Regionalization of local blood bank facility becomes interesting issue to discuss recently.\ud
Determining distribution allocation of blood product is a strategic decision-making in the blood supply chain\ud
in order to fulfill demands in both normal and emergency conditions. In this work, we develop a generalized\ud
network optimization model for the blood transportation and allocation model in Makassar City South\ud
Sulawesi Indonesia. Today, there are two main blood bank facilities in the city that operate by government and\ud
local Red Cross organization. Each hospital will connect to the one of the blood bank facility. Each hospital is\ud
to be assigned to a regional blood bank facility which will periodically supply the hospital???s blood demand for\ud
each period. The supply process depends on the maximum capacity of the each regional blood bank facility.\ud
We present algorithms to decide how many bloods banking to set up, where to locate them, how to allocate\ud
the hospital to the banks and how to route the periodic supply operation, so that the total fixed costs and\ud
transportation costs of blood bank facility location are minimum

Hasanuddin University Repository

Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2014 
________________________________________ 
† :Corresponding Author 
 
 
Blood Banks Location Model for Blood Distribution Planning 
in Makassar City 
 
Muhammad Rusman†  
Department of Industrial Engineering 
Hasanuddin University, Makassar, Indonesia 
Tel: (+62) 812-4141-2828, Email: rusman@tiunhas.net 
Amrin Rapi 
Makassar Industrial Engineering Academy (ATIM) 
Jalan Sunu No. 220, Makassar, Indonesia 
Tel: (+62) 813-4253-2055, Email: amrin_rapi@yahoo.com 
 
Abstract. Regionalization of local blood bank facility becomes interesting issue to discuss recently. 
Determining distribution allocation of blood product is a strategic decision-making in the blood supply chain 
in order to fulfill demands in both normal and emergency conditions. In this work, we develop a generalized 
network optimization model for the blood transportation and allocation model in Makassar City South 
Sulawesi Indonesia. Today, there are two main blood bank facilities in the city that operate by government and 
local Red Cross organization. Each hospital will connect to the one of the blood bank facility. Each hospital is 
to be assigned to a regional blood bank facility which will periodically supply the hospital’s blood demand for 
each period. The supply process depends on the maximum capacity of the each regional blood bank facility. 
We present algorithms to decide how many bloods banking to set up, where to locate them, how to allocate 
the hospital to the banks and how to route the periodic supply operation, so that the total fixed costs and 
transportation costs of blood bank facility location are minimum. 
 
Keywords: blood banks, facility location 
 
 
1. INTRODUCTION 
 
The location and availability of blood banks, which 
will serve some hospitals, is a strategic decision in health 
care system. In addition to well-known importance of the 
subject, it is a fact that grave shortages of blood occur in 
over 80% of the countries in the world, one of the reason is 
inadequate funding of the local transfusion service 
(Thomas, 2007), that may result from an inefficient 
allocation of sources in generally. Some cost-structure 
analyses included distribution and delivery costs of blood 
as some significant variables. Besides, accessibility to a 
blood bank is an important component of an organ 
transplant program. Transplantation requires more blood 
then most other surgeries, for instance, 100 units of blood 
for a liver transplant patient (Lindsey and McGlynn, 1988). 
Moreover, blood banks facilities also serve as important 
education centers for medical staff from universities and 
hospitals (Amin et al. 2004). 
The location of blood bank facilities is an important 
issue in any application area for both industry and 
academia. Poor location decision will impact to such as 
increased expenses, capital costs and degraded customer 
service (Daskin and Dean, 2004). In health care system, the 
facility location decisions, which are strategic not an 
everyday decision (Ozcan, 2005), are more critical due to 
that any anomaly may lead to mortality and morbidity 
(Daskin and Dean, 2004).  
In this paper, we primarily focus on blood banks 
location model for bloods distribution planning in 
Makassar City, South Sulawesi, Indonesia. Today, there are 
17 hospitals in Makassar city and two regional blood center 
(RBC). 
 
2. LITERATURE REVIEW 
 
This section discusses the research related to the 
distribution problem of blood banks including decision 
models. Blood banks can be organized in multiple manners, 
ranging between the two extremes of centralization and 
decentralization. In the book Operations Research and 
Health Care: Handbook on Methods and Applications, 
Kim and Moon 
 
Pierskalla (2004) presents an interesting overview paper, 
which is probably one of the most widely read papers in the 
area of blood supply chain management. Pierskalla’s paper 
describes strategic models for assigning donor areas and 
transfusion centers to community blood centers, 
determining the number of community blood centers in the 
region, locating these centers and coordinating supply and 
demand. The models also consider tactical and operational 
issues in collecting blood, inventory management, blood 
allocation to hospitals, blood delivery and cross matching. 
In the literature, the research on blood supply chain 
focuses on the complexity of effectiveness and efficiency 
of blood location-allocation. Or and Pierskalla (1979) 
conducted research  a regional blood management 
problem where hospitals were applied by a regional blood 
bank in their region, and developed a location-allocation 
model that minimizes the sum of the transportation costs 
and the system costs. Sapountzis (1984) introduced an 
integer-programming model to allocate blood from a 
Regional blood center (RBC) to hospitals. Brodheim and 
Prastacos (1979) showed a prototype for RBC and the 
hospital blood banks in order to optimize blood availability 
and utilization. The objective his model is to minimize the 
total expected number of units of expired blood. Jacobs et 
al. (1996) developed an integer-programming model for 
blood collection and distribution system. Their research 
presented an analysis of alternative locations and service 
areas of American Red Cross blood facilities. Şahin et al. 
(2007) presented a blood bank location model and 
developed several location-allocation models to solve the 
problems of regionalization based on a hierarchical 
structure; however, the facilities fixed costs of the RBC 
were not considered. Recent research by Çetin and Sarul 
(2009) presented a mathematical programming model for 
location of blood banks among hospitals or clinics. Their 
objectives aim to minimize the total fixed cost of LBBs and 
the total traveled distance between the blood bank and 
hospitals. 
One of the most-popular models for public facility 
location problem is the P-median model. The P-median 
problem, originally proposed by Hakimi (1964) is that of 
locating P facilities to minimize the sum of the demand 
weighted total distance between each demand node and the 
nearest facility. Daskin and Dean (2004) proposed the 
location model of P facilities to minimize the coverage 
distance subjected to a requirement that all demands are 
covered. 
Hriber and Daskin (1997) proposed a greedy heuristic 
for the P-median problem. The heuristics restrict the size of 
the state space of a dynamic programming algorithm. 
Correa et al. (2004) described the application of the 
capacitated P-median model to a real-world problem and 
proposed a genetic algorithm to solve the P-median model. 
Church (1990) proposed the regionally constrained P-
median problem (RCPMP), which can be described in 
terms of P-median problem with two additional sets of 
constraints, one to ensure a minimum number of facilities 
for each region and the other to prevent more than a 
specified maximum. Nagurney (2011) described the supply 
chain network topology for a regionalized blood bank in 
American Red Cross (ARC) the ARC is the major supplier 
of blood products to hospitals and medical centers 
satisfying over 45% of the demand for blood components 
in US (Figure 1). 
Gerrard and Church (1995) built upon the RCPMP by 
allowing regional constraints to be violated and formulating 
a model that sought to minimize both the total weighted 
distance and the number of regional constraints that were 
violated. Their model allows for identification of non-
inferior combinations of system accessibility and regional 
constraint enforcement. 
However, the maximum traveled distance between 
supply node and demand node are not considered in P-
median model. 
 
3. MODEL FORMULATION 
 
Through this paper, we concerned with blood 
distribution problem in Makassar city that consist of two 
blood banks known as PMI (Indonesian Red Cross) and 
UTDP (Regional Blood Center) will supply to 17 hospitals. 
We proposed two of the model such as single allocation 
model and double allocation model. Number of blood bags 
can be collected during 2013 as shown in Table 1. Table 2 
shows the blood supply and demand from each hospital. 
 
Figure 1: Supply Chain Network Topology for 
regionalized blood banks  
Kim and Moon 
 
 
Table 1. Number of blood bags can be collected  
No Blood Banks quantity 
1 PMI 29078 
2 UTDP 11844 
 
Table 2. Blood supply distance and demand 
No Hospitals Demand (bag) 
Distance (km) 
PMI UTDP 
1 Jala Ammari 672 4.7 14.4 
2 Akademis Jauri 1551 3.2 12.4 
3 Pelamonia 2591 2.3 12.2 
4 Mitra Husada 300 1.3 12.4 
5 Stella Maris 3238 2.4 13.2 
6 Hikmah 1011 1.8 13.3 
7 Dadi 1015 0.1 13.1 
8 Labuang Baji 2768 2 15.1 
9 Bhayangkara 3833 3.9 15.2 
10 Haji 1736 4.6 15.5 
11 Grestelina 2180 3.8 9.9 
12 Islam Faisal 2534 2.4 12.6 
13 Ibnu Sina 2421 4.2 8.1 
14 Awal Bros 2864 4.6 9.5 
15 W.Sudirohusodo 17210 10.4 2.5 
16 Pendidikan Unhas 1310 10.1 2.2 
17 Daya 2216 15 3.1 
 
We develop the model using the following notation: 
 
Subscripts: 
i = index of blood banks 
j = index of hospitals 
Sets: 
I = set of all blood banks 
J = set of hospitals 
Parameters : 
fi = fixed cost blood banks i 
hj = demand of hospital j 
cij = delivery cost from blood banks i to hospital j 
yij = the fraction of hospitals demand satisfied by the 
blood banks 
ui = capacity of blood banks i 
 
Decision variable: 
1, if hospital open as blood distribution
0, if hospital close for blood distributioni
x = ⎧⎨⎩  
 
3.1 Single Allocation Model  
Single allocation assumed that the demand of blood 
from the hospital blood can be supplied only from single 
blood banks.  
The objective function 
Minimize   
fixi + hicij yi
i∈I
∑
j∈J
∑
i∈I
∑                       (1) 
Subject to: 
yij =1, ∀j ∈ J
i∈I
∑                        (2) 
yij ≤ x j, ∀i ∈ I, ∀j ∈ J                (3) 
hiyij ≤ ui, ∀i ∈ I
j∈J
∑                     (4) 
x j ∈ 0,1{ }, ∀i ∈ I                      (5) 
yij ≥ 0, ∀i ∈ I, ∀j ∈ J                 (6)  
 
The objective function (1) minimizes the total cost of 
blood banks fixed cost, delivery cost. Constraint (2) states 
that each hospital must be assigned to exactly one blood 
bank. Constraint (3) guarantee that a hospital select a blood 
bank only from among those are chosen. Constraint (4) 
states that blood supply for each blood bank must not 
exceed the blood capacity of each blood bank. Constraint 
(5) and (6) are the standard integrality constraints. 
  
3.1 Double Allocation Model 
Double allocation assumed that the demand of blood 
from the hospital blood can be supplied from both existing 
blood banks. 
  
The objective function 
Minimize 
 
fixi + cij yij
i∈I
∑
j∈J
∑
i∈I
∑                        (7) 
Subject to: 
yij = hi, ∀j ∈ J
j∈J
∑                       (8) 
yij ≤ uj x j, ∀j ∈ J
i∈I
∑                     (9) 
yij ≥ 0, ∀i ∈ I, ∀j ∈ J                (10) 
 
The objective function (7) minimizes the total cost of 
blood banks fixed cost, delivery cost. Constraint (8) 
guarantee that a hospital select a blood bank only from 
Kim and Moon 
 
among those are chosen. Constraint (9) states that blood 
supply for each blood bank must not exceed the blood 
capacity of each blood bank. Constraint (10) is the standard 
integrality constraints. 
 
4. COMPUTATIONAL RESULTS 
 
In this section, computational experiments were 
performed for two allocation model from data set as 
summarized in Table 1 and 2. Computational experiments 
are presented to evaluate the behavior of total cost form 
two allocation model and to compare the optimal 
distribution planning from two existing blood banks to 17 
hospitals.  The experiments are performed for two 
allocation models, single and double allocation model. The 
computational experiments are solved by ILOG CPLEX 
12.2 optimization software using a computer with 2.66GHz 
core 2 duo processor and 2 GB of RAM. 
 
 
Every node denoting the hospitals is generated from 
actual location and distances to blood banks are generated 
from shortest distance road to hospitals using Google maps 
application. Then, we get the unit delivery cost by 
multiplying the unit 1.0 with the distance between blood 
banks to hospitals. 
Figure 2 shows the relationship between the total cost 
and the proposed capacity combination of blood banks. We 
proposed 9 combinations for blood banks capacity, among 
them are 1(45000, 500), 2(40000,10000), 3(35000,15000), 
4(30000,20000), 5(25000,25000), 6(20000,30000), 
7(15000,35000), 8(10000,40000), and 9(5000,45000). The 
total costs, when assigning the capacity of A larger than B, 
decrease gradually when capacity A decrease and B 
increase gradually. The optimal solution for both allocation 
models found in the capacity combination number 4 which 
is represent as A (PMI) with the proposed capacity 30000 
and B (UTDP) with the proposed capacity 20000. The total 
costs increase gradually when capacity A decrease and B 
increase gradually. 
In Figure 3 and Figure 4 illustrated the distribution of 
blood product for single allocation model and double 
allocation model respectively. More detail results for 
distribution allocation from blood banks to each hospital 
for single and double allocation are summarized in Table 3. 
 
4. CONCLUSION 
 
The single allocation model and double allocation 
model that we proposed in this paper is a capacitated 
facility location problem to accommodate blood demand 
fulfillment in Makassar city. Both models are integer 
programming model. The objective is to minimize the total 
cost of blood banks fixed cost and delivery cost. The 
proposed mathematical model can solve for optimal 
distribution planning from existing blood banks to 17 
hospitals. The solution can be used to define which 
hospitals should be supplied by existing blood banks with 
minimum delivery cost. Some direction for future research 
 
Figure 2: Total cost comparison between single allocation 
and double allocation 
A 
B1
2
3 
4 5 
7
6
8
9
10
11 12
13 14 
15
16
17
Figure 4: The optimal blood distribution for double 
allocation model 
A 
B1
2
3
45
7
6
8
9
10
11 12
13 14 
15
16
17
Figure 3: The optimal blood distribution for single 
allocation model
Kim and Moon 
 
can be done by modifying this model to help analyzing the 
optimal distribution planning when the number of blood 
banks and hospitals increased. Considering applying center 
of gravity method of continues location models in order to 
find the optimal number blood banks for the city. 
 
Table 3. Allocation distribution for blood bank capacity 
combination 4(30000,20000) 
No Hospitals 
Single 
Allocation 
Double 
Allocation 
PMI 
(A) 
UTDP 
(B) 
PMI 
(A) 
UTDP 
(B) 
1 Jala Ammari 672 - 672 - 
2 Akademis Jauri 1551 - 1551 - 
3 Pelamonia 2591 - 2591 - 
4 Mitra Husada - 300 300 - 
5 Stella Maris 3238 - 3238 - 
6 Hikmah 1011 - 1011 - 
7 Dadi 1015 - 1015 - 
8 Labuang Baji 2768 - 2768 - 
9 Bhayangkara 3833 - 3833 - 
10 Haji 1736 - 1736 - 
11 Grestelina 2180 - 2180 - 
12 Islam Faisal 2534 - 2534 - 
13 Ibnu Sina 2421 - 2421 - 
14 Awal Bros 2864 - 2864 - 
15 W.S. Husodo - 17210 736 16474 
16 Pend. Unhas 1310  - 1310 
17 Daya - 2216 - 2216 
 
 
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Blood Bank Location Model for Blood Distribution Planning in Makassar City

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Blood Bank Location Model for Blood Distribution Planning in Makassar City

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