$title AMPL Sample Problem (AMPL,SEQ=74)

$onText
A sample problem to demonstrate the power of modeling systems.

Fourer, R, Gay, D M, and Kernighan, B W, AMPL: A Mathematical Programming
Language. AT\&T Bell Laboratories, Murray Hill, New Jersey, 1987.

Keywords: linear programming, production planning, AMPL
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Set
   p     'products'       / nuts, bolts, washers /
   r     'raw materials'  / iron, nickel         /
   tl    'extended t'     / 1*5 /
   t(tl) 'periods'        / 1*4 /;

Parameter
   b(r)  'initial stock'  / iron 35.8 , nickel 7.32  /
   d(r)  'storage cost'   / iron   .03, nickel  .025 /
   f(r)  'residual value' / iron   .02, nickel -.01  /;

Scalar m 'maximum production' / 123 /;

Table a(r,p) 'raw material inputs to produce a unit of product'
              nuts  bolts  washers
   iron        .79    .83      .92
   nickel      .21    .17      .08;

Table c(p,t) 'profit'
                 1    2    3    4
   nuts       1.73  1.8  1.6  2.2
   bolts      1.82  1.9  1.7   .95
   washers    1.05  1.1   .95 1.33;

Variable
   x(p,tl) 'production level'
   s(r,tl) 'storage at beginning of period'
   profit  'income minus cost';

Positive Variable x, s;

Equation
   limit(t)      'capacity constraint'
   balance(r,tl) 'raw material balance'
   obj           'profit definition';

limit(t)..          sum(p, x(p,t)) =l= m;

balance(r,tl+1)..   s(r,tl+1) =e= s(r,tl) - sum(p, a(r,p)*x(p,tl));

obj..  profit =e= sum((p,t), c(p,t)*x(p,t))
               +  sum((r,tl), (-d(r)$t(tl) + f(r)$tl.last)*s(r,tl));

s.up(r,tl)$tl.first = b(r);

Model ampl 'maximum revenue production problem' / all /;

solve ampl maximizing profit using lp;