers ordering information from faxed paper copies to an electronic spreadsheet . Thedata are collected for CBS administration and operation purposes and are not shared with hospital bloodbanks.After a hospital blood bank receives blood products from CBS, the technical specialist enters theinformation into an electronic health system named Meditech . During the day, physicians may makeprescription orders at any time through Meditech or by fax to the hospital blood banks. Usually,physicians make daily orders per patient, and the ordered products are available for pick up at differentscheduled times. For every physician order, the technical specialist reviews the patient’s historical clinicalinformation which in this case is a custom Meditech report. The report includes the most recent labtest results and antibody screening results. These are used to determine whether special transfusionrequirements are needed. Finally, a compatible product will be assigned to the patient. Current ordering strategy:
Using their experience, the technical specialists at each Hamilton hospitaldetermine fixed inventory targets for different products. Orders are made to raise inventory up to thesetargets. We find the targets set by hospital blood banks are significantly higher than the actual demands.For example, Table 1 shows the inventory targets for RBC units by blood group at MUMC. The totalinventory target in the table is eight times larger than the mean daily demand at MUMC, which has thesmallest number of days of inventory on hand among all hospital blood banks in Hamilton, Ontario. Moredetails are described in Challenge 2 below. It is natural that hospital blood banks are most concernedabout having sufficient inventory. However, without the quantitative evidence as we provide in this study,the consequence is that the order quantities cannot reflect fluctuations in the actual demand, resulting inexcess inventory (prolonged days of inventory on hand), increased risk of wastage, and overly frequentsame-day urgent orders.
Challenge 1: Excess inventory level.
The mean and standard deviation (sd) statistics in Hamilton,Ontario for the days of inventory on hand, age (days) of blood, and daily number of units in-stock areshown in Table 2. The mean (sd) of days of inventory on hand (DOH) in 2018 was 12.33 (8.62) days,and the mean (sd) of the age of blood prior to transfusion was 23.45 (10.58) days; whereas in 2008, the To our knowledge this ordering data collection process at CBS started in 2012. Meditech is the electronic data system used in Hamilton, Ontario. Other hospitals may use a different system. Even for thehospitals using Meditech, the design of the system could also be different. umber of units Blood group O A B AB
Rh type
Positive 20 20 8 0Negative 12 8 2 0
Table 1.
RBC inventory target by ABO Rh type in MUMC blood bank mean (sd) of DOH was 8.83 (6.82) days, and the mean (sd) of the age of blood prior to transfusion was16.04 (8.41) days. The wastage rate for RBCs was slightly reduced from 2.14% in 2008 to 1.68% in 2018.From 2008 to 2018, there was a growth of 0.35 days per year for the mean DOH. It increased significantlybetween 2012 and 2015, then became more stable after 2016 (one-way ANOVA: F = . , p = . F = . , p < . Year Days on hand (DOH) Age (days) of blood Number of units in-stock Wastage (%)
Table 2.
Mean (sd) of days of inventory on hand (DOH), age (days) of blood prior to transfusion, anddaily number of units in-stock, as well as wastage rate by year in Hamilton hospital blood banks
Challenge 2: Large variation of the differences between ordered quantity and actual demand.
Themean and sd statistics for the daily number of units received, transfused and their difference are shown inTable 3. As shown in the table, although the average difference between the number of units received (asa proxy of the order quantity by hospital blood banks on the previous day) and units transfused (actualdemand) was close to zero, the standard deviation of the differences was very large. Figure 2 (a) presentsthe boxplots of the differences between ordered quantity and actual demand by year from 2008 to 2018,which shows the ranges of the differences were wide for all the years and there was no observed trendacross the years. In Figure 2 (b), the boxplots of the differences reveals a strong day-of-week effect. Thelarge variation of the differences was statistically significantly associated with the day-of-week effect andnot significantly associated with the year (two-way ANOVA: among years F = . , p = .
39; acrossdays of week, F = . , p < . lll l lll ll lll ll llll ll ll − − (a) Year D i ff e r en c e o f un i t s be t w een r e c e i v ed and t r an s f u s ed ll llllllllllllll llllllll llllllll lllllllllll lllllllll llllllllllll Mon. Tues. Wed. Thur. Fri. Sat. Sun. − − (b) Weekday D i ff e r en c e o f un i t s be t w een r e c e i v ed and t r an s f u s ed lllllllllllllllllllllllllllll lllllllllllllllll lllllllllll lllllllllllll lllllllllllllllllllllllllllll lllllllll lllllllllllllllllllllllllllllllllllllllllllllllll Mon. Tues. Wed. Thur. Fri. Sat. Sun. (c)
Weekday N u m be r o f un i t s r e c e i v ed llllllll lllllllll llllllllllllllllll lllllllllll lllllllllllllll lllllllllllll lllllllllllllllll Mon. Tues. Wed. Thur. Fri. Sat. Sun. (d)
Weekday N u m be r o f un i t s t r an s f u s ed Fig 2.
Boxplots of difference (R-T) between units received and transfused (a) by year and (b) byday-of-week; boxplots of (c) number of units received by day-of-week and (d) number of units transfusedby day-of-week
Challenge 3: Frequent same-day urgent orders.
We have described the process for routine orderingrequests between hospital blood banks and CBS above. In urgent situations, non-scheduled orders thatrequire same-day delivery can be placed. There are two types of urgent orders: “as soon as possible”(ASAP) orders and “STAT” orders. ASAP orders are usually dispatched by parcel express, and STATorders are typically required in an emergency situation for bleeding patients, thus faster transportationmethods such as taxis are used (the lead time for delivery of such orders is 2 to 3 hours to Hamilton,Ontario). From April 1st, 2012 to May 31st, 2015, of 1,156 calendar days (165 weeks), 1,012 (87.5%)days had RBC deliveries from CBS to Hamilton blood banks . Table 4 shows the number of RBCorders for each order type from Hamilton hospital blood banks to CBS during the period from April1st, 2012 to May 31st, 2015. Among the days with deliveries, 322 (31.8%) days, almost twice a week,had STAT orders, and 69 (6.8%) days had ASAP orders. Among the 165 weeks, 90 (54.5%) Fridayshad same-day urgent orders (combined STAT and ASAP). From Table 4, we have two observations: 1)
961 days excluding public holidays and Sundays during the period. That is, at least 51 deliveries happened on Sundaysand/or holidays. ear Number of units received (R) Number of units transfused (T) Difference (R-T) Table 3.
Mean (sd) of daily number of RBC units received (R), transfused (T), and their difference (R-T)by year in Hamilton hospital blood banksThere was a small number of days with same-day urgent orders but without routine orders. Of theseorders, 37 (90.2%) occurred on weekends; 2) The same-day urgent orders were mostly made on differentdays for different hospitals. Although the rate of same-day urgent orders may not be too concerning forindividual blood banks, the pooled rate for all blood banks was significantly higher than the rate stratifiedby hospitals. This reflects the need for optimizing the inventory management as a network. Table 5presents the difference in means of demand patterns between dates with same-day urgent orders and dateswith routine orders. The numbers of units received and transfused were much higher on dates with urgentorders, and there were significant differences of units transfused to trauma patients (doubled) and patientswith abnormal laboratory tests (defined in Table 6).
Hospital blood bank* Days with routineorders - n (%) ‡ Days with STATorders - n (%) ‡ Days with ASAPorders - n (%) ‡ Days with anyorder - n (%) † Hospital A 819 (96.6%) 102 (12.0%) 11 (1.3%) 848 (73.4%)Hospital B 803 (95.9%) 104 (12.4%) 23 (2.8%) 837 (72.4%)Hospital C 844 (96.8%) 72 (8.3%) 22 (2.5%) 872 (75.4%)Hospital D 789 (95.6%) 95 (11.5%) 21 (2.6%) 825 (71.4%)All hospitals 971 (95.9%) 322 (31.8%) 69 (6.8%) 1012 (87.5%)
Table 4.
Summary of RBC orders in Hamilton hospital blood banks from April 1st, 2012 to May 31st,2015 * Hospitals A, B, C, and D represent the four hospital blood banks in Hamilton, Ontario.‡ The denominators for the percentages of days with routine orders, STAT orders, and ASAP orders are the numberof days with any order in the last column.† The denominator for the percentages of days with any order in the last column is 1,156 calendar days during theperiod.
It is interesting to observe the issues of excess inventory levels and over-frequent same-day urgentorders simultaneously exist. The data shows hospital blood banks made same-day urgent orders whenmore patients were in severe condition even when there were units available in inventory, revealinga potential cognitive bias for overestimating shortage risks. These biases can be controlled usingmathematical models for quantitative analysis. The integrated data-driven demand forecasting andinventory management model we propose can produce accurate demand predictions and generate robustordering decisions based on historical data. It can significantly reduce the occurrence of ASAP and STATorders while reducing inventory levels, resulting in significant savings with respect to both costs andresources. 8 ates with urgentorders - mean (sd) Dates with routineorders - mean (sd) Difference in means(95% CI)
Number of units received by blood bank 119.35 (69.48) 89.03 (67.09) 30.32 (22.23 - 38.41)Number of units transfused 97.05 (29.71) 86.71 (27.58) 10.35 (6.94 - 13.75)Number of O units to Non-O recipients 5.12 (5.03) 3.99 (3.28) 1.14 (0.62 - 1.66)Number of units transfused toPatients with age between 18 and 75 61.09 (19.86) 54.40 (18.17) 6.69 (4.43 - 8.96)Trauma patients 3.53 (8.42) 1.74 (4.70) 1.79 (0.94 - 2.64)Patients with abnormal creatinine 29.23 (10.49) 26.76 (10.04) 2.46 (1.25 - 3.68)Patients with abnormal hemoglobin 52.73 (14.43) 49.07 (13.11) 3.66 (2.01 - 5.30)Patients with abnormal INR 88.64 (28.18) 78.79 (26.14) 9.85 (6.62 - 13.09)Patients with abnormal red cell width 36.64 (13.94) 33.22 (13.22) 3.42 (1.81 - 5.03)Patients with abnormal pO2 15.52 (9.31) 13.18 (7.97) 2.33 (1.30 - 3.37)Patients at Juravinski Hospital 39.25 (15.19) 35.52 (14.18) 3.73 (1.98 - 5.48)Patients at St. Joseph’ Healthcare 21.54 (10.80) 18.87 (10.02) 2.67 (1.43 - 3.91)
Table 5.
Comparison between dates with same-day urgent orders and dates with routine orders inHamilton hospital blood banks
Most of the existing literature considers univariate demand forecasting for RBCs using time seriesor machine learning models. Salviano et al. [9, 10] developed an automatic application for demandforecasting, based on the Box and Jenkins (BJ) procedure. Their application forecasts the demands ofblood components by using Seasonal AutoRegressive Integrated Moving Average (SARIMA) models toidentify non-stationary and seasonal features. It can perform automatic order identification, parameterestimation and model validation to reduce human intervention and improve the efficiency of decisionmaking for blood component distribution to hospitals. Kumari and Wijayanayake [11] proposed a modelthat manages the daily supply of platelets by forecasting the daily demand, where three forecastingtechniques, moving average, weighted moving average, and exponential smoothing, were comparedto minimize the shortage. Khaldi et al. [12] presented a case study of forecasting monthly demand ofthree blood components, RBC, plasma and platelets, using Artificial Neural Networks (ANNs). Guan etal. [13] built a mathematical model to forecast short-term platelet usage and minimize wastage. Lestariand Anwar [14] investigated four methods to forecast blood demand involving moving average, weightedmoving average, exponential smoothing, and exponential smoothing with trend using POM-QM softwarefor supporting decision making of a blood transfusion unit in Indonesia. Among all the studies, Khaldiet al. [12] and Guan et al. [13] appear to be the only two studies that have considered clinically-relatedindicators in short-term product-specific demand forecasting.In this study, we train a hybrid demand forecasting model using a large number of clinical indicators,including patient characteristics, laboratory test results, patient diagnoses, and hospital locations. Themodel selects the most important clinical predictors for RBC demand forecasting to produce accurateforecasting results, generating valuable feedback of RBC utilization to CBS and hospitals.
Simulation models have been developed for BSCM, including blood collection, production, inventoryand distribution. Mansur et al. [15] reviewed articles on BSCM from 1960 to 2017, and provided a9oncise summary of the articles based on four categories: blood product type, performance measurement,coordination hierarchy level, and blood inventory model. They point out that the solutions offered are notcomprehensive and sometimes are difficult, if not impossible, to implement. They then used the bloodmanagement system in Indonesia as an example to suggest the need for a reliable inventory managementsystem adaptive to demand fluctuation and blood supply pattern.Beyond the articles surveyed in [15], a number of additional references are pertinent for our proposedapproach. Sirelson and Brodheim [16] built a predictive model using simulation and linear regression thatdetermines the outdate rate and the shortage rate as a function of the fixed base stock level and the meandaily demand, for blood banks with scheduled daily deliveries of platelet components from a regionalblood centre. They showed that for blood banks with moderate to large mean demands there exist optimalbase stock levels that can effectively keep the outdate rate and the shortage rate within favorable ranges.They also extended the model to distinguish the platelet demand by blood groups. Haijema et al. [17]presented a combined Markov Decision Process and simulation approach with an application in a Dutchblood bank. Hemmelmayr et al. [18] established a two-stage stochastic optimization problem, whichrelies on sampling-based approaches involving integer programming to handle the stochastic demand andvariable neighborhood search to improve computational efficiency. Zhou et al. [19] analyzed a periodicreview inventory system for platelet components under two replenishment modes: regular orders placedat the beginning of a cycle, and expedited orders within the cycle characterized by an order-up-to levelpolicy. They started with a single-item periodic review inventory system and then expanded their work toa multi-period inventory problem. They provided a numerical illustration and a sensitivity analysis usinghistorical data, and showed that the optimal cost is significantly affected by demand uncertainty, leadtimes, seasonality, and age of expedited orders.Although there have been many studies in the field of blood demand and supply management,the methods are typically developed based on various assumptions and are difficult to implement.Furthermore, to our knowledge, no study has considered integrating demand forecasting models intoinventory management strategies for blood products. In this study, we investigate a multi-period inventoryproblem that mitigates the effects of forecasting errors from a data-driven demand forecasting model. Theproposed integration strategy can help resolve practical challenges for RBC demand and supply chainmanagement.
There have been multiple inventory management approaches implemented in healthcare systems. Heit-miller et al. [20] was the first major study focusing on reducing blood wastage from the hospital side.They used the five-part Lean Sigma process, i.e., define, measure, analyze, improve, and control, to reduceRBC wastage with an emphasis on container wastage, where a control plan and a list of interventions byLean Sigma were developed. They demonstrated there could be a 60% reduction in RBC wastage withsavings of more than $800,000 over four years.Kort et al. [21] showed significant improvements, including a reduction of the median weeklyoutdating rate and a gain in the time until outdating, after implementing a combined approach ofstochastic dynamic programming and simulation techniques. They stated the results brought confidenceto personnel to apply and adopt the mathematical approach and the thrombocyte inventory managementoptimizer software tool. Collins et al. [22] evaluated the effectiveness of multiple low-cost interventions10hat were implemented in January 2013 in the U.S., including educational outreach, print and digitalmessaging, and improved transportation and component identification modalities. They compared theRBC, platelet, and plasma wastage rates in the 16 months after these interventions with the rates priorto the interventions. They found significant decreases in the RBC and platelet wastage rates, however,there was an increase in the plasma wastage rate. The overall net cost savings of the reduced waste wasestimated at $131,520, excluding the intervention costs. Quinn et al. [23] designed and implementeda blood ordering algorithm, using a mathematical model based on the probability of RBC transfusionwithin 48 hours given certain hemoglobin levels, to provide a more accurate measure of RBC utilization.After implementation, they observed a significant reduction of the mean daily total RBC inventory leveland the monthly RBC outdated units.These applications showed significant cost savings could be achieved by applying mathematicalmodeling in BSCM. Our proposed integrated methodology framework, being data-driven produces morerobust results, is generally applicable to a range of decision problems in BSCM, e.g., for different bloodproducts. Moreover, to support accessibility and knowledge translation, we plan to develop a prototypingtool with a user-friendly interface using the proposed methods.
Our study dataset is constructed by processing the TRUST (“Transfusion Research for Utilization,Surveillance and Tracking”) database from the McMaster Centre for Transfusion Research (MCTR).The TRUST database is a comprehensive database containing blood product, demographic, and clinicalinformation on all hospitalizations at four Hamilton hospitals from April 2002 to the present. The databaseis updated monthly from two sources: the hospitals’ Laboratory Information System (LIS) and DischargeAbstract Database (DAD). This study considers RBC inventory data and RBC transfusion-related clinicaldata in the TRUST database from 2008 to 2018. The study is approved by the Canadian Blood ServicesResearch Ethics Board and Hamilton Integrated Research Ethics Board.From 2008 to 2018, the study identifies 369,481 RBC transfusions for 60,141 patients in Hamilton.These consist of 236,856 transfusions to 39,811 inpatients and 132,625 transfusions to 21,581 outpatients.The patient characteristics (features) include age, gender, patient ABO Rh blood type, patient diagnosis,hospital facility, transfusion location, laboratory test, surgical procedure, and medication. We consider thefollowing laboratory tests: hemoglobin (Hb), platelet count (PLTCT), creatinine, international normalisedratio (INR), red cell distribution width (RDW), immunoglobulins (IgG), mean platelet volume (MPV),mean corpuscular volume (MCV), white blood cell (WBC), mean corpuscular hemoglobin (MCHb),activated partial thromboplastin time (aPTT), fibrinogen, alanine aminotransferase (ALT), aspartateaminotransferase (AST), and blood gas (pO2, pCO2). RBC product-related features include meantransfusion age of blood, mean in-stock age, mean transfusion size, product ABO Rh type, expired rate,and destroyed rate. Hospital operations / policy related features include day of week, RBC transfusioncompliance rate, and single unit issue rate.The data for analysis is processed in two steps: 1) The dataset consists of all the transfused RBCunits, and each row contains a unique RBC unit with product-related information and the transfusionrecipient’s characteristics as specified above. 2) A daily aggregated dataset is then constructed for demand11orecasting. The dataset is organized by date, and each row contains the daily product and patient-relatedinformation. There are over 200 processed variables in the daily aggregated dataset using straightforwardstatistical transformations (e.g. mean, min, max, sum). Table 6 presents a selected set of variables andtheir descriptions in the daily aggregated data. Variables are identified based on clinical relevance toRBC transfusions. Variables with over 70% missing values are excluded, and methods of imputingmissing values are based on the clinical definition and the use of the variable. For example, when alaboratory test value is missing, it may mean the test value is in the normal range so that a physiciandoes not need to order additional laboratory tests. Outside of the laboratory test values, the percentageof missing values is low ( < x i = ( z i − min ( z )) / ( max ( z ) − min ( z )) .All data preprocessing, analyses and modeling are performed using the R language for statisticalcomputing [24]. For the demand forecast model construction, data from 2008 to 2017 are designated formodel training, and data in 2018 for test. Models are trained on the training dataset and cross-validationis used for hyperparameter tuning. Results are reported on the test dataset. In this study, we consider a combination of the Seasonal and Trend decomposition using Loess (STL)model and the eXtreme Gradient Boosting (XGBoost) model.
STL model:
STL [26] is a robust and efficient statistical method for time series decomposition. It candecompose a time series into three components, seasonality ( s i ), trend ( τ i ), and residual ( e i ) for timeperiod i . The trend component is the long-term pattern that represents the increase or decrease in the timeseries over the observed period. The seasonality component represents a pattern of change that repeatsitself over years at specific regular intervals less than a year, e.g., weekly, monthly, or quarterly. In thisstudy, we only consider additive decomposition, thus the time series of RBC demand, denoted as y i , canbe written as y i = s i + τ i + e i .The main advantages of STL include its flexibility to handle different types of seasonality, therobust estimates of the trend and seasonal components (they are not affected by outliers), the ability todecompose time series with missing values, and fast computation. The rate of change of the seasonalityand the smoothness of the trend-cycle can be controlled through two main parameters, the trend-cyclewindow (t.window) and the seasonal window (s.window). The parameter t.window is the span (in lags)of the Loess window for trend extraction and s.window is the span for seasonal extraction. Both shouldbe odd numbers, and s.window should be at least 7, according to Cleveland et al. [26]. Smaller valuesyield greater sensitivity to detect changes. A value of s.window must be given, while, if omitted, a defaultvalue of t.window can be calculated using the number of periods and s.window. These parameters arevery useful in this study since we observe irregular seasonality over time for which the uncertainty could This may be caused by blood production method changes, policy changes or operational changes. ame Description Format ntransfusions Number of RBC transfusions (units) Integermeanage Mean age in years of transfused patient Numericfemale Number of female patients transfused; sex is categorized by the biological attributes Integermale Number of male patients transfused; sex is categorized by the biological attributes IntegerpatientABOgroup Number of transfused patients with A / B / AB / O blood group, respectively IntegerpatientRhtype Number of transfused patients with Positive / Negative Rh type, respectively Integermedicalgroup Number of transfused patients with medical diagnosis group: Medical intensive care unit (ICU) /Cardiac surgery / Non-cardiac surgery / Emergency room (ER) / Oncology / Trauma / Outpatient/ Others, respectively Integerhospital Number of transfused patients in hospital: CMH (MUMC) / ML (Hamilton General) / HEND(Juravinski) / STJ (St. Joseph’s) / WL (West Lincoln), respectively Integerlocation Number of transfused patients in location: ICU / General medicine / Hematology / Cardiovascu-lar surgery / General surgery / Orthopedic surgery / Other surgery / Obstetrics & Gynaecology /ER / Outpatient location, respectively Integermeanhb Mean hemoglobin before RBC transfusion; unit: g/L Numericmeanpltct Mean platelet count before RBC transfusion; unit: x 10 /L Numericmeancreatinine Mean creatinine before RBC transfusion; unit: µ mol/L NumericmeanINR Mean INR before RBC transfusion Numericmeanaptt Mean aPTT before RBC transfusion; unit: seconds Numericabnormalhb Number of patients with abnormal hemoglobin; abnormal is defined as <
80 g/L Integerabnormalpltct Number of patients with abnormal platelet count; abnormal is defined as <
100 x10 /L Integerabnormalcreatinine Number of patients with abnormal creatinine; abnormal is defined as > µ mol/L (female) and > µ mol/L (male) IntegerabnormalINR Number of patients with abnormal INR; abnormal is defined as < >
17% IntegerabnormalIgG Number of patients with abnormal IgG; abnormal is defined as < < <
80 f/L IntegerabnormalWBC Number of patients with abnormal WBC; abnormal is defined as >
11 x10 /L IntegerabnormalMCHb Number of patients with abnormal MCHb; abnormal is defined as <
29 pg IntegerabnormalaPTT Number of patients with abnormal aPTT; abnormal is defined as >
60 seconds IntegerabnormalALT Number of patients with abnormal ALT; abnormal is defined as <
17 U/L IntegerabnormalAST Number of patients with abnormal AST; abnormal is defined as >
40 U/L IntegerabnormalpO2 Number of patients with abnormal pO2; abnormal is defined as >
105 mmHg IntegerabnormalpCO2 Number of patients with abnormal pCO2; abnormal is defined as >
45 mmHg IntegerproductABOgroup Number of products with A / B / AB / O blood group, respectively IntegerproductRhtype Number of products with Positive / Negative Rh type, respectively Integermeantranssize Mean number of units transfused per patient Numericmeanageofblood Mean age in days of blood from collection date to transfusion / expiry date Numericmeaninstockdays Mean days in stock from received by blood bank to transfusion / expiry date Numericexpiryrate Rate of units expired; rate is calculated by number of units expired over total number of unitsper month. Percentagedestroyedrate Rate of units destroyed due to containment or other causes; rate is calculated by number of unitsdestroyed over total number of units per month. Percentageweekday Day of week: Monday / Tuesday / Wednesday / Thursday / Friday / Saturday / Sunday Stringcompliancerate RBC transfusion compliance rate; RBC compliance is defined according to Choosing Wisely[25] and rate is calculated by number of transfusions with compliance over total number oftransfusions per month. Percentagesingleunitrate Rate of transfusions with single unit issue; rate is calculated by number of transfusion episodes(single / multiple units issued at the same time) with single unit issue over total number oftransfusion episodes per day. Percentage
Table 6.
Data variable definition and description 13e better captured by STL than other time series models such as AutoRegressive Integrated MovingAverage (ARIMA). On the other hand, STL has one critical drawback: STL is dependent on its ownhistory. STL is not capable of capturing structural changes, such as non-linear patterns, that are associatedwith explanatory variables.
XGBoost model:
XGBoost [27] is a highly efficient and widely used machine learning model under theGradient Boosting framework. In many data analytical challenges, it has proved to achieve state-of-the-artresults [28]. The idea of Gradient Boosting is to use smaller prediction models to build a more generalmodel that fits the dataset used for training. In XGBoost, we use decision trees as the smaller predictionmodel. Decision trees are useful for separating a dataset into different categories, or leaves, according todecision criteria related to the dataset’s distinct column values. Since we are working with a regressionproblem instead of classification, the leaves of the decision tree are not categories, but continuous-valuedscores. The value predicted by the model is the sum of the scores pertaining to the leaves that wereactivated according to the predictor variables.There are four unique features of XGBoost that make it a popular choice: 1) The weights in XGBoostare calculated by Newton’s method, so it works fast as it does not require a line search. However, thisalso requires that the loss function of XGBoost must be twice continuously differentiable. 2) It canhandle sparsity patterns, e.g. missing values, zero entries, in a unified way. 3) It has more regularizationparameters to control the complexity of the model and prevent over-fitting. 4) It is highly flexible. It allowscustomized optimization objective functions and evaluation measures, as well as many hyperparametersfor model tuning. Nonetheless, XGBoost is not good at dealing with time series data with long-termdependencies.Thus, this leads us to develop a hybrid model combining the two methods. The combination of thesetwo models can eliminate the drawbacks of each individual model while utilizing their advantages. Ituses the STL model to extract the linear and seasonal components, and then allows the XGBoost modelto handle the nonlinear patterns in the residuals. Similar hybrid models have been developed recently bycombining ARIMA and machine learning models for various applications [29, 30].
Pre-process data matrix (including prediction target and predictors) Prediction target
STL decomposition
XGBoostmodelResidual
Predictor matrix
Trend + Seasonalityforecast + Hybrid forecasting
Residualforecast
Fig 3.
STL + XGBoost hybrid forecasting algorithm for RBC demand
Hybrid model: STL + XGBoost
Leveraging the advantages of the STL and XGBoost models, wepropose an ensemble-based STL + XGBoost hybrid model for RBC short-term demand forecasting. Asshown in Figure 3, the hybrid model starts with a time series decomposition of the daily RBC demand14sing an STL model, after which the STL residuals are forecast with an XGBoost model using a set ofclinical predictors. The final forecast demand is the sum of the trend and seasonality components fromthe STL model and the predictions from the XGBoost model, written asˆ y i = s i + τ i + ˆ e i (1)where ˆ e i = K ∑ k = f k ( x i ) , f k ∈ F . The residuals forecast from the XGBoost model are denoted by ˆ e i , given the input predictors x i . Thespace of regression trees is F = { f ( x ) = w q ( x ) } . The structure of each tree that maps the input predictorsto the corresponding leaf index is represented by q : R d → { , . . . , θ } , where θ is the number of leaves inthe tree, and w ∈ R θ represents the weight of each leaf. Let f k correspond to an independent tree structure q and leaf weights w . Let ˆ e ( k ) i be the prediction of the i -th instance at the k -th iteration. The objectivefunction at the k -th iteration is L ( k ) = n ∑ i = l ( e i , ˆ e ( k − ) i + f k ( x i )) + Ω ( f k ) (2)where Ω ( f k ) = γθ + λ (cid:107) w (cid:107) . The function l is a differentiable convex loss function that measures the difference between the target e i and the prediction ˆ e ( k − ) i at the ( k − f k that most improves the model. Apenalization term, denoted by Ω , controls the complexity of the model to avoid over-fitting, where γ is apenalty term on the number of leaves, so the larger γ is the more conservative the model. Finally, λ is aregulation term on the weights, increasing this value will make the model more conservative.Define g ( k − ) i = ∂ ˆ e ( k − ) l ( e i , ˆ e ( k − ) i ) and h ( k − ) i = ∂ e ( k − ) l ( e i , ˆ e ( k − ) i ) as the first and second order gradientstatistics on the loss function, and I j = { i | q ( x i ) = j } as the instance set of leaf j . After applying thesecond order approximation and removing constant terms, the following loss function is minimized atstep k , ˆ L ( k ) = θ ∑ j = [( ∑ i ∈ I j g ( k − ) i ) w j + ( ∑ i ∈ I j h ( k − ) i + λ ) w j ] + γθ . (3)For a fixed structure q ( x ) , the optimal weight w ∗ j of leaf j is given by w ∗ j = − ∑ i ∈ I j g ( k − ) i ∑ i ∈ I j h ( k − ) i + λ , j = , . . . , θ (4)and substituting (4) into (3), ˆ L ( k ) ( q ) = − θ ∑ j = ( ∑ i ∈ I j g ( k − ) i ) ∑ i ∈ I j h ( k − ) i + λ + γθ . (5)This is the optimal loss for a fixed tree structure, however there might be thousands of possible trees.Instead of searching all possible tree structures, XGBoost uses a greedy algorithm to build a tree structurewhere the split is chosen with the maximum gain in the loss reduction. Let I L and I R be the instance sets15or the left and right nodes, respectively. The gain in the loss reduction is calculated by12 (cid:34) ( ∑ i ∈ I L g ( k − ) i ) ∑ i ∈ I L h ( k − ) i + λ + ( ∑ i ∈ I R g ( k − ) i ) ∑ i ∈ I R h ( k − ) i + λ − ( ∑ i ∈ I L ∪ I R g ( k − ) i ) ∑ i ∈ I L ∪ I R h ( k − ) i + λ (cid:35) − γ . (6) There are a number of hyperparameters for an XGBoost model, including learning rate, the maximumdepth of a tree, the minimum sum of weights of all observations in a leaf, the fraction of observationsto be randomly sampled for each tree, the fraction of columns to be randomly sampled for each tree,and the regularization term on weights. In addition, s.window and t.window for the STL model are alsoconsidered as hyperparameters in the hybrid model. The hyperparamters are tuned using grid searchbased on a pre-defined parameter space. The tuning process is measured by cross-validation on thetraining data and evaluated with the root mean squared error (RMSE). The optimal hyperparameters areselected with the minimum RMSE using 5-fold cross-validation.Variable selection proceeds in an iterative manner based on the variable importance scores calculatedfrom the XGBoost models. Variable importance is the relative improvement in the performance measurecontributed by a variable weighted by the number of observations for each decision tree, then averagedacross all the decision trees within the model [31]. We initialize the iterative process with a model usingall variables on the training dataset and evaluate the model performance measure on the test dataset, thenselect a subset of variables based on a pre-defined variable importance threshold for the next iteration.We repeat the process until there is no improvement observed in the performance measure, then the subsetwith the most important variables is finalized. The variables reported in the result section are the final setof variables selected through this process.The prediction target for the demand forecasting model is the daily RBC demand. In order to reducecosts, a second target, semiweekly demand, is considered. The semiweekly demand is defined as thethree-day demand for Tuesday, Wednesday and Thursday, and the four-day demand for Friday, Saturday,Sunday and Monday. The semiweekly demand is calculated from the daily demand prediction.
We evaluate the model performance using the following two accuracy measures: Mean Absolute Percent-age Error (MAPE) and Root Mean Square Error (RMSE). We report the values of MAPE and RMSE ofthe trained hybrid model on the test data. The model performance of the hybrid model is compared to asingle STL model, an STL + linear regression model, and a long short-term memory (LSTM) model. AnLSTM model [32] is one type of recurrent neural network model used in the field of deep learning. It iswell suited to handle long-term dependencies in time series data and has many applications, such as timeseries anomaly detection, short-term traffic forecast, and handwriting recognition.
We consider a multi-period inventory problem for RBC units with fixed shelf life in a rolling horizonframework. The model assumptions are as follows: i) Based on our data, we assume a fixed duration of10 days from blood collection date to received date resulting in a shelf life of 32 days for units arriving athospital blood banks. Usually, the first two days after collection are spent on testing in blood production16ites at CBS and the units are available for distribution on the third day, however, this could vary due tomany reasons. ii) The RBC issuing policy in hospital blood banks is assumed to be a First-In First-Out(FIFO) withdrawal policy. iii) We assume an infinite supply of RBC units at CBS, so that all orders madefrom hospital blood banks to CBS can be fulfilled .The order of events occurring in each period is given as follows: i) Based on the inventory policyused, an order is placed (if necessary) at the end of each period. A routine delivery cost is charged forevery order. ii) Fresh units arrive at the beginning of each period according to the quantity ordered at theend of the previous period. The inventory level of each age is then updated. iii) The demand is observedand satisfied as much as possible. If there is a shortage, an urgent delivery order for the unmet demand isrequested and the unmet demand is satisfied during the same period. iv) At the end of each period, theremaining inventory is carried over to the next period. Expired units are discarded. Wastage costs arecharged for expired units and, if applicable, same-day urgent delivery costs are charged.Usually, an optimization problem to determine the ordering strategy is set up with prior assumptionson the demand and supply distributions [33]. Recently, Bertsimas and Kallus [34] considered a conditionalstochastic optimization problem given imperfect observations, and developed a framework to prescribeoptimal decisions using observed explanatory variables. In this study, since our goal is not only to proposean ordering decision but also to develop an accurate model that identifies clinical predictors for RBCdemands, we do not formulate the optimization problem using observed clinical indicators directly, asin Bertsimas and Kallus [34]. Instead, we proceed with the demand estimation and ordering strategyoptimization in two separate steps. The structure of this data-driven inventory management problem isconsistent with the structure for a newsvendor policy proposed in Huber et al. [35].As described in Section 4.2, we have developed a demand forecasting model to predict future RBCdemand using clinical predictors. This provides important information to hospital blood banks and bloodsuppliers for model generalisation and knowledge translation. Multiple techniques have been applied toimprove model accuracy, however, the existence of forecasting errors cannot be avoided. In the inventoryoptimization step for ordering decisions, we propose an ordering strategy considering two extra decisionvariables to control the cumulative loss due to the forecasting errors from the demand predictions of thehybrid model for this mutli-period inventory problem: inventory target ( S ) and reorder level ( s ). Theproposed ordering strategy is a modified version of classical ( s , S ) policies [36]. The inventory target, S , defines an upper limit on the inventory level to avoid excessive inventory levels that may arise fromdemand over-estimation. The reorder level, s , sets a lower limit on the inventory level to avoid the needfor urgent deliveries that may arise from demand under-estimation. Under this policy, the order quantityis driven by the demand prediction from the hybrid model controlled by the following criteria: When theinventory level is below the reorder level, the order quantity is at least the number of units to bring theinventory level back to the reorder level, but cannot make the inventory level greater than the inventorytarget; if the inventory level is above the reorder level, no order is required. Thus, the final orderingstrategy is a function of the predictions from the hybrid demand forecasting model, the inventory target,and the reorder level.The age of an RBC unit is denoted by m ∈ { , . . . , M } . Let a , h , u , w be the routine delivery cost (perorder), unit inventory holding cost, unit urgent delivery cost, and unit wastage cost for each expired unit, This assumption is verified by CBS. CBS confirmed that over 98% of hospital blood bank orders were satisfied based ontheir data. I mi denote the inventory level of units of age m at the end of period i ∈ , . . . , T . Theremaining demand after withdrawing all products having ages from m to M using the FIFO withdrawalpolicy is denoted by R mi . The order quantity is denoted as z i in each period i ∈ , . . . , T , and I ( z i > ) ,is the indicator that an order occurs in period i . At the end of period i , the actual demand y i is updated.Then, the inventory level I mi for each age m , units required for urgent delivery B i , and wasted items due toexpiration I Mi are calculated. The proposed cost function is given as follows: c ( z i ) = a I ( z i > ) + h ( M − ∑ m = I mi ) + uB i + wI Mi , for i = , . . . , T , (7)where R mi = ( y i − M − ∑ j = m I ji − ) + , m = , . . . , M (8) I mi = ( I m − i − − R mi ) + , m = , . . . , M (9) I i = ( z i − R i ) + , (10) B i = ( M − ∑ j = I ji − − M ∑ j = I ji + z i − y i ) + . (11)The cost function in equation (7) includes four types of costs: routine delivery, inventory holding, urgentdelivery and wastage cost over the planning horizon of T periods. Equation (8) defines R mi accordingto the FIFO withdrawal policy. Equations (9) and (10) define the inventory dynamics. Equation (11)calculates the number of units requiring urgent delivery. In the model, all variables are non-negative. Theaverage cost can be written as E [ c ( z )] = T ∑ Ti = c ( z i ) .We propose an integrated ordering strategy where the order quantity is the predicted demand, ˆ y i , fromthe hybrid model in Section 4.2 controlled by an optimal inventory target, S ∗ , and an optimal reorderlevel, s ∗ . The optimal inventory target and reorder level values are learned through the training databy minimizing the difference between the average costs under the predicted demands and the actualdemands as a prior [37], rather than using the classical ordering structure based on estimated demanddistribution [36, 38]. We set the initial inventory, I , to be the mean inventory level according to the firstthree months of data. We assume this is an inventory level that the decision makers at hospital bloodbanks can accept, but it can be adjusted if needed (in particular the effect of lowering the initial inventorycould be explored). Let I i denote the aggregate inventory level of all non-expired units for period i , suchthat, I i = ∑ M − j = I ji for i = , . . . , T . Let S ∗ be the optimal inventory target and s ∗ be the optimal reorderlevel. The procedure to generate the ordering strategy is described as follows:1. Determine the optimal inventory target, S ∗ : First, we calculate the cost for each period using theactual demand, y i , as the ordering decision, z i , and denote the average cost as E [ c ( y )] = T ∑ Ti = c ( y i ) over the planning horizon of T periods. When the order quantity is equal to the actual demand, theinventory level is always the same as the initial inventory level for all time periods. In reality, itis not possible to know the actual demand in advance. Ordering according to the actual demandat a given initial inventory level is used as a gold standard for obtaining the optimal inventorytarget. Second, we calculate the cost of each period using the predicted demand bounded by theinventory target, defined as min ( ˆ y i , S − I i − ) , as the ordering decision. We denote the average cost18s E [ c ( ˆ y , S )] = T ∑ Ti = c ( ˆ y i , S ) under different S ∈ Ξ values, where Ξ is the feasible set of S . Theoptimal inventory target, S ∗ , is determined by minimizing the absolute difference between the twoaverage costs, such that, S ∗ = arg min S ∈ Ξ (cid:107) E [ c ( y )] − E [ c ( ˆ y , S )] (cid:107) .2. Seek the optimal reorder level, s ∗ : Using the optimal inventory target as an input variable, weconsider the decision variable as the predicted demand bounded by the optimal inventory target, S ∗ ,and the reorder level, s ∈ ξ , where ξ is the feasible set of s . If s > I i − , the order quantity is themaximum of min ( ˆ y i , S ∗ − I i − ) and ( s − I i − ) ; else the order quantity is zero. The average cost isdenoted as E [ c ( ˆ y , S ∗ , s )] . The optimal reorder level, s ∗ , is determined by minimizing the absolutedifference between E [ c ( y )] and E [ c ( ˆ y , S ∗ , s )] , such that, s ∗ = arg min s ∈ ξ (cid:107) E [ c ( y )] − E [ c ( ˆ y , S ∗ , s )] (cid:107) .3. Generate the proposed order quantity, z ∗ i : The proposed ordering decision integrating theprediction generated by the hybrid demand forecasting model, the optimal inventory target, and theoptimal reorder level can be calculated as follows: For i = , . . . , T ,if I i − < s ∗ , z ∗ i = S ∗ − I i − if ˆ y i > S ∗ − I i − , ˆ y i if s ∗ − I i − ≤ ˆ y i ≤ S ∗ − I i − , s ∗ − I i − if ˆ y i < s ∗ − I i − , (12)else z ∗ i = . The procedure is applicable to both the daily and the semiweekly demand predictions. The optimalinventory target is determined by errors in the daily demand predictions. Under a given optimal inventorytarget, since the reorder level is used to control the inventory variations due to forecasting errors, thecalculation of the optimal reorder levels for the daily and semiweekly predictions are performed separately.
A statistical summary of selected variables is presented in Table 7. As described previously, the demandforecasting model is trained on the training dataset, and evaluated on the test dataset. The mean (sd) of thedaily number of transfused units in the training dataset was 91.85 (29.62), while the mean (sd) in the testdataset was 93.05 (27.01). Over the entire time period, the estimated Sen’s slope of daily RBC demandwas 0.017 (95% confidence interval [CI]: -0.036, 0.075) units per month. Although no statisticallysignificant trend was observed over the entire period (Mann-Kendall trend test: p = . Variable Daily mean (sd) Daily range
Number of units transfused 92.43 (28.27) (18, 201)Number of units received by blood bank 103.71 (69.49) (0, 321)Number of patients (transfused and non-transfused) with abnormalMPV 755.44 (221.75) (130, 1236)RDW 297.42 (80.21) (33, 475)IgG 12.78 (9.79) (0, 43)INR 518.30 (126.06) (154, 830)Creatinine 104.31 (21) (47, 175)Hemoglobin (Hb) 157.31 (46.5) (48, 322)Platelet count (PLTCT) 209.39 (43.6) (71, 337)MCV 84.37 (27.75) (12, 163)WBC 404.27 (66.46) (74, 568)Number of units transfused to patients with abnormal pre-transfusionMPV 26.9 (25.36) (0, 116)RDW 34.67 (13.28) (4, 91)IgG 1.03 (1.56) (0, 16)INR 85.1 (26.89) (15, 180)Creatinine 27.51 (10.16) (2, 78)Hemoglobin (Hb) 54.45 (15.3) (13, 120)Platelet count (PLTCT) 28.56 (10.42) (4, 94)MCV 8.12 (4.95) (0, 34)WBC 28.52 (10.07) (4, 74)Number of units transfused atGeneral medicine location 31.7 (13.62) (2, 116)Intensive care unit 12.31 (9.11) (0, 105)Hematology location 12.53 (5.32) (0, 47)Cardiovascular surgery location 8.16 (6.06) (0, 40)General surgery location 9.07 (6.96) (0, 73)Orthopedic surgery location 3.57 (3.25) (0, 35)Outpatient location 4.85 (6.2) (0, 32)Emergency room 4.26 (3.58) (0, 26)Other surgery location 4.78 (4.21) (0, 42)Obstetrics and gynecology location 1.19 (2.17) (0, 30)Trauma 2.21 (6.7) (0, 96)Number of units transfused to patients withInpatient 62.85 (17.64) (14, 145)Age > =75 29.08 (12.43) (2, 98)Age between 18 and 74 59.04 (19.64) (13, 156)Female 41.3 (15.33) (4, 105)Male 51.14 (17.87) (5, 129) Table 7.
Statistical summary of selected variablesFigure 5 shows model performance of daily RBC demand predictions using the proposed hybridmodel. The grey line represents the actual daily demand from the data, the blue dashed line shows themodel predictions on the training dataset (partial), and the red dashed line shows the demand forecasts20 S T L T r e n d + S e a s o n a li t y S T L R e s i d u a l s L o c a t i o n − O u t p a t i e n t O l d A g e P a t i e n t s ( > = ) A b n o r m a l C r e a t i n i n e A b n o r m a l I N R A b n o r m a l P L T C T A b n o r m a l H b A b n o r m a l I g G A b n o r m a l M C VA b n o r m a l M P VA b n o r m a l R D W A b n o r m a l W B C STL Trend+SeasonalitySTL ResidualsLocation−OutpatientOld Age Patients (>=75)Abnormal CreatinineAbnormal INRAbnormal PLTCTAbnormal HbAbnormal IgGAbnormal MCVAbnormal MPVAbnormal RDWAbnormal WBC
Fig 4.
Spearman’s rank correlation among STL Trend + Seasonality, STL residuals, and selected clinicalpredictors (The pie shape in each cell represents the correlation statistics - the larger the shaded area ofthe pie shape, the higher the estimated correlation. The shape color is coded from the highest negativecorrelation -1 [dark red] to the highest positive correlation +1 [dark blue] as shown in the heat maplegend at the bottom. In this figure, all of the shapes are blue representing positive correlations.)
Date D a il y de m and ( un i t s ) Actual Train Test Train: RMSE = 11.68; MAPE = 10.72% Test: RMSE = 20.3; MAPE = 16.94%
Fig 5.
Predicted RBC demand versus actual demand21or the trained model on the test dataset. The variable selection and hyperparameter tuning processes areperformed in an iterative manner. The mean (sd) of the predicted daily demand on the test dataset is 94.85(21.72) units, and the mean (sd) of the true daily demand is 93.05 (27.01) units. The final model selectedhas an RMSE of 20.3 and a MAPE of 16.94% on the test dataset. Table 8 presents the performance of theproposed hybrid model, a single STL model, an STL + linear regression model, and an LSTM model.The accuracy of the hybrid model is significantly higher than the single STL model, indicating that theinclusion of the multivariate analysis using clinical predictors produces more accurate RBC demandforecasts. When replacing the XGBoost model with a linear regression model, the accuracy decreases,reflecting that XGBoost can better handle the nonlinear patterns in the data. There is no significantimprovement between the performance of the hybrid model and the LSTM model. However, compared toa tree-based model, such as XGBoost, building and tuning an LSTM model requires in-depth knowledgeof neural network models. The proposed STL + XGBoost model has a simpler model structure which ismuch simpler to apply, and is better able to produce statistical inference.
Train TestRMSE MAPE RMSE MAPESTL + XGBoost 11.68 10.72% 20.3 16.94%STL Alone 26.51 23.22% 30.28 25.06%STL + Linear regression 18.73 17.22% 21.67 18.56%LSTM 16.38 12.58% 21.18 16.50%
Table 8.
Model performance comparisonFigure 6 presents the relative variable importance of all 22 daily RBC demand predictors, selectedafter the iterative variable selection process described in Section 4.2.3, from highest to lowest. Amongthe top five predictors, it is not surprising that the importance of the weekday variable is high since wehave observed significant day of week effects. Interestingly, four variables refer to the number of patientswith abnormal laboratory test results that occurred seven days ago (lag 7). The next 15 variables capturethe patient characteristics and RBC inventory on the previous day (lag 1). The second-to-last variablereflects the total RBC demand of the previous week, and the last variable refers to the dates with highdaily demands, helping to correct the minor outlier effects.As shown in Figure 4, there exist significant positive correlations between the STL residuals and thelaboratory test results, respectively. A laboratory test result can be used for condition evaluation withinseven days from the date of specimen collection. The data shows that among the transfused patients,55.72% had abnormal MPV values at lag 1 and 55.18% at lag 7; 39.08% had abnormal RDW values atlag 1 and 51.64% at lag 7; 59.95% had abnormal IgG values at lag 1 and 58.62% at lag 7; and 87.68%had abnormal INR values at lag 1 and 84.25% at lag 7. These four laboratory tests (MPV, RDW, IgG,and INR) have high positive cross-correlations with the daily RBC demand at lags 1 and 7, as shownin Table 9. Thus, a higher number of patients with abnormal laboratory test results is associated withincreased RBC demand, especially for MPV, RDW, IgG, and INR at lag 7. The clinical impact of theseobservations is being pursued in a separate study.For semiweekly demand prediction, we directly calculate the results by aggregating the daily demandpredictions on Tuesday to Thursday and on Friday to Monday. The mean (sd) of the predicted semiweeklydemand on the test dataset is 325.00 (32.40) units, and the mean (sd) of the true daily demand is 323.50 Cross-correlation is used to measure the correlation between two time series at different time lags. The commonly used“correlation” refers to cross-correlation at lag 0. bnormal laboratory test Cross-correlationLag 7 Lag 1MPV 0.52 0.45RDW 0.52 0.48IgG 0.53 0.52INR 0.49 0.41 Table 9.
Cross-correlation between daily RBC demand and abnormal laboratory test results at lag 7 andlag 1(42.04) units. The RMSE is 39.22 and the MAPE is 8.97% on the test dataset. We have also trained aseparate hybrid model to predict semiweekly demand, however, the model performance (RMSE = 40.96and MAPE = 9.96%) is slightly worse than the results calculated based on daily predictions. Thus, forsimplicity, we choose not to construct a separate model for the semiweekly demand prediction.
High demand dateTotal transfused last weekLocation−Outpatient lag 1Total received lag 1Old Age patients (>=75) lag 1Abnormal WBC lag 1Abnormal INR lag 1Abnormal IgG lag 1Abnormal PLTCT lag 1Mean in−stock days lag 1Total transfusions lag 1Abnormal MCV lag 1Mean APTT lag 1Abnormal Creatinine lag 1Abnormal Hb lag 1Abnormal RDW lag 1Abnormal MPV lag 1Abnormal INR lag 7Abnormal IgG lag 7WeekdayAbnormal RDW lag 7Abnormal MPV lag 7 0.00 0.05 0.10 0.15 0.20
Variable Importance
Information value summary (daily RBC demand)
Fig 6.
Variable importance for daily RBC demand
The number of orders, inventory level, number of units requiring same-day urgent delivery, wastage,average cost, and total cost are calculated using Equations (7) to (12), assuming the routine deliverycost per order a = h =
1, unit urgent delivery cost u = w =
50. Using the procedure described in Section 4.3, the optimal inventory target is 1040 units, theoptimal reorder level for daily orders is 830 units, and the optimal reorder level for semiweekly orders is770 units. Comparisons are made during the time period of the test dataset (365 days) for four ordering23trategies: current practice (baseline), ordering according to actual demand (gold standard), the proposeddaily ordering strategy, and the proposed semiweekly ordering strategy. Ordering as current practicerefers to the current ordering strategy used in hospital blood banks that reflects the actual order quantity,inventory level, and wastage. Since the actual number of units requiring urgent delivery was not capturedin the database, the total cost calculated for the current ordering practice assumes that the urgent deliverycost is zero, and thus underestimates the actual cost. It is considered as the baseline strategy, whereasthe results for ordering according to actual demand is considered as a gold standard. Table 10 shows theresults of the four ordering strategies. A summary of findings include:1. There is a 60.55% reduction in the percentage of days with orders between the proposed semiweeklyordering strategy and baseline, whereas the proposed daily ordering strategy results in a 4%reduction.2. The average order quantities for the proposed daily and semiweekly strategies over the entire periodare less than the actual order quantities under current practice, and better reflect the actual demands.The mean order quantity for the semiweekly strategy on the 141 days with orders doubles the orderquantity under current practice, which may raise operational problems such as requiring morepacking boxes per order. Our collaborators indicate this is not of great concern for CBS.3. The average inventory level for the proposed daily strategy is significantly lower, a reduction of41%, as compared to the actual inventory level in hospital blood banks. Similarly, the proposedsemiweekly ordering strategy results in a 39% reduction of the inventory level. Both the means ofthe inventory levels for the daily and semiweekly strategies are close to the inventory level of thegold standard, but the semiweekly ordering strategy is associated with a larger variance since over60% of days have no orders. A leaner inventory leads to fresher RBC transfusions for patients. TheDOH is reduced to 8.6 days for the proposed daily and semiweekly strategies from 12.47 days forcurrent practice.4. There are no same-day urgent deliveries or wastage observed for the proposed daily and semiweeklystrategies. However, there is no guarantee that this will always happen.5. The proposed daily and semiweekly ordering strategies achieve remarkable cost savings. Figure 7illustrates the daily costs of the proposed daily strategy (red line), the semiweekly strategy (greyline), the actual costs under current practice (black line), and the constant cost of the gold standard(blue dashed line). Notably, the cost savings are driven by the significant decreases in the inventorylevel and routine order delivery costs. The proposed semiweekly strategy has the lowest averagecost since it not only leads to a lower inventory level but also requires less frequent deliveries.Overall, both of the proposed daily and semiweekly ordering strategies result in a leaner inventorylevel, fresher blood, and lower costs, while no shortages (units requiring urgent delivery) or wastageare observed. Particularly, the semiweekly ordering strategy creates a “win-win” situation, since it alsoprovides a reduced, fixed delivery schedule that reduces costs and can free human resources both at CBSand hospital blood banks. 24 ummary Current practice Ordering accordingto actual demand Daily strategy Semiweekly strat-egy(Baseline) (Gold standard) (Proposed) (Proposed)
Number (%) of days withorders‡ 362 (99.18%) 365 (100%) 347 (95.07%) 141 (38.63%)Order quantity on days withorders - mean (sd) 106.02 (66.73) 93.05 (27.01) 97.98 (21.25) 240.72 (133.73)Daily inventory level - mean(sd) 1317.46 (65.89) 780* (0) 780.59 (33.68) 800.98 (88.59)Number of units requiringurgent delivery - mean (sd) N/A§ 0 0 0Number of units wasted -mean (sd) 0.75 (1.14) 0 0 0Cost - mean (sd) 1454.03 (91.75) 880 (0) 875.66 (44.95) 839.61 (115.65)Total cost 530722 321200 319617 306457(% of baseline) (60.52%) (60.22%) (57.74%)
Table 10.
Comparisons among ordering strategies ‡ The percentage is calculated by number of days with orders over 365 days of the test data.* This number reflects the initial inventory level, I .§ The number of units requiring same-day urgent delivery was not available since the information was not captured in 2018. lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll Date C o s t l Current practice (Baseline)Daily ordering by actual demand (Gold standard)Proposed daily ordering strategy (FIFO)Proposed semiweekly ordering strategy (FIFO)
Fig 7.
Cost comparison of proposed ordering strategies versus baseline and gold standard25
Discussion
Improving the demand forecasting accuracy and building an efficient inventory management strategyfor blood products are important to modern healthcare systems. It not only impacts the blood demandand supply management for blood suppliers and hospital blood banks, but may exert positive influenceon patient outcomes. Among all fresh blood components, RBC is the most commonly administeredtherapeutic. It accounts for the largest portion of blood inventory, and determines the plan for bloodcollection and production. In Canada, due to the uncertain daily demand and the lack of quantitativeevidence to support decision making, the RBC supply chain faces multiple challenges in hospital bloodbanks including excess inventory, highly variable ordering decisions, and over-frequent urgent orders. Asa result, it has been very challenging for CBS to predict future demand and plan blood production.In this study, we develop an STL + XGBoost hybrid algorithm for demand forecasting. It has thesame level of prediction performance as a more complex LSTM model. It handles changing trendand seasonality, nonlinear patterns in residuals, and correlations among predictors in an efficient andaccurate manner. We then construct a data-driven multi-period inventory problem for RBC ordering. Theprocedure to generate the data-driven ordering strategy involves solving for an optimal inventory targetand an optimal reorder level through minimizing the absolute difference between the average costs usingthe predicted demands from the hybrid model and the actual demands. The proposed ordering strategy is amodified version of the classical ( s , S ) policies considering a specific cost function. Shi et al. [37] studieda nonparametric data-driven algorithm for the management of a stochastic periodic review inventorysystem with a constrained inventory target. There are two major differences between their optimizationproblem and ours: 1) The demand distribution is not stationary in our problem; 2) The cost function theyconsidered does not include delivery costs, consequently there is no need to consider a reorder level tocontrol the frequency of orders. They proved the asymptotical optimality of their algorithm under sometechnical assumptions and regularity conditions on the demand distribution. As a follow-up work, weplan to explore the optimality of our proposed ordering strategy in the setting for non-stationary demand.We expect that this will involve an appropriate asymptotic approach.This study considers the aggregated RBC demand of all hospitals in Hamilton, Ontario for thedevelopment of the demand forecasting model rather than the demand of each hospital stratified by ABOblood groups. We chose to forecast the aggregate demand at the city level for the following reasons: i)All Hamilton hospital blood banks are managed by one Transfusion Medicine laboratory team. This is acommon hospital blood bank management structure for Canadian cities, such as Toronto and Ottawa,Ontario. There are existing transaction networks available that allow blood delivery within cities at lowcosts. The central management structure enables the pooling of demand and inventory that may yieldoperational improvements. ii) The model accuracy is increased as the demand variability is decreased dueto pooling. In other words, considering the aggregate demand can reduce the level of demand uncertainty.iii) The model provides important clinical predictors for the aggregated RBC demand of a diverse patientpopulation in Hamilton, Ontario that could be representative of the overall Canadian RBC demand.When considering ABO blood groups, there is no significant trend observed for each ABO bloodgroup of transfused patients over the years. The proportions of ABO blood groups are consistent with theblood group distribution for Canadian population with very low variation. Our proposed methodologycan be adapted to ensure sufficient inventory for each ABO blood group. Moreover, withdrawal policiesto prioritize ABO identical RBC transfusion will be investigated in future studies.26hen defining the RBC inventory optimization problem, the assumption of a fixed storage durationat CBS from the blood collection date to received date at hospital blood banks is a limitation of this work.Seasonality and nonlinear trend patterns were observed in the blood storage duration data from 2008 to2018, reflecting the changes of the blood donation process at CBS. We found a significant increasingtrend of the storage duration after 2017. This could be associated with new tools, such as chat bots andonline appointment booking systems, launched at CBS in 2017 which increased the number of blooddonations. Since the increase in blood supply exceeded the demand, a longer storage durations resultedat the CBS distribution centres. Both the storage duration at CBS and the DOH at hospital blood banksincreased, consequently, the age of blood for transfusions has been increasing in the past couple of years.This also addresses the need of a better inventory management strategy that can help control the impactsof such changes at hospital blood banks, and share more accurate blood utilization information with CBSfor blood collection planning.To conclude, we propose a decision integration strategy for short-term demand forecasting andordering for RBC blood components. It incorporates a robust and accurate hybrid model and a multi-period inventory optimization problem for ordering decisions. This leads to a significantly lower inventorylevel under a policy that has easy-to-compute order quantities and allows for a less frequent deliveryschedule. It can potentially reduce the inventory by 40% and decrease the number of deliveries by 60%.The proposed ordering strategy can resolve the challenges faced by hospitals and CBS, and increase thetransparency of blood utilization between blood suppliers and hospitals to promote an efficient bloodsupply chain, which may lead to better patient outcomes. Furthermore, the proposed data-driven orderingstrategy is generalizable to other blood products or even other perishable products. We have initiated workto apply the proposed strategy to the inventory management of platelet components. We plan to developa software application to implement the proposed methodology at hospital blood banks in Hamilton,Ontario in the near future, and expand to other hospital blood banks across Canada as a long-term plan. This study was funded by Mitacs through the Accelerate Industrial Postdoc program (Grant Number:IT3639) in collaboration with Canadian Blood Services. The funding support from Canadian BloodServices was through the Blood Efficiency Accelerator program, funded by the federal government(Health Canada) and the provincial and territorial ministries of health. The views herein do not necessarilyreflect the views of Canadian Blood Services or the federal, provincial, or territorial governments ofCanada. The authors thank Dr. John Blake for his expertise in blood supply chain management. Theauthors thank Dr. Donald Arnold for providing valuable comments on the manuscript. The authors thankTom Courtney, Rick Trifunov, Marianne Waito, and Masoud Nasari for arranging partner interactionactivities, and providing information about blood collection, blood processing, and blood distribution atCanadian Blood Services. All final decisions regarding manuscript content were made by the authors.
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