paperco.gms : Vertically Integrated Company

**Description**

This is an alternative formulation of the model PAPERCO found in Computational Economics, Chapter 9. This version introduces several sets to partition the equation and variable space into four groups. This example further shows how to implement the suggested scenarios by using a LOOP statement.

**Reference**

- Thompson, G, and Thor, S, Computational Economics: Economic Modeling with Optimization Software. The Scientific Press, San Francisco, 1991.

**Small Model of Type :** LP

**Category :** GAMS Model library

**Main file :** paperco.gms

$Title Vertically Integrated Company (PAPERCO,SEQ=102) $Inlinecom { } $Ontext This is an alternative formulation of the model PAPERCO found in Computational Economics, Chapter 9. This version introduces several sets to partition the equation and variable space into four groups. This example further shows how to implement the suggested scenarios by using a LOOP statement. Thompson, G, and Thor, S, Computational Economics: Economic Modeling with Optimization Software. The Scientific Press, San Francisco, 1991. $Offtext Sets l log suppliers / company, farmer / w wood products / ground, chips / p pulp types / pulp-1, pulp-2 / q paper types / kraft, newsprint, printing / Table ap(w,p) pulp manufacturing input requirements pulp-1 pulp-2 ground .6 .3 chips .4 .7 Table aq(p,q) paper manufacturing input requirements kraft newsprint printing pulp-1 .68 .45 .25 pulp-2 .32 .55 .75 Table cw(w,p) wood shipment cost pulp-1 pulp-2 (ground chips ) 40 55 Table cp(p,q) pulp shipment cost kraft newsprint printing pulp-1 40 60 70 pulp-2 55 50 45 Table sdat(q,*) sales data lower upper kraft 18 25 newsprint 12 15 printing 0 7 Parameter pq(q) sales price / kraft 265, newsprint 275, printing 310 / pp(p) price of pulp pc(w) / ground 18, chips 16 / Scalar plog / 65 / Positive Variables logs(l) purchases of logs (tons) xw(w,p) shipments of wood products (tons) pulp(p) production of pulp (tons) xp(p,q) shipments of pulp (tons) paper(q) production and sales of paper products (tons) sales(p) sales of pulp (tons) purchase(p) purchase of pulp (tons) Variables profit net operating income Equations logbal wbal(w,p) pbal(p) qbal(p,q) obj; logbal.. .97*sum(l, logs(l)) =e= sum((w,p), xw(w,p)); wbal(w,p).. xw(w,p) =e= ap(w,p)*pulp(p); pbal(p).. sum(q, xp(p,q)) =e= purchase(p) - sales(p) + pulp(p); qbal(p,q).. xp(p,q) =e= aq(p,q)*paper(q); obj.. profit =e= sum(p, pp(p)*sales(p)) { sales of pulp } + sum(q, pq(q)*paper(q)) { sales of paper } - sum(l, plog*logs(l)) { cost of logs } - sum((p,q), cp(p,q)*xp(p,q)) { transport cost of pulp } - sum((w,p), (cw(w,p)+pc(w))*xw(w,p)) { transport cost of wood } - sum(p, pp(p)*purchase(p)); Model wood / all /; paper.lo(q) = sdat(q,'lower'); paper.up(q) = sdat(q,'upper'); Set scenario scenario identifier / scenario-1*scenario-3 / Table psdat(scenario,p,*) bounds on pulp trade (tons) pulp-1.s pulp-1.p pulp-2.s pulp-2.p scenario-1 scenario-2 3 5 3 5 scenario-3 6 6 10 10 Table ppdat(scenario,p) price data for pulp trade ($ per tons) pulp-1 pulp-2 scenario-1 120 140 scenario-2 120 140 scenario-3 120 150 Loop(scenario, purchase.up(p) = psdat(scenario,p,'p'); sales.up(p) = psdat(scenario,p,'s'); pp(p) = ppdat(scenario,p); Solve wood maximizing profit using lp; Option limcol=0, limrow=0 ; );