Administrative Reports
Management Policies for a Regional Blood Bank M. A. COHENAND 1%’.P. PIERSKALLA From the Department of Decision Sciences, The Wliarton School, University of Pennsylvania, Philadelphin, Pennsylvnnia nnd the Department of Industrial Engineering and Managetnei~t Sciences, Northruetlern University, Evanston, Illinois
This paper considers management strategies for the administration of a regional blood bank. The techniques of management science and mathematical inventory theory are applied to construct a model for the system, identify policy areas, and formulate management objectives. Two simulation models and data collected from both a regional and single hospital blood bank are used in the analysis. The results presented examine the interactions and saving associated with following optimal ordering, crossmatch, and issuing policies. Since each of these policies have an important effect on the number of shortages and outdates, they therefore influence optimal blood bank management. In addition, the question of centralized versus decentralized control is examined.
blood in its area of jurisdiction iii a manner which ensiires that all demands are met. I n addition to this primary goal, the central bank is also interested in minimizing outdates and emergency shipments, minimizing operating costs, :ind maintaining a high level of quality for issued units. Many of these objectives are also shared b y the member hospital blood banks. These goals are somewhat conflicting ant1 thus ultimately trade-olfs inlist be made. 1t is just such trade-offs among competing goals, that form the basis of the analysis i n this paper. Thus, we shall examine the implications of various management control policies for the regional bank based 011 tlie indicators commonly used to measure the blood system’s performance. Many of [he results presented i n this paper apply equally well to a single blood bank. I n general, for a relatively fixed supply of donors, the inventory system of whole blood units may be controlled i n three different ways, i.e., by controlling the ortlei.ing policy, the issuing policy, m c l the crossmatch policy. Although each of these policies interact with one another in 011taining the best performance, i t is interesting to see that general policy statements can be made i n each case reg:irdless of the policies followed in the other cases. We begin with a brief descril>tion of tliese policy controls.
THEPROBLEMS of blood shortages antl wastage through outdating pose a major challenge to blood bank managers. While i t is apparent that the need for more donated blood is great, it must be recognized that maximum efficiency in the management of existing units is also needed. This paper considers the latter aspect of the problem by applying the principles of management science to whole blood inventory administration. Our primary interest is with the situation of a central (regional) blood bank serving a number of hospitals. T h e major responsibility of the central blood bank is to administer the collection and distribution of Received for publication November 7. 1973; accepted -luly, 10, 1974. This research was partially supported by PHSHS00786-01 from the National Center for Health Services Research antl Development. ~
58 Transfusion Jam-Feb. 1975
Volume 15 Number 1
Volume 15 Number 1
MANAGEMENT POLICIES
Ordering Policy This policy area is concerned with the manner in which both donated and emergency units are obtained. Of specific interest in this paper is the number of units to order at the beginning of each decision period (defined by order-up-to inventory level, S). Questions of donor campaigns, donor lists, blood plans, and centralized versus decentralized ordering also fall under this heading. These latter topics will be reported on in a subsequent paper since they form the basis of a significant study in their own right. Issir ing Policies
Here we are concerned with the choice (when a choice is possible) of which units to issue from the uncrossmatched inventory to satisfy a particular demand. I n most cases, this decision focuses on the age of the unit to be issued. T w o well-known issuing policies are FIFO (First In-First Out) and L l F O (Last In-First Out). These terms have come to mean the policy of issuing the oldest available unit or the youngest available unit, respectively. Issuing policies co~iltlalso include the question of centralized versus decentralized control over issuing. For example, the oldest available unit may be a unit which has been crossmatched at a member bank for six days and the central bank may not know i t is available for reassignment or may not have the authority to reassign it. In this case, the central bank may be forced to issue a unit which is not the oldest available; however, we will still call this policy FIFO if the central bank issues the oldest available unit over which i t has control. Crossrnntch Policies . I n a regional blood bank, it is possible to consider controlling the length of time an issued and iintransfrised unit can remain assigned to a particular hospital's inventory and thus he inaccessible to demands at other locations. Although this sojourn time
59
of a unit at a hospital does not mean the unit is always on crossmatch at the hospital. this time period will be referred to as the crossmatch period and will be denoted by D days. In a local hospital, where there can be personal contact between the blood bank and the physician, such control of a fixed period of D days may not be necessary. I n fact, many hospitals release the units for other patients after a crossmatch period of 24 hours or less. At a further level of complication in the regional bank, one should consider using different crossmatch periotfs Dl, D,, etc. for different blood types and different size member hospitals. Changes in operating policy will c1e;irly have an impact on the total performance of the regional blood banking system. I n view of the regional bank's objectives concerning shortages, outdates, and costs, we will measure such performance changes with the lo1low i ng indicators : 1. T h e number of units tr;insfuserl
2.
3. 4.
5.
(or, alternatively, the percentage of demands met). T h e number of shortages (Le., emergency requests and postponed surgery). T h e number and percentage of oil tdates. T h e dollar operating cost for the blood bank (by attributing prices to shortages and outdates). T h e level of assigned (crossmatched) and unassigned (uncrossmatched) inventory versus daily average demands and tr;insfiisions.
T h e level of the indicators can be expected to vary with tliil'erent policy choices and combinations of policy choices. T h e approach that will be taken liere is to tlenionstrate the response of shortages, outtlates, transfusions, inventory levels, and costs to il variety of issuing, crossmatch, ;ind ordering policy combinations. T h i s response
COHEN AND PIERSKALLA TAHLE I . Blood Flow D o i n for North Suburbait Blood Ceiiter (~Sepirirrbei22 to h’orierrther 30, 1972)
237 2.272
of Pinson15 allows €or prescriptive analysis by measuring the effect of alternative ordering, issuing and crossmatch release policies. T h i s model forms the basis for many of the resul’ts soon to be described.,
2,384
Data
Number of units present 01- ctilei-ing the system 2,775 Nllnlt,cl o f o u t t l a t c h
Nuinbet of units transfused Number of ttemantls tint resulting in a transfusion
Transfusion Jan-Feb. 1975
will be determined with the aid of two simulation models. T h e first model is a regional simulation motlel and wils constructed to examine issuing a n t 1 crossmatch policy combinations. T h e second model is more extensive iIn(1 general in ternis of (latit, policy inpiits, and performance indicator outputs. Ordering policy iintl crossinatcli policy intei-actions itre examined in the second model. A detailed description of both models tilay he ol,t;iinetl by writing to tlie authors. Work on inotlcling blootl banks antl examining ni;inagement policies has been going on for some time. Other conipiiter simulation models which deal with order policies have been tlescribetl by Elston antl Pickrel4 itntl Jei1nings.s Jennings’ model was the first to differelltiate between t i n assigned inventory and assignet1 inventory. A simuliition niotlel by Kahinowitzlh exami net1 tlori ble crossma tch i ng a n t l ,\enn i ngs9 extended his previous motlel to analyze various transshipment policics for a regional bank. Kodilyl used Jennings’ original niodcl to analyzc the iml>ilct of lrozeii blood. Hurlburt and Jones7 used a statistical procedure to quantify the costs of excessive crossmatch release times. I n two recent papers, Yahnke et ~ 1 . 1 7 .18 examined certain aspects of a regional bank ant1 attempted to quantify the contribution of crossmatch policy to system shortages antl o~ltdiltes. A mathematical model wils constructed for the regional bank which measures tlie contribution of each member Iiospital to totitl system oiitdates.17 T h e simulation model
Data for this project and much of tlie information o n the structure of the regional bank model was made available with the cooperation of tlie North Suburban Blood Center of Gleriview, Illinois. North Suburban is a regional blood bank serving the needs of member hospitals in tlie North Shore area of Chicago with ;t volume in the fall of 1972 of about 1,000 units per month. Blood enters tliis system in the form of donations a t all locations or in the form of emergency shipments to the central bank. Donated blood is, of course, fresh, antl emergency shipments can be of any age. Blood is issued to satisfy demands a t the member hospitals. Approximately 50 per cent of all demands at the member hospitals do not result in a transfusion. T h e crossmatched units issued 1 0 meet tliese demands are returned to the unassigned inventory from which they may be reissued to different member hospitals. Tlie raw data consisted of records on each individual blood unit in tlie system. These records contained informatiori oil hlood type, date drawn, date transfused (or outdated) and the various dates a n d locations ot iuterirn shipments associated witli the unit before its final disposition. Data for all blootl types atid for ;dl member hospitals were collected for a tlireemonth period. T h e raw data represent a limited picture of tliis particular blood bank’s activities. Tlie rules used in issuing and crossmatching of the bloocl were not retrievable from the data. Moreover, an exact representation of the demands for blood made o n tlie system was not directly available. It was possible to infer information on both demand and supply from the available data. T h e resulting estimated supply and demand data were used in the simulation models of tlie blood bank inventory system. I n this way, the conclusions of the simulation iuialysis are relevant to the general class of regional IJIOOCI banks and not just to a particular bank. A total of 3,152 units was considered. T h i s number represents the total number of units which entered the blood bank system from September 1 to November 30, 1972. Since the
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61
MANAGEMENT POLICIES
As predicted by the theory of Pierskalla and Koach,l4 FIFO dominates LIFO in tlie case where D = 0. I n the simulation, the blood bank using FIFO was able to meet all demands with 0 outdates and 0 shortages while LIFO results in 477 outdates for the sample period. As 1) increases from zero, the possibility of having crossmatched units returned is admitted. Under FIFO, more outdates are generated and as D becomes sufficiently large (D 7) the system experiences shortages. I t is interesting to note tlie sensitivity of the system to small changes in D. An increase in D from one to two days results (under FIFO) in an approximate 300 per cent increase in the number of outdates. An increase in D from two to three days results in a 200 per cent increase. T h e rate of increase is such that by tlie time D lias grown from I to 7, outdates have grown from about 16 to 331. T h e number of units available in tlie unassigned inventory decreases as I) increases and tlie assigned iuventory increases. At D = 7, tlie system begins to experience shortages, since supply is not adequate to meet demands and outdate requirements over the three-month time interval. Simulation runs with values of D greater than seven were made. However, such values no longer correspond to a realistic centralized control blood bank situation and so the associated results will not he presented.
blood bank does not keep records of its total inventory, it was necessary to wait 21 days (when all units which had entered previous to September 1 had passed through the system) to accumulate a reading o n tlie initial inventory of tlie system. Those units which had already been transfused prior to September 22 were then eliminated from consideration. Daily demand and the breakdown between ultimate transfusion and return for eacli unit demanded were recorded. T a b l e I gives some further summary statistics of tlie data.
>
Results /,swing and Crossmntch Policies T h e LIFO and FIFO issuing policies were considered in conjunction with crossmatcli sojourn periods, l), of 0 tlirougli 7 days at eacli member hospital. I) = 0 corresponds to a n inventory system where all issued units are transfused. D = 7 corresponds to a blood bank where those crossmatched units which are not transfused remain in the assigned inventory for a period of one week. Thus, 16 issuingcrossmatcli policy combinations were considered. T a b l e 2 contains data which illustrate the results lor the various policies. Figure 1 is a graph of cumulated outdates versus D for both FIFO and LIFO. T h e following observations can be made from all of these results.
TABLE 2. Blood Invenfory Policy Evaltralion Runs for Issuing and Crossmalch Policies. D
0
2
I
3
4
5
I
6
FIFO Issuing
Transfused Outdated Unassigned inventory Assigned inventory Total Shortage
2,272 0 503 0
2,775 0
2.272 16.3 445.1 41.0 2,775 0
2,272 58.7 364.3 80.0 2,775 0
2,212 117.0 212 114.0 2,115 0
2,272 113.1 161.9 168.0 2,775 0
2,212 202.1 121.9 179.0 2.715 0
2,212 212.1 35.9 195 2,175 0
2.242.4 330.8 0 201.8 2,175 12.5
2,267.8 428.6 0 18.6 2,175 10.9
2,266.2 403.6 0 105.2 2,175 14.8
2,257.2 372.2 0 145.6 2,715 41.6
2,254.0 366.3 0 154.7 2,115 46.3
2,241.0 351.5 0 116.5 2,775 74.6
2234.4 338.8 0 201.8 2,115 90.6
LIFO Issuing
Transfused Outdated Unassigned inventory Assigned inventory Total Shortage
2,272 477 26 0 2.775 0
2,272 449.3 12.7 41 2,775 0
*The figures in the table represent blood flow averaged over a number of sirnulation runs (September 22 to November 30).
62
COHEN AND PIERSKALLA
Transfusion Jan.-Feb. 1975
Outdates (in units of whole blood for three months of operation)
Cross-match Release Period D (in days) FIG. 1. Outdates and crossinarch release period for FIFO and LIFO issiiing.
Intuitively, a L I F O policy seems inappropriate for whole blood since a t all times tlie system experiences a great number of outdates and often a large number of shortages. However, as D grows, a number of interesting phenomena develop. Outdates decrease from 477 to 338.8 uni.ts and tlie niimber of units transfused decreases from 2,272 to 2,234.4 units. I n addition, shortages increase from 0 to 90.6 units and tlie inventory levels cllange in a manner analogous to the FIFO issuing situation. I t is
possible to generate examples with large D where LIFO dominates FIFO i n terms of tlie number of outdates. For our simulated blood bank, this switch occurs (with the given data) a t a value of D which must be ruled out a s being excessive. Indeed, D = 7 is uiireasonable for both LIFO and FIFO, ; t i i d a l l y central bank with sucli little control over tlie crossmatch time will face excessive shortages and outdates. Katz a n d Morsel' described a regional blood bank system wit11 ;tn eff'ecrive 1) of 21 days.
MANAGEMENT POLICIES
Volume 15 Numher 1
63
TARI.E 3. Blood Invenfory Policy Ei~ciltio/ionHiins /or Crossnaolch Heleose Poia~nelerD Drown from n Truncated A'ormnl Distribution with Mean of Four Days*
Variance of D
0
1
2
3
4
6
8
2.272
2.272 I83 154
2,272 223 91 189 2,775 0
2,272 254 37 212 2.775 0
2,243 0 2222 2.775 71
2,173 350 0 252 2,775 21 I
2,245 368 0 I62 2,775 68
2,230 366 0 179 2,775
2,198 369
2,153 378
FIFO Issuing
Transfused Ou ttlal etl Uiiassigned inventory Assigned inventory Total Shortage
2,775
2,775
2,272 195 136 I72 2,775
0
0
0
2,257 378 0 140 2,775 43
225.5 378 0 142 2,775 49
2,258 367
165 170 I68
I66
310
LIFO Issuing
-. I ransfused
Outdated Unassigned inventory Assigned inventory Total Shortage
* The figures i n the table represent simulatecl
0
150 2.775 39
100
0
0
208 2,775 157
244 2,775 2.55
hlood flow from September 22 to November 30.
A central bank draws blood and sliips units to the member liospitals and little or no interhospital shipments occur. From the point of view of the central bank, no recycling occurs and hence D is essentially 21 days. These authors11 note that by changing from a pure FIFO 1)olicy to an issuing I>olicy closer to LIFO, they decrease outdates. They did not give data o n the change in shortages or emergency s h i p ments. T h e i r results are thus entirely consistent and, indeed, expected from our simiilation results. I t is apparent that FIFO dominates LIFO over a range of D of zero through seven in terms of all of the performance indicators: outdates, shortages, and number of units transfused. We may conclude, therefore, that a combination of FIFO with a minimal value of D is most desirable. As D is reduced, savings of 75 per cent to 200 per cent can be realized in outdating and shortages. A central bank probably cannot reduce D to zero, one, or two as is often the case a t a member hospital. If tlie central Ixink cannot obtain a maximal crossmatch release time D, of four or five days, then the system will be incurring excessive outdates and a high demand for emergency shipments because of tlie large increase in shortages. Furthermore, i f tlie donor supply is tight, tlie large amoitnt of additional outdates will put severe strains on the donor system, will lead to a large amoinit of emergency
sliipnients, and will came postponement of elective surgery.
Cen 1 ralized versus Decentralized Ilegional Control Centralized control is defined to mean that the crossmatcli period D is a constant which is determined and set by the central bank administrator. Decentralization is introdiiced into the model in two ways: a) by letting D be large, as described by Katz and Morse,ll or b) by treating D as a random variable. We have already discussed tlie first way and have shown that lack of central control and large D leads to excessive shortages and outdates. Tlie reasoning behind the second concept of decentralizatioil is iis I'ollows. In a decentralized blood Imnk network, tlie central bank administrator sends uiiits to each local blood bank and the local blood bank ;idministrator decides when to release the crossmatched units which were not needed. The crossmatcli release time D a t the 10c;il bank looks like a random variable to the central bank administrator since the central bank has very little control over D a n d D may vary from unii to unit a n d one local bank to another. A prolnbility distribution for D is specified and the mean of the distribution is considered to lie a broad policy guideline for releasing the unassigned blood kick to the central bank. Tlie variance is considered to be ii measure of
COHEN A N D PIERSKALLA
64
Transfusion Jan.-Feh. 1975
t 400
__
0 w
-
LIFO
-
0
w
Variance of Cross-match Release Period D (with a mean of D
= 4 days)
FIG.2. Outdates and crossmatch release period variance for FIFO and LIFO issuing.
decentralization, i.e., the lower the variance tlie more the effect of the central administrator’s influence. T h e consequences of decentralization were examined by running the model with a number of distributions for D. T h e results are given in T a b l e 3 and Figure 2. These results illuminate the costs of decentralization rather clearly. System performance deteriorates as the variability in D increases, when a FIFO issuing policy is followed. As the variance of D increases from iero to eiglit, tlie number of outdates go from a low of 165 at zero to 310 at the variance equal to six. Furthermore, for variances of six and eiglit. tlie ritimbei of units transfused drops as significant sliortages begin to appear. T h e system is rather insensitive to variability i n D under LIFO; however, tlie bystem performance for LIFO is uni-
formly batl (both outdates and shortages are extremely high). T h e gains achieved by using ii FIFO issuing policy can be wiped out merely by tlie variations i n crossmatcli release time. T h i s point is clearly seen by tlie fact that ;I decentralized blood banking system wid1 a D wliicli lias ii mean of four and a variance of six is just as batl as a ceritralizctl system with a D wliich lias ;I mean of seven : t i i d ;I viiriaiice 01 zero (see T a b l e 2). Ordering Policy
I n studying optimal ordering policies, the issuing policy was restricted to FIFO ;tnd the crossmatch policy to 1) = two, five, and seven. 1Jpon specification of a value lor S. the daily order-up-to quantity, the iriventory model is completely described. Tlic optimal order q t i a i i -
MANAGEMENT POLICIES
Volume 15 Number 1
65
100
Shortage
+
70
Outdate Cost I Day
60
($1 50 40
30
20 D = 2
10
0
0
1
I
1
I
1
20
22
24
26
28
30
32
34
36
38
40
Order quantity S (units of whole blood) FIG. 3. Average shortage/outdate costs and order quantity for FIFO issuing $55 unit shortage cost, $25 unit outdate cost, arid a 100-day simulation period.
tity, S*, is defined to be that value of S which yields a minimum daily cost. T h e costs chosen were $25 for ;in outdated unit and 5.55 for an emergency (shortage) unit. These costs are arbitrary but were chosen because studies have estimated the cost of processing one unit of whole blood at about $25 and a unit of emergency blood at $55. T h e $55 cost could be a n emergency drawing a n d / o r shipping cost or the cost of a frozen unit of packed red cells. In the study by Pinson,ls other costs were considered and it was shown that the magnitude iintl shape of tlie cost curves antl tlie magnitude of tlie order c1ii;intity S* were not greatly iiifluerrced by reasonable changes in costs. l a b l e 4 antl Figure 3 presents tlie results of the simulatioir runs wliicli were obtained I,y iising tlem;ind data
for a single common blood type from Evanston Hospital, a member of the North Suburban regional bank. Tlie following two key observations can be made from these results: 1) Costs ;ire far more sensitive to crossmatclr policy D than they are to the order policy S. (This is seen by the fact that the mean cost/tlay increases from $7.25 to $36.55 to $54.55 as D goes from two to five to seven clays.); and 2) Tlie cost minimizing value, S*, is fairly insensitive to the value of D even though the overall cost level increases significiintly witli D. T h i s is seen by the relatively flat (near S*) curves of Figure 3. Tlie implicatioirs of these two observations are ;IS follows: 1) Tlie effect on shortages xiid outtl;ites of the ordering policy is minimal for s’s in the neighborliood o l S* when compared witli
COHEN AND PIERSKALLA
TAHI.E 4. System Performance at Optimal Order Point s* Crossmarch Release Period D
2
5
7
32
29 854.55
S * , optimal order-up-to
qiianLity COSI /tl;r).
ill
0 l l l l l ; l l C s :I1
Sh0ll;lgc ;It
Trallsfllsctl
30
s+
87.25
Sf
29
$36.55 144
0
1
1
493
493
493
s* ;it s*
\,ci.:ige 11I Imsi giietl iiivcntnry at S * (Ixforc ordering) 23.99 /\vci.;ige ;issigned iiiveiitory ;it s* 18.77
21 6
/\
24.87
21.58
39.42
59.29
eitlier the issuing or crossmatdl policies. T h e insensitivity of the S's in the neigltborliood of S f (tlie optimal S) is very important because ii central bank cannot always :icliieve S* each day. Indeed, large drawings of blood tlirougli donor plans o f t e n disrupts tlie ccntral blood k i n k policy of achieving S* on ;I daily basis: ; i n t ~ 2) T I I C optim;ll ortler quantity is essentially insensitive to the value of D. T h i s also is a very important conclusion in tlie sense that tlie blood Ixink can set S* ;ind then concentrate inventory management control on reducing D knowing that S* will n o t cliange significantly.
Conclusions Thesc observations suggest the following strategy for ;I regional blood bank. If a unit is crossmatched iund not reported transfused within a short time (D equals two or three clays), further intormation on the st;itus of the demand for which the unit was issued shoulcl be oht;iinetl. I I the clemancl has disappeared, the unit slioultl Be inxle available for possible reassigttment either at the same bank or anotlier hospital blootl bank. In this manner, the crossmatch release time, D, shoulcl be kept a s low as possible. As long as D can he maintainctl helow seven days, the FIFO issuing policy should be followed. If D e x c e e d s seven, LIFO will be somewhat Iietter than FJFO but both policies will h a w excessive outdates ant1 shortages. T h e optimal beginning inventory level
Transfusion Jan.-Feb. 1975
after ordering, S*, can be computed €or a model where D is zero and all issued units are transfused. As the sensitivity analysis of this study shows, the use of this S* will be ii very good approximation to tlie actual optimal policy for the real situation where D is greater than zero. Research is currently under way for simple ways to compute S x as a function of the demand, supply, and organizational characteristics of the particular blood bank. T h e overall approach outlined in this paper is contingent on a rc;ison;rhly efficient i n forni;itioti system antl ; i n administrative structure which admits some degree of centralized control. Recently, computer technology has lieen appiiecl to the task 0 1 building an efficient blood Iiarik in formation systeni.2. 3. 5 . 6 . 10. 12. l.? T h e challenge for implementation of the proposed nian;igement strategy is primarily ;idministrativc. T h e need exists since the costs of even seemingly minor deviations from this strategy can lie quite high i i t terms of blood s h o r ~ages and out& tes. Acknowledgment We arc indebted to the North Suburban Blood Centcr of Glenview, Illinois and Evanston Hospital of Evanston, Illinois for coopcratinn i n obtaining data for this study.
References I.
2.
3.
4.
5.
Rotlily, S. E.: Determining the Place of Frozen Blood in Future Blood Ranking Systems. Technical Report No. 79, Operations Research Centcr, M.I.T., Jaiiiiary 1973. Hove, J . R . , antl D. K . McKay: Computer approach to hospital blootl bank inventory control. Trailsfasion 9: 143, 1969. Catassi, C. A,, and E. L. Peterson: T h e blood inventory control system-helping blood bank inanagement through computerized inventory cotitrol. Transfusion 7: 60. 1967. Elston, K. C., and J. C. Pickrcl: Guides to inventory levels for a hospital I~lnntl bank determined by electronic computer simulation. Transfusion 5: 46.5, 1965. Frankfurter. G . M., A. E. Jelmcrt, C. C. Pegels, J . P. Seagle, antl E. L. Wallace: A regional computer-based blood inventory informaI ioii system. Transfusioir 10: 203, 1970.
Volume 1 5 Number 1
MANAGEMENT POLICIES
6. Hirsch. R. L., F. E. Brodheim, and F. E. Ginsberg: A computer-based hlootl inventory and information system for hospital blood banks as part of a regional blood-management program. Transfusion 10: 194, 1970. 7. Hurlhurt, E. L., and A. R. Joiies: Blood bank inventory control. Transfusion 4: 126. 1964. 8. Jeiinings, J. B.: An analysis of hospital blood I u i i k ~ r h o l eblood inventory control policies. Traiisfusioii 8: 33.5, 1968. 9. -. . Blood bank inveiicory control. Man. Science 19: 637. 1973. 10. Katz. A. J., R. S. Holtlt. and E. E. Morse: Electronic data processing as a n aid to statewitlc hlootl m;iiiagemciic. Trailsfitsinti 12: 267. 1972. I I . ___ , antl E. E. Morse: Distribution of fresher blootl i i i a statewide blood program. Traiisfusioii 13: 324, 1973. 12. Masouredis, S. P.. D. K. Roscth. K. T. Sielloh, J. I’erine, I. D. Nehama. T. M. Hursi. A. A. Kimm. C . A. Reckcr. E. A. Strct. S. J. Krenz, aiici R. H. Aster: Development of ail automatetl I h o t l inveiltory and informarioii system for a regional traiisfitsioii service. Trailsfusion 10: 182, 1970. 13. O’Hara, M.. antl A. M. J ~ J S ~ ~ ~Regional SOII: ;I iitom:i t ctl (la ta-proccssi iig systcni f o r I,lootl Ii:iiiks. 7‘raiisl‘usion 10: 215, 1970.
67
14. Pierskalla, W. P., and C. D. Roach: Optimal issuing policies for perishable inventory.
Man. Science 18: 603, 1972. 15. Pinson, S. D.: A s t u d y of tlecisioii policies i i i hlootl bank inventory control: A computer simulati~napproach. M.S. thesis, Northwesrern University, August 1973. 16. R;ibiriowitz, M.: Hospital blood banking: An evaluation of inventory control policies. City University of New York, Mt. Sinai School of Medicine. September 1970. t i . Yahnke, 1). P., A . A. Rimni. C. J. Mundt, K . H. Aster. antl T. M. Hurst: Analysis antl optiiniz;itioii of a regioiial blood h i i k tlistrihution process. I. iiitrocluction a i i t l descript i v c aiialysis. Transfusioii 12: 1 I I , 1972. 18. A. A. Rimm, C;. (;. Makowski, aiitl K. H. Aster: Aiialysis :iiitl optimization of a regional 1,lootl hailk tlistributioii process. 11. tlcrivatioii and use of a method for evaluatiiig hospital niaiiegeniciit prncetliires. TIXIISfusiorr 13: 156. 1973. Slorris A . Coheii. Lkpartmciit of Decision SciThe \\’harton School, Uiiivcrsity of Peiinsylvaiiia. Phil;itlclphia. Peiinsylvaiiia 19174.
CIICCS ,
\Villiain P. Pierskalla, Department of Industrial Eiiaincering i i i i t l Maiiagonent Scieiices. Northwestern Univcvsity. F.vanstoii. Illiirois 60201,
Announcements International Society on T h r o m b o s i s and Haemostasis T h e 5th Congress of the International Society on Tlirombosis and Haeniostwis will bc lieid in Paris from July 21-26, 1975, a t tlie Faculti: d e Droit, 92 rue d’Ass;is. Professor J . 1’. Soulier is l’resitlent ant1 I’rofessor 1 . 1’. Caen is Vice-l’resident a n d Secretary General. T h e main topics of t h e plenary sessions are ;IS follows: platelets, vessel w;ill interaction, I~looclcoagulation, thrombosis. Simultaneous sessions a i i d symposia ;ire sclietluletl every day in tlie moriiing ;inti afternoon. Tlie participants wisliing to present ;I paper iire invited to send 11s ;iI,stracts oii tlie proposed topics: platelets-vessel wall. co;tgulation, tliroml~osis (clinical ;ind ilierapeniic aspects), fibrinolysis, immiinoli;iemost;isis, artificial s u r f x e s , ;intl experimetit;il tlirombosis. U n p u l ~ l i s h e dworks will be presentecl, whether in simultatieous sessions or ;is posters. Speaking time in simult;ineous sessions will be limited to teii minutes. A cliscussioii 0 1 o n e h o u r with the authors of posters will be Iield every ;ifternoon. Tlie posters will bc changed every day. T h e abstracts should not exceed 200 words. Deadline for tlie registration of papers a n d for submission of abstracts is h,l;ircli I , 1975. Englislr will be the otIici;il I;tngii:ige of the Congress. All scientific correspondence reg;trdiitg the Congress sliodd be’sent to prof. J . 1’. C;len. Service Central d’Hi:matologie, HOpital Lariboisitxe, 2 rue Ambroise Pare, 75475 I’iiris Cetlcx 10. All ;itlministr;itive corresporiclence sliould be sent to Congres-Services, I riic Jules-Lefebvre, 75009 Paris.
Management Policies for a Regional Blood Bank M. A. COHENAND 1%’.P. PIERSKALLA From the Department of Decision Sciences, The Wliarton School, University of Pennsylvania, Philadelphin, Pennsylvnnia nnd the Department of Industrial Engineering and Managetnei~t Sciences, Northruetlern University, Evanston, Illinois
This paper considers management strategies for the administration of a regional blood bank. The techniques of management science and mathematical inventory theory are applied to construct a model for the system, identify policy areas, and formulate management objectives. Two simulation models and data collected from both a regional and single hospital blood bank are used in the analysis. The results presented examine the interactions and saving associated with following optimal ordering, crossmatch, and issuing policies. Since each of these policies have an important effect on the number of shortages and outdates, they therefore influence optimal blood bank management. In addition, the question of centralized versus decentralized control is examined.
blood in its area of jurisdiction iii a manner which ensiires that all demands are met. I n addition to this primary goal, the central bank is also interested in minimizing outdates and emergency shipments, minimizing operating costs, :ind maintaining a high level of quality for issued units. Many of these objectives are also shared b y the member hospital blood banks. These goals are somewhat conflicting ant1 thus ultimately trade-olfs inlist be made. 1t is just such trade-offs among competing goals, that form the basis of the analysis i n this paper. Thus, we shall examine the implications of various management control policies for the regional bank based 011 tlie indicators commonly used to measure the blood system’s performance. Many of [he results presented i n this paper apply equally well to a single blood bank. I n general, for a relatively fixed supply of donors, the inventory system of whole blood units may be controlled i n three different ways, i.e., by controlling the ortlei.ing policy, the issuing policy, m c l the crossmatch policy. Although each of these policies interact with one another in 011taining the best performance, i t is interesting to see that general policy statements can be made i n each case reg:irdless of the policies followed in the other cases. We begin with a brief descril>tion of tliese policy controls.
THEPROBLEMS of blood shortages antl wastage through outdating pose a major challenge to blood bank managers. While i t is apparent that the need for more donated blood is great, it must be recognized that maximum efficiency in the management of existing units is also needed. This paper considers the latter aspect of the problem by applying the principles of management science to whole blood inventory administration. Our primary interest is with the situation of a central (regional) blood bank serving a number of hospitals. T h e major responsibility of the central blood bank is to administer the collection and distribution of Received for publication November 7. 1973; accepted -luly, 10, 1974. This research was partially supported by PHSHS00786-01 from the National Center for Health Services Research antl Development. ~
58 Transfusion Jam-Feb. 1975
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Volume 15 Number 1
MANAGEMENT POLICIES
Ordering Policy This policy area is concerned with the manner in which both donated and emergency units are obtained. Of specific interest in this paper is the number of units to order at the beginning of each decision period (defined by order-up-to inventory level, S). Questions of donor campaigns, donor lists, blood plans, and centralized versus decentralized ordering also fall under this heading. These latter topics will be reported on in a subsequent paper since they form the basis of a significant study in their own right. Issir ing Policies
Here we are concerned with the choice (when a choice is possible) of which units to issue from the uncrossmatched inventory to satisfy a particular demand. I n most cases, this decision focuses on the age of the unit to be issued. T w o well-known issuing policies are FIFO (First In-First Out) and L l F O (Last In-First Out). These terms have come to mean the policy of issuing the oldest available unit or the youngest available unit, respectively. Issuing policies co~iltlalso include the question of centralized versus decentralized control over issuing. For example, the oldest available unit may be a unit which has been crossmatched at a member bank for six days and the central bank may not know i t is available for reassignment or may not have the authority to reassign it. In this case, the central bank may be forced to issue a unit which is not the oldest available; however, we will still call this policy FIFO if the central bank issues the oldest available unit over which i t has control. Crossrnntch Policies . I n a regional blood bank, it is possible to consider controlling the length of time an issued and iintransfrised unit can remain assigned to a particular hospital's inventory and thus he inaccessible to demands at other locations. Although this sojourn time
59
of a unit at a hospital does not mean the unit is always on crossmatch at the hospital. this time period will be referred to as the crossmatch period and will be denoted by D days. In a local hospital, where there can be personal contact between the blood bank and the physician, such control of a fixed period of D days may not be necessary. I n fact, many hospitals release the units for other patients after a crossmatch period of 24 hours or less. At a further level of complication in the regional bank, one should consider using different crossmatch periotfs Dl, D,, etc. for different blood types and different size member hospitals. Changes in operating policy will c1e;irly have an impact on the total performance of the regional blood banking system. I n view of the regional bank's objectives concerning shortages, outdates, and costs, we will measure such performance changes with the lo1low i ng indicators : 1. T h e number of units tr;insfuserl
2.
3. 4.
5.
(or, alternatively, the percentage of demands met). T h e number of shortages (Le., emergency requests and postponed surgery). T h e number and percentage of oil tdates. T h e dollar operating cost for the blood bank (by attributing prices to shortages and outdates). T h e level of assigned (crossmatched) and unassigned (uncrossmatched) inventory versus daily average demands and tr;insfiisions.
T h e level of the indicators can be expected to vary with tliil'erent policy choices and combinations of policy choices. T h e approach that will be taken liere is to tlenionstrate the response of shortages, outtlates, transfusions, inventory levels, and costs to il variety of issuing, crossmatch, ;ind ordering policy combinations. T h i s response
COHEN AND PIERSKALLA TAHLE I . Blood Flow D o i n for North Suburbait Blood Ceiiter (~Sepirirrbei22 to h’orierrther 30, 1972)
237 2.272
of Pinson15 allows €or prescriptive analysis by measuring the effect of alternative ordering, issuing and crossmatch release policies. T h i s model forms the basis for many of the resul’ts soon to be described.,
2,384
Data
Number of units present 01- ctilei-ing the system 2,775 Nllnlt,cl o f o u t t l a t c h
Nuinbet of units transfused Number of ttemantls tint resulting in a transfusion
Transfusion Jan-Feb. 1975
will be determined with the aid of two simulation models. T h e first model is a regional simulation motlel and wils constructed to examine issuing a n t 1 crossmatch policy combinations. T h e second model is more extensive iIn(1 general in ternis of (latit, policy inpiits, and performance indicator outputs. Ordering policy iintl crossinatcli policy intei-actions itre examined in the second model. A detailed description of both models tilay he ol,t;iinetl by writing to tlie authors. Work on inotlcling blootl banks antl examining ni;inagement policies has been going on for some time. Other conipiiter simulation models which deal with order policies have been tlescribetl by Elston antl Pickrel4 itntl Jei1nings.s Jennings’ model was the first to differelltiate between t i n assigned inventory and assignet1 inventory. A simuliition niotlel by Kahinowitzlh exami net1 tlori ble crossma tch i ng a n t l ,\enn i ngs9 extended his previous motlel to analyze various transshipment policics for a regional bank. Kodilyl used Jennings’ original niodcl to analyzc the iml>ilct of lrozeii blood. Hurlburt and Jones7 used a statistical procedure to quantify the costs of excessive crossmatch release times. I n two recent papers, Yahnke et ~ 1 . 1 7 .18 examined certain aspects of a regional bank ant1 attempted to quantify the contribution of crossmatch policy to system shortages antl o~ltdiltes. A mathematical model wils constructed for the regional bank which measures tlie contribution of each member Iiospital to totitl system oiitdates.17 T h e simulation model
Data for this project and much of tlie information o n the structure of the regional bank model was made available with the cooperation of tlie North Suburban Blood Center of Gleriview, Illinois. North Suburban is a regional blood bank serving the needs of member hospitals in tlie North Shore area of Chicago with ;t volume in the fall of 1972 of about 1,000 units per month. Blood enters tliis system in the form of donations a t all locations or in the form of emergency shipments to the central bank. Donated blood is, of course, fresh, antl emergency shipments can be of any age. Blood is issued to satisfy demands a t the member hospitals. Approximately 50 per cent of all demands at the member hospitals do not result in a transfusion. T h e crossmatched units issued 1 0 meet tliese demands are returned to the unassigned inventory from which they may be reissued to different member hospitals. Tlie raw data consisted of records on each individual blood unit in tlie system. These records contained informatiori oil hlood type, date drawn, date transfused (or outdated) and the various dates a n d locations ot iuterirn shipments associated witli the unit before its final disposition. Data for all blootl types atid for ;dl member hospitals were collected for a tlireemonth period. T h e raw data represent a limited picture of tliis particular blood bank’s activities. Tlie rules used in issuing and crossmatching of the bloocl were not retrievable from the data. Moreover, an exact representation of the demands for blood made o n tlie system was not directly available. It was possible to infer information on both demand and supply from the available data. T h e resulting estimated supply and demand data were used in the simulation models of tlie blood bank inventory system. I n this way, the conclusions of the simulation iuialysis are relevant to the general class of regional IJIOOCI banks and not just to a particular bank. A total of 3,152 units was considered. T h i s number represents the total number of units which entered the blood bank system from September 1 to November 30, 1972. Since the
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61
MANAGEMENT POLICIES
As predicted by the theory of Pierskalla and Koach,l4 FIFO dominates LIFO in tlie case where D = 0. I n the simulation, the blood bank using FIFO was able to meet all demands with 0 outdates and 0 shortages while LIFO results in 477 outdates for the sample period. As 1) increases from zero, the possibility of having crossmatched units returned is admitted. Under FIFO, more outdates are generated and as D becomes sufficiently large (D 7) the system experiences shortages. I t is interesting to note tlie sensitivity of the system to small changes in D. An increase in D from one to two days results (under FIFO) in an approximate 300 per cent increase in the number of outdates. An increase in D from two to three days results in a 200 per cent increase. T h e rate of increase is such that by tlie time D lias grown from I to 7, outdates have grown from about 16 to 331. T h e number of units available in tlie unassigned inventory decreases as I) increases and tlie assigned iuventory increases. At D = 7, tlie system begins to experience shortages, since supply is not adequate to meet demands and outdate requirements over the three-month time interval. Simulation runs with values of D greater than seven were made. However, such values no longer correspond to a realistic centralized control blood bank situation and so the associated results will not he presented.
blood bank does not keep records of its total inventory, it was necessary to wait 21 days (when all units which had entered previous to September 1 had passed through the system) to accumulate a reading o n tlie initial inventory of tlie system. Those units which had already been transfused prior to September 22 were then eliminated from consideration. Daily demand and the breakdown between ultimate transfusion and return for eacli unit demanded were recorded. T a b l e I gives some further summary statistics of tlie data.
>
Results /,swing and Crossmntch Policies T h e LIFO and FIFO issuing policies were considered in conjunction with crossmatcli sojourn periods, l), of 0 tlirougli 7 days at eacli member hospital. I) = 0 corresponds to a n inventory system where all issued units are transfused. D = 7 corresponds to a blood bank where those crossmatched units which are not transfused remain in the assigned inventory for a period of one week. Thus, 16 issuingcrossmatcli policy combinations were considered. T a b l e 2 contains data which illustrate the results lor the various policies. Figure 1 is a graph of cumulated outdates versus D for both FIFO and LIFO. T h e following observations can be made from all of these results.
TABLE 2. Blood Invenfory Policy Evaltralion Runs for Issuing and Crossmalch Policies. D
0
2
I
3
4
5
I
6
FIFO Issuing
Transfused Outdated Unassigned inventory Assigned inventory Total Shortage
2,272 0 503 0
2,775 0
2.272 16.3 445.1 41.0 2,775 0
2,272 58.7 364.3 80.0 2,775 0
2,212 117.0 212 114.0 2,115 0
2,272 113.1 161.9 168.0 2,775 0
2,212 202.1 121.9 179.0 2.715 0
2,212 212.1 35.9 195 2,175 0
2.242.4 330.8 0 201.8 2,175 12.5
2,267.8 428.6 0 18.6 2,175 10.9
2,266.2 403.6 0 105.2 2,175 14.8
2,257.2 372.2 0 145.6 2,715 41.6
2,254.0 366.3 0 154.7 2,115 46.3
2,241.0 351.5 0 116.5 2,775 74.6
2234.4 338.8 0 201.8 2,115 90.6
LIFO Issuing
Transfused Outdated Unassigned inventory Assigned inventory Total Shortage
2,272 477 26 0 2.775 0
2,272 449.3 12.7 41 2,775 0
*The figures in the table represent blood flow averaged over a number of sirnulation runs (September 22 to November 30).
62
COHEN AND PIERSKALLA
Transfusion Jan.-Feb. 1975
Outdates (in units of whole blood for three months of operation)
Cross-match Release Period D (in days) FIG. 1. Outdates and crossinarch release period for FIFO and LIFO issiiing.
Intuitively, a L I F O policy seems inappropriate for whole blood since a t all times tlie system experiences a great number of outdates and often a large number of shortages. However, as D grows, a number of interesting phenomena develop. Outdates decrease from 477 to 338.8 uni.ts and tlie niimber of units transfused decreases from 2,272 to 2,234.4 units. I n addition, shortages increase from 0 to 90.6 units and tlie inventory levels cllange in a manner analogous to the FIFO issuing situation. I t is
possible to generate examples with large D where LIFO dominates FIFO i n terms of tlie number of outdates. For our simulated blood bank, this switch occurs (with the given data) a t a value of D which must be ruled out a s being excessive. Indeed, D = 7 is uiireasonable for both LIFO and FIFO, ; t i i d a l l y central bank with sucli little control over tlie crossmatch time will face excessive shortages and outdates. Katz a n d Morsel' described a regional blood bank system wit11 ;tn eff'ecrive 1) of 21 days.
MANAGEMENT POLICIES
Volume 15 Numher 1
63
TARI.E 3. Blood Invenfory Policy Ei~ciltio/ionHiins /or Crossnaolch Heleose Poia~nelerD Drown from n Truncated A'ormnl Distribution with Mean of Four Days*
Variance of D
0
1
2
3
4
6
8
2.272
2.272 I83 154
2,272 223 91 189 2,775 0
2,272 254 37 212 2.775 0
2,243 0 2222 2.775 71
2,173 350 0 252 2,775 21 I
2,245 368 0 I62 2,775 68
2,230 366 0 179 2,775
2,198 369
2,153 378
FIFO Issuing
Transfused Ou ttlal etl Uiiassigned inventory Assigned inventory Total Shortage
2,775
2,775
2,272 195 136 I72 2,775
0
0
0
2,257 378 0 140 2,775 43
225.5 378 0 142 2,775 49
2,258 367
165 170 I68
I66
310
LIFO Issuing
-. I ransfused
Outdated Unassigned inventory Assigned inventory Total Shortage
* The figures i n the table represent simulatecl
0
150 2.775 39
100
0
0
208 2,775 157
244 2,775 2.55
hlood flow from September 22 to November 30.
A central bank draws blood and sliips units to the member liospitals and little or no interhospital shipments occur. From the point of view of the central bank, no recycling occurs and hence D is essentially 21 days. These authors11 note that by changing from a pure FIFO 1)olicy to an issuing I>olicy closer to LIFO, they decrease outdates. They did not give data o n the change in shortages or emergency s h i p ments. T h e i r results are thus entirely consistent and, indeed, expected from our simiilation results. I t is apparent that FIFO dominates LIFO over a range of D of zero through seven in terms of all of the performance indicators: outdates, shortages, and number of units transfused. We may conclude, therefore, that a combination of FIFO with a minimal value of D is most desirable. As D is reduced, savings of 75 per cent to 200 per cent can be realized in outdating and shortages. A central bank probably cannot reduce D to zero, one, or two as is often the case a t a member hospital. If tlie central Ixink cannot obtain a maximal crossmatch release time D, of four or five days, then the system will be incurring excessive outdates and a high demand for emergency shipments because of tlie large increase in shortages. Furthermore, i f tlie donor supply is tight, tlie large amoitnt of additional outdates will put severe strains on the donor system, will lead to a large amoinit of emergency
sliipnients, and will came postponement of elective surgery.
Cen 1 ralized versus Decentralized Ilegional Control Centralized control is defined to mean that the crossmatcli period D is a constant which is determined and set by the central bank administrator. Decentralization is introdiiced into the model in two ways: a) by letting D be large, as described by Katz and Morse,ll or b) by treating D as a random variable. We have already discussed tlie first way and have shown that lack of central control and large D leads to excessive shortages and outdates. Tlie reasoning behind the second concept of decentralizatioil is iis I'ollows. In a decentralized blood Imnk network, tlie central bank administrator sends uiiits to each local blood bank and the local blood bank ;idministrator decides when to release the crossmatched units which were not needed. The crossmatcli release time D a t the 10c;il bank looks like a random variable to the central bank administrator since the central bank has very little control over D a n d D may vary from unii to unit a n d one local bank to another. A prolnbility distribution for D is specified and the mean of the distribution is considered to lie a broad policy guideline for releasing the unassigned blood kick to the central bank. Tlie variance is considered to be ii measure of
COHEN A N D PIERSKALLA
64
Transfusion Jan.-Feh. 1975
t 400
__
0 w
-
LIFO
-
0
w
Variance of Cross-match Release Period D (with a mean of D
= 4 days)
FIG.2. Outdates and crossmatch release period variance for FIFO and LIFO issuing.
decentralization, i.e., the lower the variance tlie more the effect of the central administrator’s influence. T h e consequences of decentralization were examined by running the model with a number of distributions for D. T h e results are given in T a b l e 3 and Figure 2. These results illuminate the costs of decentralization rather clearly. System performance deteriorates as the variability in D increases, when a FIFO issuing policy is followed. As the variance of D increases from iero to eiglit, tlie number of outdates go from a low of 165 at zero to 310 at the variance equal to six. Furthermore, for variances of six and eiglit. tlie ritimbei of units transfused drops as significant sliortages begin to appear. T h e system is rather insensitive to variability i n D under LIFO; however, tlie bystem performance for LIFO is uni-
formly batl (both outdates and shortages are extremely high). T h e gains achieved by using ii FIFO issuing policy can be wiped out merely by tlie variations i n crossmatcli release time. T h i s point is clearly seen by tlie fact that ;I decentralized blood banking system wid1 a D wliicli lias ii mean of four and a variance of six is just as batl as a ceritralizctl system with a D wliich lias ;I mean of seven : t i i d ;I viiriaiice 01 zero (see T a b l e 2). Ordering Policy
I n studying optimal ordering policies, the issuing policy was restricted to FIFO ;tnd the crossmatch policy to 1) = two, five, and seven. 1Jpon specification of a value lor S. the daily order-up-to quantity, the iriventory model is completely described. Tlic optimal order q t i a i i -
MANAGEMENT POLICIES
Volume 15 Number 1
65
100
Shortage
+
70
Outdate Cost I Day
60
($1 50 40
30
20 D = 2
10
0
0
1
I
1
I
1
20
22
24
26
28
30
32
34
36
38
40
Order quantity S (units of whole blood) FIG. 3. Average shortage/outdate costs and order quantity for FIFO issuing $55 unit shortage cost, $25 unit outdate cost, arid a 100-day simulation period.
tity, S*, is defined to be that value of S which yields a minimum daily cost. T h e costs chosen were $25 for ;in outdated unit and 5.55 for an emergency (shortage) unit. These costs are arbitrary but were chosen because studies have estimated the cost of processing one unit of whole blood at about $25 and a unit of emergency blood at $55. T h e $55 cost could be a n emergency drawing a n d / o r shipping cost or the cost of a frozen unit of packed red cells. In the study by Pinson,ls other costs were considered and it was shown that the magnitude iintl shape of tlie cost curves antl tlie magnitude of tlie order c1ii;intity S* were not greatly iiifluerrced by reasonable changes in costs. l a b l e 4 antl Figure 3 presents tlie results of the simulatioir runs wliicli were obtained I,y iising tlem;ind data
for a single common blood type from Evanston Hospital, a member of the North Suburban regional bank. Tlie following two key observations can be made from these results: 1) Costs ;ire far more sensitive to crossmatclr policy D than they are to the order policy S. (This is seen by the fact that the mean cost/tlay increases from $7.25 to $36.55 to $54.55 as D goes from two to five to seven clays.); and 2) Tlie cost minimizing value, S*, is fairly insensitive to the value of D even though the overall cost level increases significiintly witli D. T h i s is seen by the relatively flat (near S*) curves of Figure 3. Tlie implicatioirs of these two observations are ;IS follows: 1) Tlie effect on shortages xiid outtl;ites of the ordering policy is minimal for s’s in the neighborliood o l S* when compared witli
COHEN AND PIERSKALLA
TAHI.E 4. System Performance at Optimal Order Point s* Crossmarch Release Period D
2
5
7
32
29 854.55
S * , optimal order-up-to
qiianLity COSI /tl;r).
ill
0 l l l l l ; l l C s :I1
Sh0ll;lgc ;It
Trallsfllsctl
30
s+
87.25
Sf
29
$36.55 144
0
1
1
493
493
493
s* ;it s*
\,ci.:ige 11I Imsi giietl iiivcntnry at S * (Ixforc ordering) 23.99 /\vci.;ige ;issigned iiiveiitory ;it s* 18.77
21 6
/\
24.87
21.58
39.42
59.29
eitlier the issuing or crossmatdl policies. T h e insensitivity of the S's in the neigltborliood of S f (tlie optimal S) is very important because ii central bank cannot always :icliieve S* each day. Indeed, large drawings of blood tlirougli donor plans o f t e n disrupts tlie ccntral blood k i n k policy of achieving S* on ;I daily basis: ; i n t ~ 2) T I I C optim;ll ortler quantity is essentially insensitive to the value of D. T h i s also is a very important conclusion in tlie sense that tlie blood Ixink can set S* ;ind then concentrate inventory management control on reducing D knowing that S* will n o t cliange significantly.
Conclusions Thesc observations suggest the following strategy for ;I regional blood bank. If a unit is crossmatched iund not reported transfused within a short time (D equals two or three clays), further intormation on the st;itus of the demand for which the unit was issued shoulcl be oht;iinetl. I I the clemancl has disappeared, the unit slioultl Be inxle available for possible reassigttment either at the same bank or anotlier hospital blootl bank. In this manner, the crossmatch release time, D, shoulcl be kept a s low as possible. As long as D can he maintainctl helow seven days, the FIFO issuing policy should be followed. If D e x c e e d s seven, LIFO will be somewhat Iietter than FJFO but both policies will h a w excessive outdates ant1 shortages. T h e optimal beginning inventory level
Transfusion Jan.-Feb. 1975
after ordering, S*, can be computed €or a model where D is zero and all issued units are transfused. As the sensitivity analysis of this study shows, the use of this S* will be ii very good approximation to tlie actual optimal policy for the real situation where D is greater than zero. Research is currently under way for simple ways to compute S x as a function of the demand, supply, and organizational characteristics of the particular blood bank. T h e overall approach outlined in this paper is contingent on a rc;ison;rhly efficient i n forni;itioti system antl ; i n administrative structure which admits some degree of centralized control. Recently, computer technology has lieen appiiecl to the task 0 1 building an efficient blood Iiarik in formation systeni.2. 3. 5 . 6 . 10. 12. l.? T h e challenge for implementation of the proposed nian;igement strategy is primarily ;idministrativc. T h e need exists since the costs of even seemingly minor deviations from this strategy can lie quite high i i t terms of blood s h o r ~ages and out& tes. Acknowledgment We arc indebted to the North Suburban Blood Centcr of Glenview, Illinois and Evanston Hospital of Evanston, Illinois for coopcratinn i n obtaining data for this study.
References I.
2.
3.
4.
5.
Rotlily, S. E.: Determining the Place of Frozen Blood in Future Blood Ranking Systems. Technical Report No. 79, Operations Research Centcr, M.I.T., Jaiiiiary 1973. Hove, J . R . , antl D. K . McKay: Computer approach to hospital blootl bank inventory control. Trailsfasion 9: 143, 1969. Catassi, C. A,, and E. L. Peterson: T h e blood inventory control system-helping blood bank inanagement through computerized inventory cotitrol. Transfusion 7: 60. 1967. Elston, K. C., and J. C. Pickrcl: Guides to inventory levels for a hospital I~lnntl bank determined by electronic computer simulation. Transfusion 5: 46.5, 1965. Frankfurter. G . M., A. E. Jelmcrt, C. C. Pegels, J . P. Seagle, antl E. L. Wallace: A regional computer-based blood inventory informaI ioii system. Transfusioir 10: 203, 1970.
Volume 1 5 Number 1
MANAGEMENT POLICIES
6. Hirsch. R. L., F. E. Brodheim, and F. E. Ginsberg: A computer-based hlootl inventory and information system for hospital blood banks as part of a regional blood-management program. Transfusion 10: 194, 1970. 7. Hurlhurt, E. L., and A. R. Joiies: Blood bank inventory control. Transfusion 4: 126. 1964. 8. Jeiinings, J. B.: An analysis of hospital blood I u i i k ~ r h o l eblood inventory control policies. Traiisfusioii 8: 33.5, 1968. 9. -. . Blood bank inveiicory control. Man. Science 19: 637. 1973. 10. Katz. A. J., R. S. Holtlt. and E. E. Morse: Electronic data processing as a n aid to statewitlc hlootl m;iiiagemciic. Trailsfitsinti 12: 267. 1972. I I . ___ , antl E. E. Morse: Distribution of fresher blootl i i i a statewide blood program. Traiisfusioii 13: 324, 1973. 12. Masouredis, S. P.. D. K. Roscth. K. T. Sielloh, J. I’erine, I. D. Nehama. T. M. Hursi. A. A. Kimm. C . A. Reckcr. E. A. Strct. S. J. Krenz, aiici R. H. Aster: Development of ail automatetl I h o t l inveiltory and informarioii system for a regional traiisfitsioii service. Trailsfusion 10: 182, 1970. 13. O’Hara, M.. antl A. M. J ~ J S ~ ~ ~Regional SOII: ;I iitom:i t ctl (la ta-proccssi iig systcni f o r I,lootl Ii:iiiks. 7‘raiisl‘usion 10: 215, 1970.
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14. Pierskalla, W. P., and C. D. Roach: Optimal issuing policies for perishable inventory.
Man. Science 18: 603, 1972. 15. Pinson, S. D.: A s t u d y of tlecisioii policies i i i hlootl bank inventory control: A computer simulati~napproach. M.S. thesis, Northwesrern University, August 1973. 16. R;ibiriowitz, M.: Hospital blood banking: An evaluation of inventory control policies. City University of New York, Mt. Sinai School of Medicine. September 1970. t i . Yahnke, 1). P., A . A. Rimni. C. J. Mundt, K . H. Aster. antl T. M. Hurst: Analysis antl optiiniz;itioii of a regioiial blood h i i k tlistrihution process. I. iiitrocluction a i i t l descript i v c aiialysis. Transfusioii 12: 1 I I , 1972. 18. A. A. Rimm, C;. (;. Makowski, aiitl K. H. Aster: Aiialysis :iiitl optimization of a regional 1,lootl hailk tlistributioii process. 11. tlcrivatioii and use of a method for evaluatiiig hospital niaiiegeniciit prncetliires. TIXIISfusiorr 13: 156. 1973. Slorris A . Coheii. Lkpartmciit of Decision SciThe \\’harton School, Uiiivcrsity of Peiinsylvaiiia. Phil;itlclphia. Peiinsylvaiiia 19174.
CIICCS ,
\Villiain P. Pierskalla, Department of Industrial Eiiaincering i i i i t l Maiiagonent Scieiices. Northwestern Univcvsity. F.vanstoii. Illiirois 60201,
Announcements International Society on T h r o m b o s i s and Haemostasis T h e 5th Congress of the International Society on Tlirombosis and Haeniostwis will bc lieid in Paris from July 21-26, 1975, a t tlie Faculti: d e Droit, 92 rue d’Ass;is. Professor J . 1’. Soulier is l’resitlent ant1 I’rofessor 1 . 1’. Caen is Vice-l’resident a n d Secretary General. T h e main topics of t h e plenary sessions are ;IS follows: platelets, vessel w;ill interaction, I~looclcoagulation, thrombosis. Simultaneous sessions a i i d symposia ;ire sclietluletl every day in tlie moriiing ;inti afternoon. Tlie participants wisliing to present ;I paper iire invited to send 11s ;iI,stracts oii tlie proposed topics: platelets-vessel wall. co;tgulation, tliroml~osis (clinical ;ind ilierapeniic aspects), fibrinolysis, immiinoli;iemost;isis, artificial s u r f x e s , ;intl experimetit;il tlirombosis. U n p u l ~ l i s h e dworks will be presentecl, whether in simultatieous sessions or ;is posters. Speaking time in simult;ineous sessions will be limited to teii minutes. A cliscussioii 0 1 o n e h o u r with the authors of posters will be Iield every ;ifternoon. Tlie posters will bc changed every day. T h e abstracts should not exceed 200 words. Deadline for tlie registration of papers a n d for submission of abstracts is h,l;ircli I , 1975. Englislr will be the otIici;il I;tngii:ige of the Congress. All scientific correspondence reg;trdiitg the Congress sliodd be’sent to prof. J . 1’. C;len. Service Central d’Hi:matologie, HOpital Lariboisitxe, 2 rue Ambroise Pare, 75475 I’iiris Cetlcx 10. All ;itlministr;itive corresporiclence sliould be sent to Congres-Services, I riic Jules-Lefebvre, 75009 Paris.
