Non-linearity in GAMS model

GAMS
1

I wrote a relatively simpler model where the acreage will be allocated
between two different crops (Grasses and Stover).

There are no non-linearities involving the acreage terms. Still, I got
this error #56

“56 Endogenous operands for * not allowed in linear models.”

In stead of LP, I used NLP to solve the problem and I was able to
obtain feasible results. But, I was surprised why this would happen -
since I use only a products but without any non-linear operations (no
power ** or Max/Min/ABS functions?

The following are the only two equations, where the vStoverAc(zone,
quarter) and vGrassac(z) appear. Other equations in the model are
based upon the total biomass derived from these acreages.

What other factors should I be careful about to understand such error
message of non-linearity? I seek this because I am planning to
introduce some non-linearity in acreage terms (or a round-about method
of iterative solve command).

eCostFunction… vCumulativeCost =e=

Sum[(z,q), vcost(“Grass”,z,q) * Yield(“Grass”,q) * vGrassAc(z)]

  • Sum[(z,q), vcost(“Stover”,z,q) * Yield(“Stover”,q) * vStoverAc(z,q)]
  • Sum[(F,q),(D * vStorage(F,q))]
  • [Sum(z,vTerminalcost(‘Stover’,z))/Card(z)]* vExcessStover_T
  • [Sum(z,vTerminalcost(‘Grass’,z))/Card(z)]*
    vExcessGrass_T ;


    *Supply of Stover and Grass in quarter q
    eGrassSupply(q)… vGrassS(q) =e= Sum(z,Yield(“Grass”,q) *
    vGrassAc(z)) ;
    eStoverSupply(q)… vStoverS(q) =e= Sum(z,Yield(“Stover”,q) *
    vStoverAc(z,q)) ;

Thank you for your reply.

Subbu Kumarappan
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2

Hi Subbu

Is Yield(crop, quater) a variable? Non-linearity occurs when there is a product of two variables x1*x2. This is what I suspect is going on in your case.

Hope this helps.

Rahul

On Fri, Apr 24, 2009 at 8:09 PM, kmsubbu wrote:


I wrote a relatively simpler model where the acreage will be allocated
between two different crops (Grasses and Stover).

There are no non-linearities involving the acreage terms. Still, I got
this error #56

“56 Endogenous operands for * not allowed in linear models.”

In stead of LP, I used NLP to solve the problem and I was able to
obtain feasible results. But, I was surprised why this would happen -
since I use only a products but without any non-linear operations (no
power ** or Max/Min/ABS functions?

The following are the only two equations, where the vStoverAc(zone,
quarter) and vGrassac(z) appear. Other equations in the model are
based upon the total biomass derived from these acreages.

What other factors should I be careful about to understand such error
message of non-linearity? I seek this because I am planning to
introduce some non-linearity in acreage terms (or a round-about method
of iterative solve command).

eCostFunction… vCumulativeCost =e=

Sum[(z,q), vcost(“Grass”,z,q) * Yield(“Grass”,q) * vGrassAc(z)]

  • Sum[(z,q), vcost(“Stover”,z,q) * Yield(“Stover”,q) * vStoverAc(z,q)]
  • Sum[(F,q),(D * vStorage(F,q))]
  • [Sum(z,vTerminalcost(‘Stover’,z))/Card(z)]* vExcessStover_T
  • [Sum(z,vTerminalcost(‘Grass’,z))/Card(z)]*
    vExcessGrass_T ;


    *Supply of Stover and Grass in quarter q
    eGrassSupply(q)… vGrassS(q) =e= Sum(z,Yield(“Grass”,q) *
    vGrassAc(z)) ;
    eStoverSupply(q)… vStoverS(q) =e= Sum(z,Yield(“Stover”,q) *
    vStoverAc(z,q)) ;

Thank you for your reply.

Subbu Kumarappan



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3

Thanks. I think you are right - I am yet to find which two variables
would be product.
May be the inventory requirements that connect two periods – create
multi-period equations. When these equations are simultaneously
solved, the non-linearities occur.

am not sure yet. Thanks again.
Subbu

On Apr 24, 5:31 pm, Rahul Anantharaman
wrote:

Hi Subbu

Is Yield(crop, quater) a variable? Non-linearity occurs when there is a
product of two variables x1*x2. This is what I suspect is going on in your
case.

Hope this helps.

Rahul

On Fri, Apr 24, 2009 at 8:09 PM, kmsubbu wrote:

I wrote a relatively simpler model where the acreage will be allocated
between two different crops (Grasses and Stover).

There are no non-linearities involving the acreage terms. Still, I got
this error #56

“56 Endogenous operands for * not allowed in linear models.”

In stead of LP, I used NLP to solve the problem and I was able to
obtain feasible results. But, I was surprised why this would happen -
since I use only a products but without any non-linear operations (no
power ** or Max/Min/ABS functions?

The following are the only two equations, where the vStoverAc(zone,
quarter) and vGrassac(z) appear. Other equations in the model are
based upon the total biomass derived from these acreages.

What other factors should I be careful about to understand such error
message of non-linearity? I seek this because I am planning to
introduce some non-linearity in acreage terms (or a round-about method
of iterative solve command).

eCostFunction… vCumulativeCost =e=

Sum[(z,q), vcost(“Grass”,z,q) * Yield(“Grass”,q) * vGrassAc(z)]

  • Sum[(z,q), vcost(“Stover”,z,q) * Yield(“Stover”,q) * vStoverAc(z,q)]
  • Sum[(F,q),(D * vStorage(F,q))]
  • [Sum(z,vTerminalcost(‘Stover’,z))/Card(z)]* vExcessStover_T
  • [Sum(z,vTerminalcost(‘Grass’,z))/Card(z)]*
    vExcessGrass_T ;

*Supply of Stover and Grass in quarter q
eGrassSupply(q)… vGrassS(q) =e= Sum(z,Yield(“Grass”,q) *
vGrassAc(z)) ;
eStoverSupply(q)… vStoverS(q) =e= Sum(z,Yield(“Stover”,q) *
vStoverAc(z,q)) ;

Thank you for your reply.

Subbu Kumarappan

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