Constraint shadow prices for MIP models

[srikkanth madhavan]

Hi,

 Can anyone let me know if its possible to display constraint equation shadow prices for MIP models? In the MIP model I am executing, I find that the constraint equations have no data to display.

Regards,
Srikkanth M

[Steven Dirkse]

Srikkanth,

It is possible to get shadow prices for the equations in a MIP model.  Here is one example I just ran on my Linux machine:

gamslib rotdk

gams rotdk.gms mip=cplex gdx=results

gdxdump results.gdx  symb=capbal

with the gdxdump output below:

Equation capbal(t) capacity balance /

't1'.M -1.81, 

't2'.M -1.81, 

't3'.M -1.805, 

't4'.M -1.705, 

't5'.M -0.785, 

't6'.M -0.695, 

't7'.M -0.67, 

't8'.M -0.67, 

't9'.M -0.3, 

't10'.M -0.19, 

't11'.M -0.12, 

't12'.M -0.055 /;

Hope this helps,

-Steve

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Steven Dirkse, Ph.D.
GAMS Development Corp.,  Washington DC
Voice: (202)342-0180     Fax: (202)342-0181
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[srikkanth madhavan]

Steven,

   Thanks for getting back. I do see it does produce the shadow prices for equations in the MIP model you sent as an example. But in the model below with binary variables, I either find the equations shadow prices to be empty or having level, lower and upper values but no marginal values. How do I interpret the results?

$gdxin CapacityModInputData.gdx

sets

wmid(*) Unit WM ID

dstep(*) Demand Steps

;

$load wmid dstep

Parameters

cap(wmid) Capacity of each unit

bid(wmid) Bid price per MW for each unit

delta(wmid) Delta MW for each unit

ajunit(wmid) Ajunit ON or OFF

dmd(dstep) Demand per step

dprice(dstep) Price per each demand step

$load  cap bid delta ajunit dmd dprice

$gdxin

;

VARIABLES

z objective function value;

BINARY VARIABLES

units_vars(wmid)         Unit ON OR OFF

dmd_steps_vars(dstep)  DMD ON OR OFF

ajunits_vars(wmid)       AJUNIT ON OR OFF

EQUATIONS

OBJ                    Total Cost of operating the units(Bid cost + AJ Unit cost) - Total Area under demand curve

Supply_EQ_Demand_CONST Supply equals demand constraint

AJ_UNIT_CONST          AJ UNIT Demand Constraint

NON_AJ_UNIT_CONST(wmid)          NON AJ UNIT Demand Constraint

Unit_Var_Unique_CONST(wmid) EITHER AJ OR NON AJ

;

OBJ..           z =E= sum(wmid , bid(wmid)*cap(wmid)*units_vars(wmid))+sum(wmid, delta(wmid)*cap(wmid)*ajunits_vars(wmid))-sum(dstep, dprice(dstep)*dmd(dstep)*dmd_steps_vars(dstep));

Supply_EQ_Demand_CONST.. sum(wmid,(ajunits_vars(wmid)+units_vars(wmid))*cap(wmid)) =e= sum(dstep,dmd_steps_vars(dstep)*dmd(dstep));

AJ_UNIT_CONST..          sum(wmid,ajunits_vars(wmid)*cap(wmid)) =g= 0.8*sum(dstep,dmd_steps_vars(dstep)*dmd(dstep));

NON_AJ_UNIT_CONST(wmid).. ajunits_vars(wmid)$(ajunit(wmid) = 0) =e= 0;

Unit_Var_Unique_CONST(wmid).. ajunits_vars(wmid)+units_vars(wmid) =l= 1;

MODEL PJMCapacityMOD /all/;

SOLVE PJMCapacityMOD using MIP minimizing z;

Regards,
Srikkanth M

[Steven Dirkse]

Srikkanth,

I don't see any results, so I can't help interpret them.  If you send the GDX input I could try to run this and offer more help.

-Steve

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[Masoud Barati]

In general the shadow price of the MIP problem is invalid. 

First, you should find the equivalent LP problem and use its shadow prices. 

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