International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249 – 8958, Volume-8 Issue-6, August 2019
4166
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number F9337088619/2019©BEIESP
DOI: 10.35940/ijeat.F9337.088619
Application of Linear Programming for Profit
Maximization of the Bank and the Investor
Amit Kumar Jain, Ramakant Bhardwaj, Hemlata Saxena, Anurag Choubey
Abstract- The main objective of this paper is to optimize
(maximize) the net return of Central Bank of India in the area of
interest from loans such as Personal loan, Car loan, Home loan,
Agricultural loan, Commercial loan, Education loan and also
maximize the net return of the investor by investing some amount
in the investment policy of Central Bank of India such as Fixed
Deposit, Saving Account, Public Provident fund and other
investment Policies. The linear programming technique is
applied to maximize profit of the Bank and the investor.
Index Terms- Linear Programming Model, Objective
function, Constraints, Decision variables, Simplex method,
Maximization, Marginal cost of funds based Lending Rate
(MCLR).
I. INTRODUCTION
Linear Programming is a mathematical technique which is
used to determine the optimal allocation of the limited
resources, among the competitive activities provided all the
relationships among the variables are linear. It is mainly
concerned with a method of finding the optimum value
(Maximum or Minimum) of a function of n variables.
It is used extensively in business, economics and
engineering. An example of an engineering application
would be maximising profit in a factory that manufactures a
number of different products from same raw material using
same resources. The constraints would be decided by
amount of raw materials available. The problems related to
product mix and distribution of goods is solved by the
technique of linear programming for optimization. In a
business setting, profit maximization in always emphasized
which inevitably means the minimization of some cost
function. For Linear Programming Problems, the Simplex
algorithm provides a powerful computational tool, able to
provide fast solution to very large-scale application. Many
Researchers worked for maximum profit using Linear
Programming in different fields as:
Chambers and Charnes (1961) developed linear
programming models for bank dynamic balance sheet
management determine the sequence of period-by-period
balance sheets which will maximize the bank’s net return
subject to constraints on the bank’s maximum exposure to
risk, minimum supply of liquidity, and a host of other
relevant considerations. Akhigbe, A. and MC Nulty, J.E.
(2003) used Linear Programming for the profit efficiency of
small U.S. Banks. Joly (2012) used linear programming in
the oil sector to find optimal production process towards the
maximum profit. Waheed et al (2012) used linear
programming for profit maximization in a product-mix
company.
Revised Manuscript Received on August 25, 2019.
Amit Kumar Jain, Research Scholar, School of Science, Career Point
University, Kota, Rajasthan, India
Ramakant Bhardwaj, Professor, Technocrats Institute of Technology,
Bhopal, MP, India
Hemlata Saxena, Professor, Career Point University, Kota, Rajasthan,
India
Anurag Choubey, Professor, Technocrats Institute of Technology,
Bhopal, MP, India
B.I. Ezema et. al (2012) used linear programming in Golden
plastic Industry for maximizing profit. F. Majeke (2013)
used this technique for optimization of available farm
resources. Musah Sulemana, et. al (2014) applied Linear
programming for profit optimization of Bank. E.M.,
Igbinehi et al (2015) used linear programming method in
manufacturing of local soap for maximum profit. Akpan,
N.P. et. al (2016) used linear programming for optimal use
of Raw materials in Gorretta bakery limited, Nigeria for the
purpose of profit maximization.
The intention of this paper is to find the maximum profit of
Central Bank of India in the area of interest from loans and
maximum profit of investor by investing some amount in
different policies of the Bank under some conditions.
The general form of linear programming problem is
Optimize
1 1 2 2 n n
z cx cx ... cc (objective function)
…..(2.1)
subject to the constraints
11 1 12 2 1n n 1
21 1 22 2 2n n 2
m1 1 m2 2 mn n m
ax a x ... a x(, , )b
a x a x ... a x(, , )b
....... ....... ......... .........
....... ....... ......... .........
a x a x ... a x(, , )b
…..(2.2)
and non-negative restrictions
j
x 0, j 1, 2...n
Where a
ij
’s, b
i
’s and c
j
’s are constants and x
j
’s are variables.
In the conditions given by (2.2) there may be any of the
three signs ,, .
Standard form of a Linear programming problem for solving
by simplex method is as
(a) Using slack and surplus variables to express all
constraints as equation.
(b) For each constraints all b
i
0, if any b
i
is negative
then multiply the corresponding constraint by 1.
(c) Always, problem must be of maximization type if
not convert it in maximization type by multiplying
objective function by 1.
Using slack and surplus variables the linear programming
problem of n variables and m constraints can be written as
follows:
Optimize
1 1 2 2 n n 1 2 m
z cx cx ... cc 0.s 0.s ... 0.s
(objective function) …..(2.3)
subject to the constraints