Introduction

Transfusion medicine is arguably one of the most industrial-like specialities in modern medical science. Although some studies are ongoing, the state of the art for artificial substitutes of human blood is far from satisfactory, meaning that healthy donors are the only suppliers [1, 2]. Moreover, blood components have a limited shelf life (up to 42 days for red cells, 5 or 7 days for platelets depending on the regulatory environment, and 2 years for plasma), which prevents strategic long-term storage [3, 4].

Blood is provided to healthcare systems through the so-called Blood Donation Supply Chain (BDSC), whose management includes both strategic and operational decisions. Following the descriptions provided by Sundaram and Santhanam [5] and Osorio et al. [6], the BDSC can be divided into four stages: (i) collection (including donor registration, donation and blood screening); (ii) transportation; (iii) storage; (iv) utilization (including demand prediction, supply management and distribution).

In particular, collection is one of the most important stages in making the BDSC work properly. In fact, collecting an adequate amount of blood is a key requirement, as an unbalanced supply of units could trigger alternating periods of blood shortage and wastage. Therefore, its proper management is essential to improve all downstream steps, including patient care. Moreover, its management is particularly critical because blood collection merges the characteristics of a production system, where both demand and production are stochastic, and those of a service provider regarding the collection from donors [7, 8]. However, some stages of the BDSC are not adequately addressed in the literature yet. For example, while storage is extensively studied, collection is only marginally considered despite its relevance [9].

Given the increasing global demand for blood and the need to comply with budgetary and legal requirements, there is a growing need to reengineer the BDSC and in particular the management of collection centres by implementing efficient evidence-based policies. Moreover, as these centres are typically managed by non-technicians, these policies should be implemented using highly intuitive tools [10].

In this context, our paper focuses on the operational management of blood collection centres with a double motivation. On the one hand, we analyse different centre configurations to identify the best ones in terms of cost and service quality, considering the perspectives of the three main actors involved (donors, workers and managers). On the other hand, we assess the interactions of the operational level with higher planning levels and, in particular, we evaluate the operational effectiveness and feasibility of the schedules deriving from donor appointments defined at the tactical level.

Quantitative analyses are performed through a discrete event simulation (DES) model that describes a general and customizable blood collection centre. The DES architecture was chosen over other methodologies because of its inherent flexibility, the reduced number of assumptions required to mimic reality, and its ability to determine the best configuration among a series of alternatives under uncertainty, by exploiting what-if analysis. Even if this may lead only to nearly-optimal policies, those are sufficient in most cases where the optimal solution is indeterminable or impractical: for instance, other methods such as Integer Linear Programming require high computation power and more restrictive assumptions to provide a solution. Moreover, DES gives an intuitive representation of the flows, which can be readily understood by non-technical personnel without a strong operations research background, as often is the staff in blood collection centres. Finally, it has a short learning curve and allows users to easily verify the effectiveness and feasibility of decisions made at higher levels, enabling optimization-simulation frameworks in case these decisions need to be revisited.

The structure of the DES model is formalized with Business Process Model and Notation (BPMN) standards [11], while the inputs are provided by a donor appointment schedule. To validate the DES model and demonstrate its practical applicability, numerical experiments have been conducted considering the real case of the Milan branch of the main Italian blood provider, the Associazione Volontari Italiani Sangue (AVIS), hereinafter referred to as AVIS Milan. For such a case, the input schedule has been provided by the Blood Donor Appointment Scheduling (BDAS) tool presented in Baş Güre et al. [12] and Yalçındağ et al. [13].

In the literature, one of the earliest works dealing with BDSC from a non-clinical point of view was proposed by Millard [14], who suggested applying industrial inventory models to blood collection. However, BDSC only began to receive broader attention a decade later, as reported in several literature reviews [9, 15, 16]. Although BDSC has been extensively studied in the operations research literature, the different steps of the BDSC have not received the same attention. For example, as mentioned above, storage is the most addressed step, and collection the least one [9].

Several techniques can be applied to study blood collection, for example evaluation of best practices, linear and integer programming, queuing models and Markov decision processes [17-24]; however, simulation-based works outnumbered those with any other solution method over the years. Indeed, simulation is a rather effective approach to address BDSC management problems, according to Beliën and Forcé [15], because of the complexity of the system. It usually leads to the identification of near-optimal policies, which may be sufficient in cases where the optimal solution is indeterminable or impractical. In particular, DES has been highlighted as the most effective and practical approach for many aspects of BDSC management.

Finally, it is worth mentioning that DES has been successfully applied to the optimization of operations in other healthcare services, for example in operating theatres [25], in specific home care services [26] and in resource allocation for screening [27].

In the following, we focus on simulation techniques applied to the management of a blood collection centre to highlight the differences and underline the contributions of our work.

Jennings [28] used simulation to evaluate the impact of different policies on stock levels, shortages and the expiration of blood units. Pratt and Grindon [29] developed a computer simulation model to study flow and queuing problems arising in blood collection, considering various scheduling strategies. Sirelson and Brodheim [30] built a simulation model to evaluate the performance of a platelet inventory system in terms of out-of-stock and expired units. Brennan et al. [31] studied service and productivity problems for American Red Cross blood collection using a general purpose simulation software, with the goal of understanding which donor arrival patterns make the system more efficient under different configurations, staff allocations and work rules. Michaels et al. [32] studied the impact of several planning strategies to schedule the arrival of donors at a corporate blood collection. More recently, De Angelis et al. [33] integrated a simulation model with a neural network to find an optimal resource configuration for a transfusion centre in Rome, modelling the operations as a set of consequential servers with a given nominal capacity. Rytilä and Spens [34] simulated the Finnish transfusion system, while Katsaliaki and Brailsford [35] analysed a British hospital supplied by a regional blood centre. Alfonso et al. [36] applied Petri net models and quantitative simulation to the case of a blood collection centre in France, defining performance indicators to evaluate human resource planning and donor arrival patterns both for booked apheresis donors and walk-in whole blood donors, in mobile and in fixed collection settings alike. Blake and Shimla [37] used a flow shop model to create a linear model that determines the most efficient staffing configuration in a Canadian blood centre. Finally, Moons et al. [38] exploited a software designed for industrial simulation to determine optimal staffing and resource planning.

According to Pirabán et al. [16], no work dealing with the simulation of a blood collection centre implemented an optimized appointment schedule so far. In fact, the available models are intended to identify the best input management policies given a set of organizational constraints, while in our work we focus on merging simulation with the output of an optimized scheduler. Some of the listed works also included a visual representation of the simulator, to make its functioning more intuitive for the managers of blood donation centres, who usually are medical (non-technical) personnel [10]. Some also considered multiple stakeholders’ perspectives to evaluate their results. Therefore, to make its functioning more intuitive, our tool also includes a visual representation of the simulated environment.

Table 1 summarizes the main characteristics of the studies dealing with simulation for blood collection and compares them with our work. None of the other published papers included all the characteristics that are considered together in our work, and in particular the integration with an optimized schedule. Among the available works, the one proposed by Alfonso et al. [36] is the most similar to ours, but this also neglects the just-mentioned feature.

Table 1. Characteristics considered in the available works dealing with a simulator for blood collection and in this work: booked donors (BD); unbooked donors (UD); fixed setting (FS); mobile setting (MS); visual representation (V); assessment of three stakeholders’ perspectives (P); interaction with optimized schedule (OS) BD UD FS MS V P OS Pratt and Grindon [29] X X Brennan et al. [31] X X Michaels et al. [32] X X X De Angelis et al. [33] X X X Alfonso et al. [36] X X X X X X Blake and Shimla [37] X X X X X Moons et al. [38] X X X This work X X X X X X

The remainder of this paper is structured as follows. Section 2 describes the proposed DES model, its implementation, validation and application to the AVIS Milan case. Section 3 presents the results for both the analysis of alternative layouts and the feedback to the appointment scheduler. Finally, Section 4 and 5 discuss the results and provides the conclusion to the work.

Materials and methods

The operations at the blood centre are based on the observations made in AVIS Milan and integrated with those reported in the literature, mainly in Alfonso et al. [36]. The resulting description is general and customizable enough to describe several blood collection centres.

Process description

The whole blood donation process for a donor generally consists of four main steps:

All donors who arrive at the donation centre show up at the reception, where an employee records their information. Donors are also given a pre-donation anamnestic questionnaire to fill out. Donors enter a consultation room with a physician. Relevant vital signs are measured, including blood pressure, heart rate and haemoglobin concentration. After all data have been collected, the physician determines whether each donor can donate that day or whether they must be deferred temporarily or permanently. If not deferred, donors can proceed with the donation. Donors are assigned to a donation bed, where all necessary devices and consumables have been prepared. The skin of the donor's inner elbow is disinfected, a vein of the arm is punctured and the phlebotomy begins. The first millilitres of blood are collected in test tubes, which will be sent for screening. Then, the withdrawn blood is directed to the donation bag. After the target extraction level (∼450 ml) is reached, the needle is removed and donors are left on the bed for a few additional minutes. This prevents vagal fainting that may occur when the donor suddenly switches from lying to standing [39]. Finally, donors are directed to a canteen area to get refreshed, and above all for post-donation supervision, to detect possible negative outcomes before they leave the centre.

All works report that the blood collection process begins with donor registration and ends with the donor being offered a light meal after phlebotomy in a canteen or snack room. However, other activities such as questionnaire filling, haemoglobin testing, vital signs check and clinical counselling are taken into account differently in each work. For example, haemoglobin can also be measured before filling out the questionnaire or in the donation room just before the donation.

The arrival of donors can occur in different ways and according to different rules. In our DES model, input arrivals are given by an appointment schedule and in particular by the BDAS scheduler of Baş Güre et al. [12], whose aim is to balance the production of the different blood types (combination of group and Rhesus factor) between days while penalizing overtime and periodic accumulation of donors (queues). This scheduler divides each day into periods (e.g. ‘early morning’, ‘late morning’ and ‘early afternoon’) considering already booked appointments and the expected number of walk-in (unbooked) donors for each period to pre-allocate group-specific donation slots with the aim of balancing blood type production. Then, when donors make a reservation, they fill one of these slots. The system is dimensioned on the basis of the overall physician capacity for each period and standard time for a medical consultation and is capable of penalizing donor accumulation using period-specific weights. The choice of physician time as the scarce resource derives from the characteristic of the system under analysis. Indeed, different from other health facilities where beds represent the bottleneck of the system, the cost for adding a physical bed, if there is room, is not so relevant for the considered system. Here the highest costs are associated with disposables, tests performed on donated units, and staff; while the former two items are fixed, given the number of units, staff represents the most relevant cost item on which a proper management of the blood collection centre may have an impact. Finally, if the number of booked donors for a given blood type is high, the scheduler dynamically reacts by increasing the number of new slots to allocate to that given blood group rather than simply allowing overbooking. The interested reader is referred to Baş Güre et al. [12] for more details.

The following assumptions have been made to formalize the design of the DES model. Only donations at a fixed-site blood collection centre are included, while mobile settings are excluded (e.g. blood collection vehicles sent by the centre for collection in schools, companies and at events). Only whole blood donations are considered, and they are all assumed to be successful, because the actual usability of a donation does not have an impact on the system in terms of resource occupation. A given percentage of booked donors is expected to not show up at the assigned appointment. Moreover, a given percentage of donors is estimated to be deferred from the donation after being visited; these donors leave the centre without going through the next steps and will return from a date set by the physician. Apart from this, donors do not voluntarily leave the process once they enter, contrary to what was assumed by Alfonso et al. [36]; instead, we model queues without a maximum waiting time and use the time spent in the queue as a performance metric.

The DES model refers to voluntary centres in Western countries; however, international standards contribute to unify the key steps, and the World Health Organization is actively promoting homogeneity among all transfusion systems [2, 40].

The DES includes the following configurations to cope with the alternative layouts for the activities in steps 1 and 2, to guarantee generality and flexibility to the description:

Questionnaire filling: it is combined with waiting and physician’s consultation times. Haemoglobin measurement: it can be performed either in conjunction with the consultation or separately, before or after it. Vital signs measurement: it is included in the consultation. Consultation: it is the last step before phlebotomy, performed in a physician’s office or equivalent setting. It must be remarked that, in some contexts, consultation can be performed by non-physician personnel. However, this is not a decision that can be taken individually by a blood centre, as it intertwines with local legislations, and, moreover, it does not impact on queuing or staff deployment. Conceptual modelling with BPMN notation

A BPMN scheme of the system has been constructed to serve as the basis for the DES model. The BPMN notation allows to present the actions taken by the different actors involved in the process separately and to easily show how they interact and at which stage of the process [11].

The BPMN diagram is shown in Fig. 1. Each horizontal section is devoted to the actions taken by an actor: (i) donors, (ii) receptionists and administrative staff, (iii) physicians and (iv) nurses. The two blocks within coloured lines refer to the activities carried out at a higher level by the BDAS [12], included here as they characterize the system input. In particular, the green dashed line and the red dotted line identify the offline pre-allocation and the online allocation phases, respectively. All logical blocks, included in the DES model, represent the actual blood donation process according to the 4 steps presented in Section 2. Summing up, during the reception phase the donors arrive at the centre and interact with an administrative figure (receptionist or employee), who registers their arrival. The medical consultations are done by physicians, who decide whether each donor can donate that day or whether they should be deferred. During the phlebotomy, donors are assisted by a nurse, who takes care of the pre-setup and post-setup of the collection equipment. Finally, donors get a refreshment before leaving the facility.

BPMN model of the operations carried out at the blood collection centre.

Model implementation

The DES model has been implemented in FlexSim (FlexSim Software Products Inc., Orem, UT, USA), in a parametric form so that the parameters of the distributions can be easily adjusted or tailored. This implementation also provides a real-time 3D visual counterpart of the simulated environment, shown in Fig. 2.

Bird’s eye view of the 3D environment of the simulator.

The arrivals of both booked and unbooked donors at the centre are taken for each period from the BDAS pre-allocation solution. As for booked donors, their arrival times are generated using a uniform probability distribution within their respective period. Since the scheduler assigns donors to periods, rather than giving them a specific appointment, the uniform distribution provides a satisfactory and unbiased proxy for the behaviour of booked donors, reflecting the situation of AVIS Milan in which no particular donor arrival pattern has been observed. By directly considering the BDAS pre-allocation as input rather than the actual reservations of donors who call to make a reservation (see Baş Güre et al. [12]), not all pre-allocated slots are expected to be filled and converted into booked donors’ slots. Therefore, each pre-allocated slot is considered to become booked following a Bernoulli distribution with probability . In addition, some booked donors may not show up for the donation with respect to the nominal arrivals. To model this, each booked donor is considered not to show up following a Bernoulli distribution with probability . Finally, unbooked donors are generated in quantities equal to the expected value considered in the BDAS pre-allocation solution, within their respective period, using a uniform probability distribution for the arrival time. This also reflects the situation of AVIS Milan where these donors tend to show up randomly.

The activities are organized and modelled as detailed below.

Each donor goes immediately to the registration desk upon arrival. Registration is set up to run differently depending on whether the donor is booked or not. In particular, the registration time is longer for unbooked donors, due to the fact that their data must be entered into the database by the clerk who serves them, and this process takes additional time.

After being successfully registered, donors must see a physician for consultation. Each physician is located in a separate office. If there is a free physician, donors can access the office directly; otherwise, they must stay in a waiting area until their turn comes. Different logics for queue management have been considered in the DES model; in the baseline scenario, the queue is served using a First In First Out (FIFO) logic. During the waiting time, donors fill out a questionnaire they received during registration; therefore, the time for compilation is not modelled separately.

When a physician is available, donors go to his/her office and undergo a consultation. One aspect of the assessment is haemoglobin measurement, which as mentioned can be carried out together with the consultation or not. It is considered jointly in the baseline scenario, and separately in the variants. The two process times (consultation and haemoglobin measurement) are modelled separately; in the baseline scenario, we consider their sum.

The outcome of the clinical assessment for donation eligibility depends on whether donors are booked or not. In fact, unbooked donors are assumed to have a rejection rate at least five times higher than the booked ones, who receive initial feedback during the reservation and are more familiar with the reasons why one should self-abstain from donating. Separately for the two types of donors, rejections are modelled using Bernoulli distributions with different parameter values.

Afterwards, accepted donors enter the donation room. The first available nurse accompanies them to the first available bed according to a FIFO policy in all scenarios. Then, the pre-setup of the machine is performed by the nurse, including the puncture of the donor’s vein.

During phlebotomy, the nurse is able to attend other activities that need to be performed, including taking care of other donors. After the donation, when the planned amount of blood has been withdrawn, a nurse is again engaged to disconnect the donor from the bag and for the post-setup activities.

After successfully completing the donation, donors are asked to rest on the bed to avoid vasovagal fainting related to the orthostatic reflex. Then, they can leave the donation room and move to a canteen area, where they have a refreshment before leaving the centre. This last step is not fundamental to the workflow of the donation centre, especially because it is managed separately and usually organized as a self-service area. However, the time spent in the canteen is an integral part of the psychological time that donors spend inside the centre. In this light, the refreshment phase is included in the calculation of the total donors’ cycle time.

Experimental setting

A first set of experiments was conducted to validate the DES model. Then, an experimental plan was designed to compare different configurations and evaluate the best ones in terms of cost and service quality for the three main stakeholders involved (donors, workers and managers). Finally, a feedback loop from the DES to the higher scheduling level was implemented and evaluated, to adjust scheduling decisions if they determined criticalities or infeasibilities at the operational level. More specifically, the feedback consisted in the re-calibration of some parameters used by scheduler, based on the outcomes obtained from the DES model.

All experiments have been tailored to the AVIS Milan case, in terms donor flow and number of resources involved.

In the following, after reporting the adopted parameters and the Key Performance Indicators (KPIs) designed to evaluate the performance of the collection centre in Sections 2.4.1 and 2.4.2, respectively, we present the validation of the DES model in Section 2.4.3 and the tested alternative layouts in Section 2.4.4.

Simulation parameters

Already booked donors, pre-reserved slots and expected walk-in donors were taken from the first day solution of the BDAS scheduler was taken in Baş Güre et al. [12]. In particular, we randomly extracted a solution generated after the ramp-up period from the scheduling experiments reported in that work. Moreover, as similar amounts of donors were observed in the BDAS between days, the solution is representative of the considered collection centre.

The distributions of the different process times used are from the available literature. Since AVIS Milan could not provide us all the data required to build the whole simulation model, we referred to the literature as a proxy. The adopted distributions were evaluated against qualitative observations reported by AVIS Milan, and it was observed that the two sets were comparable. On this basis, process times were defined as follows:

Registration for booked donors: normal distribution with mean value and standard deviation (Alfonso et al. [36]). Registration for unbooked donors: log-normal distribution with mean value and standard deviation (Brennan et al. [31]). Consultation: triangular distribution with minimum value maximum value and modal value (shape from Alfonso et al. [36], with parameters modified to fit the AVIS Milan case). Haemoglobin testing: uniform distribution between minimum value and maximum value (Alfonso et al. [36]). Pre-setup of collection equipment: normal distribution with mean value and standard deviation (Alfonso et al. [36]). Phlebotomy: Weibull distribution with scale , shape and location (Alfonso et al. [36]). Post-setup of collection equipment: uniform distribution between minimum value and maximum value (Alfonso et al. [36]). Resting: triangular distribution with minimum value , maximum value and modal value (Tomasulo et al. [39]). Post-donation refreshment: log-normal distribution with mean value and standard deviation (Alfonso et al. [36]).

Note that parameters , , and related to the consultation and haemoglobin distributions are calculated such that the expected value of the sum of these two times is equal to the standard consultation time used in the BDAS pre-allocation.

The periods used in the BDAS solution were translated into 3 blocks of two hours: 7:30 a.m. to 9:30 a.m.; 9:30 a.m. to 11:30 a.m.; 11:30 a.m. to 1:30 p.m.. However, the simulation did not stop at the end of the third period to measure the time the last donor leaves the system after completing the donation process, even if it falls after the centre closes. In this way, it was possible to assess whether queuing causes some donors to remain in the system beyond opening hours.

Moreover, the following parameters were taken for the Bernoulli densities: no-show rate of already booked donors ; filling rate of pre-allocated slots ; deferral rate at the consultation for booked donors equal to ; deferral rate at the consultation for unbooked donors equal to ; deferral rate at the haemoglobin testing equal to for both booked and unbooked donors. Deferral rates were chosen to give a total acceptance rate of and for booked and unbooked donors, respectively, as provided by AVIS Milan. These high acceptance rates are associated with the fact that booked donors are usually pre-screened during reservation and with the fact that also unbooked donors are regular donors aware of the acceptance criteria for donating.

Finally, the other parameters used in the DES model are in agreement with the BDAS solution considered: collective nominal physician capacity equal to  min for all periods; mean consultation time equal to  min.

Key performance indicators

Several KPIs have been identified taking into account the point of view of the three main stakeholders involved: donors, staff and managers of the centre, each one with their own prerogatives. Targets regarding KPIs were discussed with AVIS Milan, but different centres with different needs may personalize their own set of KPIs to reflect the individual needs of the centre.

Two indicators have been identified for donors: total time spent in the system (cycle time, also used in Section 2.4.3 for validation), and time spent in queue. They have also been differentiated between booked and unbooked donors. In particular, cycle time (encompassing all donors) has been our main metric of interest.

Utilization statistics have been considered for resources: three types of personnel (physicians, nurses and clerks) and beds. As for physicians, who are considered the scarce resource, the aim is to limit their utilization, while for the other resources the target is to increase it. This is in agreement with the DBAS scheduler we used.

The main indicator from the management point of view is cost-efficiency, where efficiency is evaluated in terms of donors’ cycle times. Moreover, two other indicators have been considered in each period to evaluate the periodic accumulation of donors in the bottleneck of the system (the queue before consultation): the used physician capacity, and the exit time from consultation of the last donor of the period.

A summary of all KPIs is provided in Table 3.

A non-monetary cost unit (CU) has been associated with all variable resources, ignoring all fixed costs that do not vary with the layout (e.g. structures and physicians, whose number is constant as the layout changes). In particular, the following CUs have been considered, in agreement with Alfonso et al. [36]: clerk salary equal to 5 CUs/workday; nurse salary equal to 10 CUs/workday; the cost of a bed equal to 1 CU/workday. In the AVIS Milan case, 1 CU corresponds to about 20 euros.

Model validation

The DES model was verified and validated in two stages.

First, a face validation and a verification for reasonableness analysis were performed. Face validation was carried out iteratively, comparing model results with feedback from subject-matter experts [41] from AVIS Milan, and adjusting parameters accordingly (the above presented parameters are already those set after validation). As for the verification, the inputs were varied and the adequacy of the system response was verified, for example we checked that queue length and delays increased/decreased as donor arrival rates increased/decreased. System sensitivity to different probability distributions was also checked and found to be low.

Second, and more importantly, a statistical validation of model performance was performed by considering replications of the baseline DES solution, modelling the current configuration of the centre, and focusing on the main metric of interest, that is the donor cycle time (referred here as ). In fact, it is a comprehensive metric, able to define the throughput of the collection centre. AVIS Milan reported that the true value of for their centre is minutes. First, we tested the 5 replications for normality. The sample mean for donor cycle time () was , and its sample standard deviation (