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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
h5budget.mos (!****************************************************** Mosel Example Problems ====================== file h5budget.mos ````````````````` Planning the family budget A mother wants to plan her family's annual budget. A list of monthly expenses is provided as well as the family salary and allowances. Each month, the mother pays at least a given amount for leisure, but she would like to spend more in such activities. How should she balance the budget through the year to maximize the money available for leisure? This is a LP model similar to a production planning model where money can be transferred from one time period to the next one. To deal with the different periodicities of the expenses, the Mosel operator 'mod' is introduced. For the savings at the beginning of the first period, the conditional 'if' is used in the constraint formulation. (c) 2008-2022 Fair Isaac Corporation author: S. Heipcke, Mar. 2002, rev. Mar. 2022 *******************************************************!) model "H-5 Family budget" uses "mmxprs" declarations MONTHS = 1..12 ! Time period ITEMS: set of string ! Set of shops INCOME, ALLOW: integer ! Monthly income and allowance HMIN: integer ! Min. amount required for hobbies EXPENSE: array(ITEMS) of integer ! Expenses FREQ: array(ITEMS) of integer ! Frequency (periodicity) of expenses hobby: array(MONTHS) of mpvar ! Money to spend for leisure/hobbies saving: array(MONTHS) of mpvar ! Savings end-declarations initializations from 'h5budget.dat' INCOME ALLOW HMIN [EXPENSE, FREQ] as 'PAYMENT' end-initializations ! Objective: money for hobby Leisure:= sum(m in MONTHS) hobby(m) ! Monthly balances forall(m in MONTHS) sum(i in ITEMS | m mod FREQ(i) = 0) EXPENSE(i) + hobby(m) + saving(m) <= INCOME + ALLOW + if(m>1, saving(m-1), 0) forall(m in MONTHS) hobby(m) >= HMIN ! Solve the problem maximize(Leisure) ! Solution printing writeln("Money for hobby: ", getobjval) write("Month ") forall(m in MONTHS) write(" ", strfmt(m,4)) setparam("realfmt", "%4g") ! Reserve 4 char.s for display of real numbers write("\nHobby: ") forall(m in MONTHS) write(" ", getsol(hobby(m))) write("\nSavings:") forall(m in MONTHS) write(" ", getsol(saving(m))) writeln end-model | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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