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Journal of the Academy of Hospital Administration

Inventory Management of Blood Bank: Theory and Practices

Author(s): Sai Prasad, K.K*, K.V.S. Sarma**

Vol. 13, No. 1 (2001-01 - 2001-06)

Abstract : This paper presents some aspects of managing blood in a hospital blood bank. The practices adopted are studied and their utility is reported. We have also suggested some measures taken to improve the quality of blood in the bank and also to avoid professional donors. A theoretical inventory model is suggested which can be applied for other banks also.

Keywords : Inventory management, donor motivation

Introduction

One of the areas of hospital management is that of controlling the inventory of drugs, photo films, blood etc., which have fixed life time. According to the classical inventory models the optimum inventory levels are maintained with the objective of minimising the sum of costs of excess and under stocking. Dunkan and Norwitz1 have however observed that in case of hospital inventories, the concepts of holding and ordering costs is not very suitable. The use of Markov Chains for blood bank management has been illustrated by Andrew and Herbert2. This paper deals with a case study on blood bank management.

Blood is a perishable commodity with limited life. Its only source is the healthy human being. The demand for it originates from the injured or ailing human being. The blood supplied by one person can not be used randomly for another person, unless the 'group' matches with each. The blood bank is a valuable resource for the health and wealth of human beings. It is here stock of blood is maintained in healthy conditions to meet the demand. By the very nature of this perishable commodity, the policy matters regarding blood bank inventory management are i) average inventory level to be maintained for each group, ii) average age of blood at the time of transfusion and iii) average amount of blood that perished. There is strong need to enlarge the army of blood donors by encouraging voluntary donors, since the number of such donors is small. According to a news report, there is short fall of 30-40% in the demand-supply position of blood in India. One way of ensuring enough stock in the bank is to encourage this voluntary donors and this requires proper motivation.

The objective of this study is to develop a systems approach through mathematical modelling, for the optimal operation of the blood bank in a Government run hospital.

Pattern of Demand for Blood

The pattern of demands and transfusions have been observed on current data for 55 weeks and all parameters including the group are recorded. The average weekly demand and its standard deviation during a period of 55 weeks has been collected and the statistics is shown in Table-1

Table-1: Summary statistics of demand for various blood groups

Group 0 A B AB & -ve
Average 12 6 10 5
S.D 10 5 8 3

For the purpose of predicting the aggregate demand for blood irrespective of the group, the frequency distribution has been analyzed and the following empirical pattern has been obtained.

Table-2: Distribution of demand for blood

Demand 20-24 25-29 30-34 35-39 40 & More
Frequency 6 13 18 11 7

This distribution is fairly symmetric and could be represented by a Truncated Normal distribution with a mean of 32 units and standard deviation of 12 units per week. The demand for individual groups however has shown approximately Poisson behaviour.

The number of transfusions done per week is an index of the usage of blood that has been stored in the bank. Due to various reasons, a transfusion either gets postponed or sometimes cancelled. The observed distribution of transfusions is shown in table-3.

Table-3: Distribution of transfusions

Transfusions 11-15 16-20 21-25 26-30 30 & more
Frequency 2 14 14 17 8

The average number of transfusions per week is 25 with a standard deviation of 6.

One of the measures of performance commonly adopted by the management of a blood bank is the ratio of "cross matches to transfusions" or the CT-ratio. We will denote this by CTR. The weekly CTR is 1.3236 with a standard deviation of 0.1747, while the hypothetical value is 1.50. Assuming normal distribution for this ratio , the deviation from the norm has been found to be insignificant as confirmed by Z-test. The most probable CTR in a week will be in the interval (1.1076,1.6844) with 95% confidence.

Since the system of the distributions is not normal, the buffer stock for each blood group can be determined using a statistical principle called the Chebyscheff's inequality as given by Starr and Miller3. According to this, the probability that the actual demand exceeds the average demand during a period is approximately 1/(1+K2) where K is a constant chosen as 4.35 in order to provide a service level of 95%. The target inventory will then be equal to average demand plus 4.35 times the standard deviation and the latter is called the buffer stock. Now for the O+ group, the buffer stock required will be (4.35 X 3) or 13 units on an average. For the A+ group this will be 9 units, for B+, it is 25 units and for the AB+ group, it is 13 units. A large buffer stock will be required when the standard deviation is large.

On the number of replacement donors against each demand

Whenever a patient is advised to bring a replacement donor, it is observed that many a time more than one person is found to get motivated for donating blood. The probability is high to get a compatible donor among them. Even otherwise, a unit of rare group like -negative, may be available from them which will be of much use in dire emergency. This observation reveals the impact of AIDS awareness programme and it is an indirect way of measuring its efficacy.

We have carried out a detailed study on the motivational effect on the voluntary donors who have offered to donate blood to the patient. Most of these are either relatives or friends of the patient and the counselling by the medical officer and his team had a positive effect in securing compatible screened blood.

The patient or his attendant is educated about the importance of donating blood and avoiding professional donors. The following statistical data shows how the motivation has worked in this hospital bank, where it is found that on an average, for every unit of blood that has been requested, there is an offer to donate nearly 1.5 units voluntarily. However, when it comes to actual bleeding, the ratio is found to be only 1 : 1.1 for the following reasons;

  1. Most of the voluntary donors wish to donate blood only to the patient and not for storage and general use. So they simply get their blood group tested and depart from the bank.
  2. Some donors are discarded on medical grounds.

Data has been collected from the records of the blood bank and the exact record made is the number of offers for donating either of the same groups or a different group. The following is the summary statistics of offers for various groups of blood. The number of compatible donors and non compatible donors are shown separately. For each group we have defined an index called Donor Motivational Index (DMI) and has been calculated as the ration of the number of people responded to the actual calls made for donating blood.

Table-4: Summary statistics of motivational effect

Groups Total Donations Offers Compatible Offers-non Compatible Total Offers D.M.I
0 52 60 50 110 1.7742
A 26 24 45 69 2.6538
B 59 50 49 99 1.6780
AB* 7 4 6 10 1.4286

(*includes other rare groups).

From the above table, we observe that the probability of securing a compatible donor is 0.9678 for O+, 0.9231 for A+, 0.8475 for B+ and 0.5714 for AB+ as estimated from the above data. These probabilities are high mainly because most of the voluntary donors will be either siblings or parents of the patient and naturally there will be compatibility.

We define the Donor Motivational Index (DMI) as the ratio of the total offers received at the bank against the actual requirements (donations made). We have computed this index for various groups based on the data available with us. It is evident from this data that the motivational effect is resulting in a good response. This is one way of procuring input of good quality into the blood bank. The non compatible donors have to be motivated further, to come forward and donate blood, because they have any arrived at the hospital and got their blood group. They may alternatively be motivated to make themselves available when needed at their nearest blood bank. This is being done in this hospital and they are advised to inform the nearest Primary health Centre (PHC) about their blood groups and their readiness to donate in case of need. This would have a further motivational effect among the residents of the village/locality itself and helps in eradicating a 'fear' about blood donation.

Unplanned inputs into the bank

The inputs into the blood bank are sometimes related to social factors such as mass blood donations as a mark of celebrating important events like Independence day, republic day, birth and death day celebrations of national leaders etc. On such occasions, large number of voluntary donors come forward and insist on donating blood. Accepting all of them would only increase the existing stock levels of this perishable commodity! This happens quiet regularly and the excess blood has to be either lysed or distributed to other needy hospital. In terms of inventory management, this phenomenon is called "uncertainty in the quantity supplies" leading to higher stock levels than planed/required.

VIP visits and demand for blood

It is common feature that many VIPs and VVIPs will be visiting pilgrim centres like Tirupati and during their visit it is mandatory to send one unit of compatible blood to the visiting guest and also to his wife if she accompanies him. Many of the visits are either unscheduled or have a short notice. In such cases, the medical officer of the blood bank of a Government hospital has to deplete the stock from the bank and meet the demand. Due to the random nature of the time of visits and the number of such visits in a week, the stock levels are bound to show significant change.

An alternative policy can be adopted to meet this type of random demand. Instead of carrying a unit of screened blood, it is advisable to make arrangements for having two or three screened compatible voluntary blood donors (regionally located) who will accompany the VIP so that in case of an emergency, transfusion can be taken up immediately by the accompanying medical team.

Decentralizing blood bank service activities

The observations made so far suggest that the inventory management of blood is best done by properly balancing the supply and the requirement which is currently done. This is something like "act according to the situation". The utility of existing inventory models to determine the optimal stock levels appears to be limited since most of the assumptions made in such models do not hold good. Further, the concept of cost of holding or placing an order are not meaningful since this is a Government run hospital.

In order to minimize the wastage of blood and blood products, it is advisable to set up 'Satellite Blood banks'. This system adopts 'out-reach service approach' which is already proved to be highly successful in the implementation of International Programs like Universal Programme of immunization and Family Planning programme. The infrastructure required for this programme will be as follows.

The Transfusion Service is to be integrated into the 'Primary Health Care' infrastructure and the staff of the Primary Health center may be successfully utilized for this purpose after imparting necessary training in the blood banking technique at the regional level. The blood bank under the teaching hospital will be designated as Central Blood Bank and will do the job of collection, screening and storage of blood units and its products. Depending on the morbidity pattern and demographic profile, satellite blood banks will be established, each of them catering the transfusion needs of population for at least two Primary health centres. Air-conditioned vehicles with cold-chain facility (can be obtained through International voluntary Organizations like Red-Cross or UNICEF) will be used to transport blood units from the centre to the periphery. Region-wide donor-directories will be prepared by the satellite blood banks, which will feed the central blood bank and help to keep the buffer stocks at the optimum level. The satisfied blood donors must be properly utilized to motivate the rest of the population and maximize the donor-potential, half-yearly updating of the donors'-directory is highly essential to keep the track of the donor availability.

In this following section, we discuss the use of simple theoretical model that can be applied without requiring cost information. Since a unit of blood is normally brought into the bank only against a demand (on a replacement basis), the following model appears to be satisfactory for defining an inventory policy.

The base stock policy for stock keeping

One of the policies for controlling the stock is the Base Stock system. According to this, we have a target inventory of R units called the Base Stock. Whenever a demand arises for one unit of blood, it is issued from the base stock R and the stock on hand drops to (R-1). An order is immediately placed for one unit so that the stock on-hand plus on-order is always R.

The ordered unit of blood would be available either immediately or after a lead time. During this time the patient for whom the demand was made is requested to 'bring' a donor of the same group and this donor is called the 'replacement donor'. The time required to secure a replacement donor is a random variable and could be any thing between 0 days (no delay) to a maximum of 4 days. Some times the replacement do not match with the required blood but it has been estimated from the past records that the chance of such a non-matching replacement is not more that 0.05 or 5% of cases. According to the experience at the blood bank covered in this study, the issue of non-matching replacement donor can be ignored for the reason that among the four groups, 0 is as good as a matching replacement due to its universal acceptability. Hence it is reasonable to assume that the ordered group becomes available most of the time.

Inventory systems operated by the base-stock policy have been studied extensively by many authors for the control of spare parts in work-shops and for other slow moving items. We found that the present system in the blood bank can be operated by this policy subject to a few valid assumptions. This policy is also known as R-policy since the base-stock R is the only decision variable.

Inventory models of the above type with variable lead times (time between triggering an order and receiving the order) can be explained by the methods of queuing theory. Johnson and Montgomery4 have discussed such a model with all mathematical details. We now adopt those results to the operation of the blood bank.

The demand for teach the group of blood is assumed to follow Poison distribution with a mean of l units per week for the chosen blood group. On the arrival of demand, the medical officer verifies with the stock and assigns the oldest available blood to the calling patient and immediately places an order for the replacement of one unit. Now the patient's attendant usually comes forward to donate the blood and it will be taken if it is found compatible. The lead time is zero if the blood is replenished by the donor, on arrival but there will be positive lead time when the replacement donor is not available and the patient has to try for securing the donor . The maximum lead time is found to be 4 days with more weight to zero or one day than more than 2 days. This has suggested the use of exponential distribution to describe the lead times. Thus we have the following input information.

The number of demands for blood during a week is a discrete random variable such that the probability of having x or less demands is given by the cumulative Poison distribution:

P(l, x) = S {e-l lx} / x! and the probability that the lead time is less than y days is g(m, y) = 1 - e -y. The average lead time will be 1/m.

Define p=1/m and let P (x, r) denote the cumulative Poisson distribution up to and including x with parameter r. Let bibe the probability of having i units of blood as on-hand inventory. Then it can be shown that

bi = ri {S rk/k!}i!, i = 0, 1,2, ....,R

The average on-hand inventory is:

I = R - {P(R-1, k = r)/ P (R, k = r)}.

The fraction of time the system will be out of stock is given by: g = rR e -r / {R! P(R, r)}

and the service level will then be (1 - g).

Suppose the demand for a particular group of blood occurs at the rate of l = 6 cases per week and the lead time for replacement is 2 days. It means the average lead time is 2/7 weeks. The intensity factor r = 1/m which becomes 1.71. If we prefer to keep a stock of 5 units at the beginning of the week, then the on-hand inventory will be -I = 6 - 1.71(0.976/00.993)= 4.32 or 4 units approximately. The service level will be (1-g) which becomes (1-0.0002) = 99%. This is only an illustration and the working of the model depends on the values of and R. Taking l = 12 for the O+ group, the intensity factor was found to be r = 3.48. For selected values of R, the beginning stock for the week, the average on-hand stock and the service level have been computed and the results are shown below.

Base Stock 6 8 10 12
Avg. Stock 2.2 4.5 6.6 8.5
Service Factor 0.91 01 0.9825 0.9999

It is clear from the above illustration, that the on hand inventory increases with the increase in the beginning stock for the week. This model can be extended to include an optimization process by which we can determine the optimal beginning stock R for the week.

Conclusions

In this study we have examined a case of a hospital attached blood bank and examined its functions regarding blood inventory and management. Though there are many theoretical mathematical models for inventory control, the study has revealed that the principle of act according to the situation' appears to be in use and the service level is quite high as evidenced by the CT ratio. For a more scientific approach to the management of this valuable good, we have suggested a few methods of regulating the inputs into the bank as well as defining a central blood bank that could cater the needs of other local banks/hospitals. We have also suggested a policy for stock-keeping and illustrated the same numerically.

References

  1. Duncan B.I and Norwitz S.H(1973), Opportunity costs and elementary inventory theory in the hospital service, Opl.Res.Qty., Vol(24), pp 27-34.
  2. Andrew. V and herbert F.Spirer, Quantitative analysis for business, Prentice Hall Chap. 15.
  3. Starr M.K. and Miller D.W. (1974), Inventory Control, Theory and Practice, Prentice-Hall, Chap.3,5.
  4. Johnson L.A and D.C. Montgomery (1974), Operations Research in Production Planning and Inventory Control, John Wiley, 68-71.

* Medical Officer, R.O.H.E., S.V.R.R. Government Hospital & S.V. Medical College, Tirupati -517 502
** Department of Statistics, S.V. University, Tirupati- 517 502

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