$title Test of EMP equilibrium models and flip operator (EMP10,SEQ=499)

$onText
Reformulate a simple LP using EMP and the "equilibrium"
keyword/strategy, and check that the solution is unchanged if we:
  a) flip equations manually (i.e. f(x) =L= b becomes -f(x) =G= -b
  b) flip equations using the -equName syntax in the info file
  c) both a and b

In addition, the resulting MCPs generated have the following property:
flipping manually gives the same MCP as flipping with the flip
operator, and flipping twice (both manually and with the flip
operator) gives the same MCP as flipping not at all.  How to check for
this though?

Contributor: Steven Dirkse, September 2010

$offText

SETS
   i   'sources' / i1 * i3 /
   j   'sinks'   / j1 * j3 /
   ;

PARAMETERS
   sup(i) 'supply limit at source' /
     i1   300
     i2   400
     i3   500
   /,
   dem(j) 'demand at sink' /
     j1   400
     j2   350
     j3   300
   /
   ;

TABLE c(i,j) 'cost'
      j1        j2      j3
i1    2       2.8125   4.5
i2  2.8125      2     2.8125
i3   4.5      2.8125    2  ;

POSITIVE VARIABLES   x(i,j);

VARIABLE z;

EQUATIONS
   cost
   supply(i)  'traditional orientation'
   supplyX(i) 'flipped'
   demand(j)  'traditional orientation'
   demandX(j) 'flipped'
   ;

cost ..        z =E= sum {(i,j), c(i,j)*x(i,j)};

supply(i) ..   sum {j, x(i,j)} =L= sup(i);
supplyX(i)..   sup(i) =G= sum {j, x(i,j)};
demand(j) ..   sum {i, x(i,j)} =G= dem(j);
demandX(j)..   dem(j) =L= sum {i, x(i,j)};

model m  'original orientation' / cost, supply,  demand  /;
model mX 'flipped  orientation' / cost, supplyX, demandX /;

* first solve to get the (unique?) solution loaded up
solve m using lp min z;
supplyX.m(i) = -supply.m(i);
demandX.m(j) = -demand.m(j);

file fInfo / '%emp.info%' /;
file fOpt  / 'jams.opt' /;

put fInfo 'equilibrium' /;
putclose  'min z *  cost supply demand' /;

m.iterlim  = 0;
mX.iterlim = 0;
m.optfile  = 1;
mX.optfile = 1;

* model with original orientation, no flip operator
putclose fOpt 'fileName mcp__.gms';

Solve m using emp;
abort$[m.modelstat  > 2] 'bad model status', m.modelstat;
abort$[m.solvestat <> 1] 'bad solve status', m.solvestat;

put fInfo 'equilibrium' /;
putclose  'min z *  cost -supply -demand' /;

* model with original orientation, flip operator
putclose fOpt 'fileName mcp_F.gms';

Solve m using emp;
abort$[m.modelstat  > 2] 'bad model status', m.modelstat;
abort$[m.solvestat <> 1] 'bad solve status', m.solvestat;

put fInfo 'equilibrium' /;
putclose  'min z *  cost -supplyX -demandX' /;

* model with flipped orientation, flip operator
putclose fOpt 'fileName mcpXF.gms';

Solve mX using emp;
abort$[mX.modelstat  > 2] 'bad model status', mX.modelstat;
abort$[mX.solvestat <> 1] 'bad solve status', mX.solvestat;

put fInfo 'equilibrium' /;
putclose  'min z *  cost supplyX demandX' /;

* model with flipped orientation, no flip operator
putclose fOpt 'fileName mcpX_.gms';

Solve mX using emp;
abort$[mX.modelstat  > 2] 'bad model status', mX.modelstat;
abort$[mX.solvestat <> 1] 'bad solve status', mX.solvestat;

* the solutions for all four models should be the same -
* if we get to here we've successfully tested that the same point
* solves all four

* In addition, models mcp__ and mcpXF should be the same, and
* models mcpX_ and mcp_F should be the same.