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ajax.gms : Ajax Paper Company Production Schedule

This sample model is taken from the cybernet pds/apex sample
library of models. A paper manufacturer can produce four different
types of paper on three different machines. Given a fixed demand
schedule the objective is to find a production plan that
maximizes monthly profits.
Reference:
Small Model of Type: LP
$Title Ajax Paper Company Production Schedule (AJAX,SEQ=60) $Ontext This sample model is taken from the cybernet pds/apex sample library of models. A paper manufacturer can produce four different types of paper on three different machines. Given a fixed demand schedule the objective is to find a production plan that maximizes monthly profits. CDC, PDS/APEX Sample Model Library, 1977. Control Data Corporation $Offtext Sets m machines at mills / machine-1, machine-2, machine-3 / g paper grades / 20-bond-wt, 25-bond-wt, c-bond-ext, tissue-wrp / Table prate(g,m) production rate (tons per hour) machine-1 machine-2 machine-3 20-bond-wt 53 52 49 25-bond-wt 51 49 44 c-bond-ext 52 45 47 tissue-wrp 42 44 40 Table pcost(g,m) production cost ($ per ton) machine-1 machine-2 machine-3 20-bond-wt 76 75 73 25-bond-wt 82 80 78 c-bond-ext 96 95 92 tissue-wrp 72 71 70 Table dempr(g,*) demand and prices demand price 20-bond-wt 30000 77 25-bond-wt 20000 81 c-bond-ext 12000 99 tissue-wrp 8000 105 Parameter avail(m) available machine time (hours per month) / machine-1 672, machine-2 600, machine-3 480 / Variables outp(g,m) production (tons per month) profit profit ($ per month) Positive Variable outp Equations cap(m) machine capacity (hours per month) dem(g) demand (tons per month) pdef profit definition ($ per month) ; cap(m).. sum(g, outp(g,m)/prate(g,m)) =l= avail(m); dem(g).. sum(m, outp(g,m)) =e= dempr(g,"demand"); pdef.. profit =e= sum(g, dempr(g,"demand")*dempr(g,"price")) - sum((g,m), pcost(g,m)*outp(g,m)); Model ajax /all/; Solve ajax using lp maximizing profit; $Stitle report definitions Parameter mtr(m,*) machine time report par(g,*) production allocation report ; mtr(m,"avail-h") = avail(m); mtr(m,"used-h") = cap.l(m); mtr(m,"unused-h") = avail(m) - cap.l(m); mtr(m,"marginal") = - cap.m(m); par(g,"demand") = dempr(g,"demand"); par(g,"sold") = dem.l(g); par(g,"unsold") = dempr(g,"demand") - dem.l(g); par(g,"marginal") = dem.m(g); Display mtr, par , outp.l, outp.m ;