$title TYCO from Winston and Albright, 2nd ed., p. 154 et seq.

* It's called FunToys there, as the company name "Tyco" has become
* somewhat notorious

option limcol = 0;

set months / Jan, Feb, Mar, Apr, May, Jun,
       Jul, Aug, Sep, Oct, Nov, Dec/;

* cash inflow (negative value indicates net outflow)
parameter cashIn(months) cash inflow in thousands of dollars /
Jan -12, Feb -10, Mar -8, Apr -10, May -4, Jun 5,
Jul -7,  Aug -2,  Sep 15, Oct 12,  Nov -7, Dec 45/;

* minimum cash balance at end of each month ($k)

scalar cashBalMin /5/;
scalar initialCap /6.5/;

set accounts /long-loan, short-loan, cash/;

parameter interestRate(accounts) /long-loan 1, short-loan 1.5, cash 0.4/;
* convert from percentage to proportion  by dividing by 100
interestRate(accounts) = interestRate(accounts) / 100;

variable
   longLoan  	amount of long-term loan taken in January ($K)
   shortLoan(months)  amount of short-term loans taken out this month ($K)
   shortPaid(months)  amount of short-term loans paid off this month ($K)
   shortNet(months)  net amount of short-term loans owing at end of this month ($K)
   cashBal(months)  cash balance at end of each month ($K)
   cashInt(months)  interest earned on last month's cash balance ($K)
   longInt    interest paid on long-term loan each month ($K)
   shortInt(months)  interest paid on short-term loan each month ($K)
   cashFinal    final cash position ($K);

positive variables longLoan, shortLoan, shortPaid, shortNet, cashBal, cashInt, longInt, shortInt;

equations
  EQcashInt(months)  define interest earned on cash balance each month
  EQlongInt  	define interest paid on long-term loan this month
  EQshortNet(months)  figure net amount of short-term loans owing at end of month
  EQshortInt(months)  define interest paid on short-term loan this month
  EQcashBal(months)  figure cash balance at end of the month
  EQcashFinal  	figure final cash position;

* note that for months=Jan, cashInt will be zero
EQcashInt(months)..
  cashInt(months) =e= (initialCap$(ord(months) = 1) + cashBal(months-1)) * interestRate('cash');

* set longInt to zero for months=Jan
EQlongInt..
  longInt =e= longLoan * interestRate('long-loan');

* for months=Jan, shortInt will be zero (no interest paid in first month)
* "months-1" goes out of range for this value - check listing file
EQshortInt(months)..
  shortInt(months) =e= shortNet(months-1) * interestRate('short-loan');

* figure balance of short-term loans at the end of this month
EQshortNet(months)..
  shortNet(months) =e=
       shortNet(months-1)
       + shortLoan(months)
       - shortPaid(months);


* figure cash balance at end of month
EQcashBal(months)..
  cashBal(months) =e=
      (initialCap + longLoan)$(ord(months) = 1)
      + cashBal(months-1)
      + cashInt(months)
      + shortLoan(months)
      - shortPaid(months)
      + cashIn(months)
      - longInt$(ord(months) > 1)
      - shortInt(months);

EQcashFinal..
  cashFinal =e=  cashBal('Dec')
      + cashBal('Dec') * interestRate('cash')
      - longInt
      - longLoan;

* pay off all short-term loans by next January
shortNet.fx("Dec") = 0;
* set minimum cash balance at end of each month
cashBal.lo(months) = cashBalMin;

model tyco/all/;

solve tyco using lp maximizing cashFinal;

* convert results to $ from $K
longLoan.l = 1000*longLoan.l;
shortLoan.l(months) = 1000*shortLoan.l(months);
shortPaid.l(months) = 1000*shortPaid.l(months);
shortNet.l(months) = 1000*shortNet.l(months);
cashBal.l(months) = 1000*cashBal.l(months);
cashInt.l(months) = 1000*cashInt.l(months);
longInt.l = 1000*longInt.l;
shortInt.l(months) = 1000*shortInt.l(months);
cashFinal.l = 1000*cashFinal.l;

* globally set number of decimals displayed to 2
option decimals=2;

display  longLoan.l, longInt.l;

* for shortLoan, display 2 decimal places; 0:1 indicates maximum 1 label
* displayed on each line
option shortLoan:2:0:1; display shortLoan.l;
option shortPaid:2:0:1; display shortPaid.l;
option shortNet:2:0:1; display shortNet.l;
option shortInt:2:0:1; display shortInt.l;
option cashBal:2:0:1; display cashBal.l;
option cashInt:2:0:1; display cashInt.l;
display cashFinal.l;