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A SIMULATION-BASED FEEDBACK CONTROL FOR A REAL-TIME SCHEDULING SYSTEM OF BLOOD DRIVE CAMPAIGNS Jung Hyup Kim, Pennsylvania State University Harold and Inge Marcus Department of Industrial and Manufacturing Engineering
Abstract In this project, distributed discrete-event simulation with continuous feedback control was constructed in order to improve the performance (e.g. minimizing waiting time for first time blood donors) of the blood drive campaign. Based on feedback control theory, system performance was improved by using an integral controller. In addition, a work force management heuristic algorithm was used for minimizing the number of workers. The blood drive campaign is a basic physical model for this simulation. The goal of this project is to develop a system which can generate a best scheduling (minimum waiting time) for blood donors with the minimum number of workers. The verification of this system was done by using different scenarios. Then, the simulated result of the system was compared with a physical system in order to support a system improvement. Keywords: feedback process control, blood drive, discreteevent simulation, healthcare improvement
I.
Introduction
In the service industry, quality of service strongly depends on a customer’s waiting time in the system. Minimizing waiting time is one of the most important issues in every service industry. The easiest way to solve the waiting time problem is by hiring more workers to serve many customers at same time. However, this requires numerous additional costs. This is a multi-criteria decision making problem; minimizing waiting time while also minimizing the number of worker. The Red Cross is an organization which has this problem. The blood drive is one of the important public campaigns. In order to provide adequate supply of blood to hospitals, it needs lots of blood. It helps to save many accident victims, patients, and others. To improve the donor’s satisfaction, it is necessary to reduce the waiting time of donor. As I mentioned earlier, solving this problem is directly involved with the number of volunteers and nurses in the blood drive campaign. Therefore, rescheduling service order for donors to minimize their waiting time and finding minimum workforce to achieve this service level is the key of this
project. In other words, the project goal is finding a good answer for the question: “How services can be scheduled in order to minimize average waiting time of the donors while the system requirement for workforce (nurse & volunteers) is low?”
II.
Literature Review
Modeling for discrete-event simulation of blood drive system is very similar to modeling call center. The reason is that the blood drive system is a serial set of resources such as medical equipment, workers (nurse and volunteers), computers, and beds in order to deliver the services of collecting blood from donors. In the same way, a call center is also a serial set of resources; workers, phones, and computers to provide high quality customer service. For that reason, the basic system frame between blood drive campaign and a call center are similar, and we are going to review several studies for the call center in order to build the blood drive system. One of the main problems of modeling a call center is how to determine and manage the uncertainty of the arrival process because it is hard to predict arrival times of customers. Usually, we assume that the arrival time follows a Poisson distribution. Jongbloed and Koole(2001) support this assumption by analyzing data from a Dutch bank. They propose a doubly stochastic model under which arrivals follow Poisson process with a random arrival rate [1]. Blood drive campaign also faces the same issue. In order to make a more practical model, we cannot ignore this problem. They provide properties of call center arrival process in the paper. Property 1: The total daily demand has overdispersion relative to the Poisson distribution. Property 2: The arrival rate is strongly timevarying within each day. Property 3: stochastic dependence between arrival rates within each day has a positive relationship Property 4: stochastic dependence between arrival rates across successive days has a positive relationship.
The second important issue for modeling the blood drive campaign is service times of the system. Call centers have the same issue because it is a service network in which agents provide telephone-based service. For that reason, defining relation of each station with other service network will seriously influence the total system performance such as average waiting time of the customer. Brown et al. (2005) discover that the lognormal distribution provides an excellent fit to data, especially after excluding short service times. [2] The blood donation process consists of the following steps; registration, health history, venipuncture, and canteen. This means that blood drive campaign is also a service network to provide service. Therefore, we are able to assume that the distribution of service time will be followed by the lognormal distribution. Jennifer and John et al. (1993) support that the excellent fit of the log-normal was presented after analyzes data from blood donors. [3] Figure 2-1 (a), (b), and (c) are the histogram of service time for each station.
system. In addition, we assume that there is no disqualified donor in a system because there is no data to predict the probability of distribution for disqualified donor, and this case uncommonly happen in the real system. In order to improve the system performance such as the minimizing waiting time of blood donors and size of the workforce, we decide to apply the concept of real-time distributed arrival time control which is used in heterarchical manufacturing systems. According to Prabhu (2000), the manufacturing system ability to minimize the mean and variance of due-date deviation was improved by using the real-time control of just-in-time manufacturing production. [5] There are several scheduling approaches in manufacturing systems, including mathematical programming [6], heuristics [7], simulated annealing [8], distributed dispatching rules [9], and dispatching rules combined with simulation [10]. Many authors support that one of the best ways to increase scheduling effectiveness is increasing flexibility in order to counter uncertainties [1113]. According to Prabhu’s research, it is possible to provide more and better flexibility into the system by using a set of communication protocols which is based on the distributed arrival time control (DATC) algorithm because the relative arrival times among parts will determine the competition for a machine and the resulting dynamics [5].
The last important issue for modeling is abandonment. If there is heavy traffic in the system, it will have a large possibility of abandonment. Based on the research done by Gans et al (2003), the huge impact of the system performance will occur in the system although a small fraction of calls are abandoned from the queue. This means that the blood donation system should consider abandonment because there are two possible ways for the abandonment condition to occur. First one is a same situation as the call center case; donors’ waiting time is over their maximum willingness waiting time. In this case, they leave the system by themselves. Another case can only happen in the blood drive system; disqualified donor. It usually happens to the first time donor. Their physical conditions are not eligible to donate blood. For example, if a donor traveled to another country which is classified for the nations with dangerous disease she or he cannot donate blood because of the possibility of infection. In order to consider the abandonment based on theoretical side, Whitt (2004) shows that steady-state performance depends strongly upon the distribution of his or her patience time, also known as time-to-abandonment, but not upon the service distribution [4]. For the blood drive system, we would like to minimize the impact of abandonment to the
Entities continually generate their own local schedules in real time and select the best schedule for execution. In this project, we would like to apply this continuous feedback control concept to improve the system performance of the blood drive campaign.
III.
Project Objective
There are two main objectives for the system. First one is minimizing average waiting time for first and repeated donors. To achieve first objective, DATC (Distributed Arrival Time Control) integral controller is applied in the model. It helps to find the best service scheduling in order to reduce average waiting time. The second objective is minimizing the size of workforce that needs to operate the system properly. There are two types of workers in the system; nurses and volunteers. It will be possible to find the minimum workforce capacity at each station in order to achieve a certain level of service quality by using a workforce management heuristic algorithm.
IV.
Blood Drive System
The American Red Cross operates different kinds of blood drives. In this project, we focus on the open blood drive. Anyone can participate in the campaign and donate their blood. There are two types of donors; repeated and first time donor. First time donors are donors who visit the blood drive campaign first time. The common characteristic of first time donor is no appointment and short willingness waiting time. On the other hand, repeated donors have opposite style of characteristic as compared with the first time donor. They have longer willingness waiting time and usually visit the blood drive their appointment time. Simone (2002) supports that the major reasons to donate blood were altruism (75% ~ 87%) and awareness of the need for blood (34% ~ 43%). [14] In other words, repeated donors are less sensitive for the waiting time than first time donors because altruism is primarily the reason for donating their blood repeatedly. By using these differences of first time and repeated donor, we are able to build the system which can minimize average waiting time of donors. i.
As you can see above, Figure 4-1 shows the workflow of blood donation process. For the purpose of this project, transit times between stages are ignored. Based on the observation of physical blood drive system, there is no control and waiting time after donors leave the blood donation stage because there is no capacity limitation for canteen stage and donor can decide the departure time. Therefore, the simulated system eliminated the canteen stage from the blood drive campaign. Figure 4-2 shows the workflow diagram for the simulated system of the blood drive campaign.
Blood Donation Process The blood donation process consists of the following steps: 1.
2.
3. 4.
Registration –volunteer asks donors to read materials on blood donation and the donor’s demographic information is recorded on the system Health History – nurse records the donor’s temperature, blood pressure, and hemoglobin level, then series of questions will be asked pertaining donor’s medical history and lifestyle. Donation – nurse takes a unit of blood Canteen – the donor recovers after completing the donation process.
ii.
Communication Protocol and System variables In order to provide the highest level of autonomy to various decision makers and ensure the highest level on control distribution, communication between donors, nurses, and volunteers are followed by DATC protocol. Figure 4-3 shows how the protocol cooperates in distributed manner with donors, nurse, and volunteers. There are two types of control variable in the system. First is the number of volunteers and nurses at each section of the system. Second is the service order of donors. It will be controlled by DATC integral controller. In order to adopt DATC concept in this system, we must redefine the meaning of due time. In this system, due time is the willingness waiting time of donor + process time. We assume that quality of service will not be damaged by this time. As we mentioned earlier in section 4, we have two types of donors and each type has different characteristic (repeated donor: longer willingness waiting time, first donor: short willingness waiting time). Therefore, we can assume that repeated donors have longer due time as compared with first time donor. It is a very important concept to find the efficient scheduling (minimizing waiting time of donors). Two types of feedback variables are also used for the system. Waiting time for donors at
each station is the first type of feedback variable. It will be used for the local integral controller (DATC). Cumulated status of workforce capacity at each station is another type of feedback variable. It will be used for the work force management heuristic algorithm. We will explain later how to control the system by using these feedback variables.
Registration 1: Donors enter the System 2: Volunteer greet donor and request ID 3: Identity Check (Classify type: R or F) 4: Ask Donor to read the required info
5: Ask each donor to wait until a nurse calls him/her to health history station Health History
iii.
Sequence Diagram The discrete event flow of donor actions and nurse & volunteers movement are reflected in the sequence diagram shown in Figure 4-4.
6: Wait for Service (After ai(t) ) 7: Nurse available 8: Request Health History Service 9: Confirm the request and Start Service 10: Check Result
Blood Donation 11: Wait for Service 12: Nurse available 13: Request Blood Donation 14: Confirm request and Start Service 15: Donors leave the System iv.
Scheduling and Workforce Controllers Integral Scheduling Controller (ISC) By using the DATC algorithm with integral controller, it will be possible to find the best scheduling for the service order. Figure 4-5 shows a generic local arrival- time controller.
due time (willingness waiting time for ith donor + arrival time ith donor at health history stage + process time for this stage), it means no feasible solution for ith donor at current condition. In other words, it is time to change the workforce condition for ith . Equation (1) is a general form to get an arrival time of next iteration by using DATC algorithm. w(0) is a willingness waiting time for ith donor, and ai2(0) is initial arrival time of second stage, ε is error. ai2 1 = ai2 0 + k i ai2 0 + wi (0) + pi2 0 − ci2 0 +ε ai2 2 = ai2 1 + k i ai2 1 + qi2 1 − wi 0 − ai2 1 − ai2 (0) + pi2 1 − ci2 1
+ε
ai2 3 = ai2 2 + k i ai2 2 + qi2 2 − wi 0 − ai2 2 − ai2 0
+ pi2 2 − ci2 2
+ε
a i (t) k i d i - c i ( ) d a i (0) (1) t
0
ai(t) is the arrival time of second stage (health history), not arriving time on the system. The reason is that it is impossible to control donors’ arrival time. However, we can adjust the service order for the next stage in order to improve the system performance. As I mentioned in earlier section, the repeated donors are usually less sensitive than first time donor for the waiting time. By using this advantage, it is possible to find the best scheduling for the system performance. ki is the integral control gain for the ith donor in the system. di is the due time (willingness waiting time for ith donor + arrival time ith donor at health history stage + process time for this stage) for the ith donor, Ci(t) means the completion time for the ith donor at the health history section, and ai(0) is an initial condition. The key point of DATC algorithm is that minimizing due time deviation by changing arrival time of ith donor (or part in usual manufacturing system) [5]. Stability Conditionfor ISC In order to improve and stabilize global merits of the system, DATC controller adjust arrival time of an individual part toward reducing MSD = ( i (di − ci )2 /n. However, we redefine the meaning of due time for the blood drive system. Therefore, it is necessary to define new stability condition for the system. The point is that arrival time of second stage must be adjusted to minimize average time of donors within given willingness waiting time (wi(0). If arrival time of next iteration is bigger than
ai2 t + 1 = ai2 t + k i 2 ∗ ai2 t + qi2 t − wi 0 − ai2(0)+ pi2t−ci2t+ ε(1) Based on equation (1) and the system objective (minimizing waiting time and workforce), DATC controller for blood drive system should move to minimize deviation between ai2(0) and ai2(t). Figure 4-6 shows the trajectory of deviation for integral controller. As you can see below, the system cannot reach the steady-state condition until it gains enough power to process the feasible solution for a given workload. After that point, the system quickly stabilizes and produces the best scheduling to reduce the average waiting time of the system. The gain value was selected based on the analytic stability condition and numerical simulation result. There was no big impact for the gain value in the service order scheduling. However, the time to reach the steady-state condition was different when the gain value was changed; the more time for smaller k value. Based on the analysis results, range between 0.1 and 0.8 are efficient. 0.7 is the best value for the k.
Work-Force Management Heuristic Algorithm If current system condition is not eligible to find the feasible solution, WFM (Work-Force Management) algorithm will update the workforce capacity of each stage based on the value of Qt.
In the blood drive system, the buffer between first and second stage is a center position of WFM algorithm because it is the biggest bottleneck of the system. As you can see above, if a certain local condition is satisfied at the bottleneck point for donor ith, it will increase the number of signal variable. It means that additional workforce require to serve donor ith . Then, it will influence the next iteration if there is no harmful factor for a certain global condition. The following will be two main rules for WFM algorithm at Blood Drive System: - WFM Backward Rule: If the number of case for ai t − 1 > ai (t) is bigger than Qt, then improve the workforce capacity of previous station.
This algorithm is inspired by “Toyota Sewn Products Management System” and “Bucket Brigade System”. Blocking is one of the main reasons why waiting time occurs in serial process line. When blocking appears frequently at the certain point of process line, this point is called bottleneck. The performance of the system will be damaged by it. In order to minimize the impact of the bottleneck, average process time for the current station should be faster than the previous stages. That is the reason why the process line which workers stand in line a row from the slowest worker to fastest worker has better efficiency than others at the bucket brigade system. However, it is hard to make it for the blood drive system because of uncertainty or workforce management problems of the system. Therefore, it would be better to use the bottleneck in order to achieve the system purpose instead of eliminating it. The key point of WFM algorithm is that the using the bottleneck point for the watch tower of the whole process line. If something happen in the system, the bottleneck will be the first point to catch performance change. Therefore, we can respond quickly and successfully from this point to improve the system performance. Figure 4-8 shows the flow diagram of workforce management heuristic algorithm.
- WFM Forward Rule: If the number of case for ci t − ai next t − pi next t − (di − ai t > 0 is bigger than Qt, then improve the workforce capacity of next station.
V. i.
Simulation Model
Scenario This simulation is based on the medium size of blood drive campaign. Some reasonable assumptions are made in order to make this simulation more realistic Assumption of Scenario 1. The demand is 89 donors for maximum per day 2. Willingness waiting times for repeated and firsttime donors are 15 min and 7 min respectively. 3. There is no disqualified donor. 4. Initial number of worker is 8 (Registration: 2, Health History: 3, Donation: 3). 5. About 60% of donors are repeated donors, and rests of donors are first donors (based on the paper done by Jennifer D. Michaels [3]). 6. Arrival Rate for first time donor is exponentially distributed by mean 15 min
7.
Table 5-1 shows the Arrival Rate for Repeated donor(based on the data collection Sep, 2009, Appendix A) 4
As you can see above, the average waiting time of donors is 8.21 minutes. Based on the result, 16 nurses and 3 volunteers are needed in order to provide satisfy less than 9 minutes of waiting time service quality.
Description of Scenario
- Scenario 1: average waiting time for first + repeated donors should be less than 9 minutes - Scenario 2:average waiting time for first donors should be less than 7 minutes
The result for Scenario 1 The target level of service quality is less than 9 minutes for the average waiting time for both types of donors. Figure 5-2 shows the service order change as the number of iteration increase. Donor number 12, 13, 14, and 15 are repeated donors. Donor number 65, 66, and 68 are first time donors. They are seven donors who arrive in blood drive at the beginning of simulation. The service order was 65, 13, 12, 66, 14, 15, and 68 when iteration was 2. However, service order was changed at iteration 65. 2900
12
Arrival Time
Illustration
Arrival Time
ii.
The result for Scenario 2 The target level of service quality is less than 7 minutes for the average waiting time of only first time donors. Figure 5-3 shows the service order change as the number of iteration increase. Table 5-2 shows the system performance for scenario 2. Figure 5-3 and 5-4 show the improvement in global merit of Blood Drive Simulation for Scenario 2. 12
1900
13 1400
14 15
900 2
4
15
40
65 134
65
Iteratioin
66
2400
13
Total number of Volunteer at Register
4
1900
14
Total number of Nurse at Health History
12
1400
15
Total number of Nurse at Donation Stage
8
900
65
Average Waiting Time for repeated donors
4.61 min
66
Average Waiting Time for first donors
6.43 min
Total Waiting Time
28553 sec
Average Waiting Time
5.35 min
2
3
6 Iteration
58 65
68
Based on the results of workforce capacity from previous section, number of volunteer and nurse are fixed. Then, average waiting time for both, repeated and first-time donor of two results are compared. As you can see Table 6-1, the solution with controller shows the better performance as compared with another solution. The improvement of performance is 14.4% for repeated donor, 19.3% for first-time donors, and 17.2% for total donors.
Average Waiting Time for repeated donors Average Waiting Time for first donors
400000
Total Waiting Time
Global Merit (seconds)
600000
Average Waiting Time
300000
Solution With Controller
Solution Without Controller
Improvement of System Performance
4.61 min
4.64 min
- 0.03 min
6.43 min
6.24 min
0.19 min
28553 sec
28212 sec
341 sec
5.34 min
5.28 min
0.06 min
200000
100000
There is no improvement of system performance when the result from scenario2 is compared with the solution (no controller). The reason for this result will discuss in section 6.2 scheduling comparison.
0
ii.
VI.
Schedule Comparison with vs. without Controller
Verification Scenario 1 (Register: 3, Health History: 9, Donation: 7)
i.
Solution Comparison with vs. without Controller In order to verify the improvement of the system by using distributed controller, two results (the simulation with controller and without controller) of each scenario are compared. Scenario 1 (Register: 3, Health History: 9, Donation: 7) Solution With Controller Average Waiting Time for repeated donors Average Waiting Time for first donors Total Waiting Time Average Waiting Time
Solution With Controller
Solution Without Controller
Improvement of System Performance
6.37 min
7.29 min
- 0.92 min
10.93 min
13. 0375 min
- 2.1 min
43851 sec
51364 sec
- 7533 sec
8.211 min
9.62 min
- 1.4 min
Figure 6-1 shows the scheduling difference because of the controllers. The arrival time to the system is in the left side of table. After donors finish a registration stage, the services order without controller show in the second table. Based on the comparison of second table with last table, DATC controller influences the service order of donors due to their willingness waiting time. The condition of first scenario is that finding the best scheduling and workforce capacity in order to achieve less than 7 minutes of service quality for both types of donors. Therefore, it is possible to provide more efficient scheduling by using the willingness waiting time of repeated donor to improve the system performance of all.
iii.
Scenario 2 (Register: 4, Health History: 12, Donation: 8) There was no improvement of system performance based on the comparison result for scenario 2 in section 6.1. The cause of this result is deeply related with the target level of service quality. In scenario 2, target level for service is less than 7 minutes of average waiting time for first-time donor. It means that willingness waiting time of repeated donors will not influence to improve the system performance. The system only focus on the first-time donors who are arrived at the system randomly manner. Hence, the system requires higher capacity of process ability as compared with scenario 1 in order to satisfy the level of service quality which is given by the condition of scenario 2. It changed the behavior pattern of system to focus on process ability instead of service order.
Inter-arrival time of donors will significantly influence the system performance. In the scenarios, we assume that the arrival rate for first time donor is exponentially distributed by mean 15 min. In this section, we run seven replications for each scenario with difference random seeds. It will create different arrival pattern for first-time donor and reveal the influences of uncertainty on the system. The results in section 6.1 and 6.2 werebased on seed = {6235897, 9323846, 2018281, 8465927, 8932572, and 2649673}. Every run in figure 6-3 has same distribution function with same mean, but they have difference seed to create different random number. As compared with the results in previous section, there is no significant difference for the system performance and workforce capacity. iv.
As you can see above, there are only few small changes of schedule between second and last table. However, the workforce capacity is increased by 26.3% as compared with scenario 1.
Replication with Different Random Seeds
Performance Comparison Physical vs. Simulated System According to the telephone conversation with American Red Cross (Greater Alleghenies Blood Services region), the number of workers in blood drive campaign depends on average demand per day. The level of service quality for current physical system is 15 minutes of average waiting time. Based on their historical data, 15 ~ 19 workers (registration: 3, health history: 6 ~ 8, blood donation: 6 ~8) are usually assigned if daily demand is 80 ~ 90 donors. As the similar condition (daily demand: 89 donors, target service level: less than 15 minutes of average waiting time) apply to the simulated blood drive system, we can conclude that the simulated system provide better solution than the current solution of American Red Cross. Table 6-3 is the result of it.
Total number of Volunteer at Register Total number of Nurse at Health History Total number of Nurse at Donation Stage Average Waiting Time for repeated donors Average Waiting Time for first donors Total Waiting Time Average Waiting Time
2 8 5.5 10.48 min 18.2 min 72662 sec 13.6 min
4.
5.
6.
As you can see above, 15 ~ 16 workers need to operate the blood drive system based on the given condition. It means that we can save 2 or 3 workers by using the simulated system. In addition, average waiting time is 13.6 minute, so the quality of service will be improved by 10.2% based on the result we got from the simulation.
VII.
Conclusions
In this project, we developed the real-time scheduling and workforce controlling system for the blood drive campaign. The project goal is to find an answer to the question: “How services can be scheduled in order to minimize average waiting time of the donors while the system requirement for workforce (nurse & volunteers) is low? “. In order to get the answer of this question, we applied DATC (Distributed Arrival Time Control) algorithm for the local controller and WFM (Work-Force Management) algorithm for the global controller. By using these, we are able to find the best service scheduling system for donors in order to reduce average waiting time and the minimum workforce capacity at each station due to achieve certain level of service quality. Applying more complex system (more than 3 process stages in the system) will be one of directions for future research. In addition, developing effective user interface with better analysis tool will be another direction for future research because building a model and checking the integrity of the model is time consuming job for the donors scheduling problem. It will help to reduce the time and effort for this. REFERENCE 1.
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3.
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Jung Hyup Kim is a doctoral candidate student in the department of industrial and manufacturing engineering at the Pennsylvania State University. His research focuses on the cognitive human factor as well as the human performance assessment in the healthcare system. Now, he is a research assistant of HPAM (Human Performance, Assessment and Modeling) lab. The current project is doing a cognitive research with Honeywell Company.
