| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Economics and finance Description
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 13: Economics and finance problems
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
Data Files
h4retire.mos (!****************************************************** Mosel Example Problems ====================== file h4retire.mos ````````````````` Financing an early retirement scheme To finance a pre-retirement scheme, a bank can invest in three different types of bonds during a given period of years. Bonds can be acquired only at the beginning of the first year. Some technical conditions are defined on the money not invested, the quantity of bonds to be bought and the available money to be distributed. How many bonds of each type should the bank acquire to minimize the money spent to cover the retirement scheme? A MIP model is implemented to determine the best way to finance the retirement plan. To model the constraints based on the maturity (duration) of the bond, conditionals over sums and the inline 'if' are used to generalize the set of constraints. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Mar. 2002 *******************************************************!) model "H-4 Retirement" uses "mmxprs" declarations BONDS = {"SNCF","Fujitsu","Treasury"} ! Set of bonds NT = 7 ! Length of planning period YEARS = 1..NT DEM: array(YEARS) of integer ! Annual payments for retirement VALUE: array(BONDS) of real ! Unit price of bonds RATE: array(BONDS) of real ! Remuneration rates paid by bonds RET: array(BONDS) of real ! Unit annual interest of bonds DUR: array(BONDS) of real ! Duration of loans INTEREST: real ! Interest for other secure investment buy: array(BONDS) of mpvar ! Number of bonds acquired invest: array(YEARS) of mpvar ! Other annual investment capital: mpvar ! Total capital required end-declarations initializations from 'h4retire.dat' DEM VALUE RATE DUR INTEREST end-initializations forall(b in BONDS) RET(b):= VALUE(b)*RATE(b)/100 ! Annual balances capital - sum(b in BONDS) VALUE(b)*buy(b) - invest(1) = DEM(1) forall(t in 2..NT) sum(b in BONDS | DUR(b)+1>=t) (RET(b)*buy(b) + if(DUR(b)+1=t, VALUE(b)*buy(b), 0)) + (1+INTEREST/100)*invest(t-1) - if(t<NT, invest(t), 0) = DEM(t) forall(b in BONDS) buy(b) is_integer ! Solve the problem: minimize invested capital minimize(capital) ! Solution printing writeln("Total capital: ", getobjval) writeln("Number of bonds to buy:") forall(b in BONDS) write(b, ": ", getsol(buy(b)), " (price: ", VALUE(b)*getsol(buy(b)), ") ") writeln("\nOther investment:") forall(t in 1..NT-1) write(" year ", t) writeln forall(t in 1..NT-1) write(strfmt(getsol(invest(t)),9,3)) writeln end-model | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

© Copyright 2024 Fair Isaac Corporation. |