EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
Vol 2, No. 1, 2009 (112-124)
ISSN 1307-5543 – www.ejpam.com
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A Blood Bank Location Model: A Multiobjective Approach
Eyüp ÇETİN*, Latife Sinem SARUL
Department of Quantitative Methods, School of Business Administration
Istanbul University, Istanbul 34320, Turkey
Office phone: + 90 212 4737070
Fax: +90 212 590 88 88
Abstract This effort derived a mathematical programming model, which is a hybrid
from set covering model of discrete location approaches and center of gravity method
of continuous location models, for location of blood banks among hospitals or clinics,
rather than blood bank layout in health care institutions. It is initially unknown the
number of blood banks will be located within capacity, their geographical locations
and their covering area. The solution of the model enlightens the initial darkness in a
multiobjective view. The objectives, which are handled via binary nonlinear goal
programming, are minimizitation of total fixed cost of location blood banks, total
traveled distance between the blood banks and hospitals and an inequality index as a
fairness mechanism for the distances. A hypothetical numerical example is solved
using MS Excel as a powerful spreadsheet tool. The recipe, which is an application of
medical operations research, may be a useful tool for health care policy makers.
Key words: Set covering model; Center of gravity method; Binary nonlinear goal
programming; Spreadsheet modeling, Medical operations research.
E. Çetin, L. Sarul / Eur. J. Pure Appl. Math, 2 (2009) 113
The location of facilities is an important issue in any application area for both
industry and academia. Any poor location decision will result in undesired
pathological situations such as increased expenses, capital costs and degraded
customer service . In health care, the facility location decisions, which are strategic
not an everyday decision , are more critical due to that any anomaly may lead to
mortality and morbidity .
The availability and location of blood banks, which will serve some hospitals or
clinics, is also a strategic decision in health care delivery 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 , that may result from inefficient allocation of sources in
general. In investigating blood transfusion cost, one important element of variability
can be attributed to geographic location of the blood supply source . Some cost-
structure analyses (eg, ) included distribution and delivery costs of blood as some
major 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 . Moreover,
blood banks may also serve as important education centers for medical staff from
hospitals and clinics .
It may be said that the literature is rich in general facility location and health care
location modeling. Some highlights of the literature are as follows. Hale and Moberg
 present a broad review of facility location and location science research. Recently,
Daskin and Schilling  gave the summaries of general location models. Daskin and
Dean  reviewed some selected location models in both general and health care
focus. Some authors studied the location analysis from stochastic standpoint. For
instance, Chen et al.  developed a model for stochastic facility location modeling.
Verter and Lapierre  developed a binary programming model for location of
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