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FortMP MEX Example

Problem Statement: National Insurance Associates carries an investment portfolio of stocks, bonds and other investment alternatives. Currently £200,000 of funds is available and must be considered for new investment opportunities. The four stock options National is considering and the relevant financial data are as follows:

	Stock
	A	B	C	D
Price per share (in Rs.)	100	50	80	40
Annual rate of return	0.12	0.08	0.06	0.10
Risk measure per Rs. invested	0.10	0.07	0.05	0.08

Table-1: Financial Data
The risk measure indicates the relative uncertainty associated with the stock in terms of it realising the projected annual return: higher values indicate greater risk.
National’s top management has stipulated the following investment guidelines

1. The annual rate of return for the portfolio must be 9%
2. No one stock can account for more than 50% of the total sterling investment

They request you to find the investment decisions.

Mathematical formulation of the problem

                Minimize
                        Risk = 10*StockA + 3.5*StockB + 4*StockC + 4*StockD
            Variables
                        StockA  ≤ 1000
                        StockB  ≤ 2000
                        StockC  ≤ 1250
                        StockD  ≤ 2500
            Subject to
                        100*StockA + 50*StockB + 80*StockC + 40*StockD  ≤ 200000
                        12*StockA + 4*StockB + 4.8*StockC + 4*StockD ≤ 18000

 

Solving the Problem using FortMP-MEX

FortMP-MEX uses the following data representation to solve an LP problem.

The MATLAB function we will need is FMP_SOLVE
Open MATLAB and change to the MFortMP-MEX directory, then type the following command at the prompt
>>help FMP_SOLVE
Usage : [obj, sol ,dsl ,bas ,stsl, tctn] = FMP_SOLVE(A,L,U,l,u,k,c,mitype)
Description: Solves a model entered in canonical form
Inputs:-
k - is a scalar constant offset to the objective
c - is an n- vector of the cost coefficients c1,c2,...cn.
x - is an n- vector of the structural variables x1,x2,...xn
L - is an m-vector of lower right hand sides L1,L2,...Lm
A - is an m x n matrix of coefficients aij
U - is an m-vector of upper right hand sides U1,U2,...Um
l - is an n- vector of lower bounds l1,l2,...ln
u - is an n- vector of upper bounds u1,u2,...un
mitype - see manual
Output - see manual
Referring to our problem, now enter the inputs A, L, U, l, u, k, c and mitype into matlab:

We can now solve the problem by issuing the following commands at the MATLAB prompt -

Notice that we used -c because we want to maximize and the default is minimization. The exit code (tctn) is zero signifying that there was no error and a status code (stsl) of 3 meaning that an optimal linear solution was found.
The objective value -obj or sol(1) and the solution vectors are given by typing the following.