Originally posted by: sandeepsinghchauhan

I have a doubt regarding Linearization of constraint like:

1) In Decentralization example Linearization done by:

forall(ordered d1,d2 in Depts, c1, c2 in Cities) {
      Link[d1][c1][d2][c2] - IsIn[d1][c1] <= 0;
      Link[d1][c1][d2][c2] - IsIn[d2][c2] <= 0;
      IsIn[d1][c1] + IsIn[d2][c2] - Link[d1][c1][d2][c2] <= 1;
   }

linearization of IsIn[d1][c1]xIsIn[d2][c2]

Very clear even validating inequality conditions (when IsIn[d2][c2]=0 ->Link[d1][c1][d2][c2] =0   and   IsIn[d2][c2] =0 ->Link[d1][c1][d2][c2] = IsIn[d1][c1])

2) But, the linearization in Yield management is very different :

forall (s1 in scenarios, c in classes, o in options) {
      Revenue1[s1][c][o] - priceOptions[1][c][o]*Seats1[s1][c][o] <= 0;
      priceOptions[1][c][o]*Seats1[s1][c][o] - Revenue1[s1][c][o] + priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= priceOptions[1][c][o]*demand[1][s1][c][o];
   }

not validating inequality condition ( PriceLevel1[c][o] = 0 -> Revenue1[s1][c][o] = 0)

Please help me to clearify this confusion i will really thankful to you

please help

//      Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0;

Hi,

Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0;

if

PriceLevel1[c][o]

is 0 then

Revenue1[s1][c][o]  <= 0;

else

Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o] <= 0;

Right ?

So where is the confusion ?

regards

Originally posted by: sandeepsinghchauhan

But In yield management problem they not mentioned this equation

Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0;

This is my confusion

Originally posted by: sandeepsinghchauhan

This is my confusion without including  Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0;

How they formulate it ?

hi,

in the .mod

we have

Revenue1[s1][c][o] - priceOptions[1][c][o]*Seats1[s1][c][o] <= 0;

and in the book we see

It is the same

regards

Originally posted by: sandeepsinghchauhan

Yes in book also they have
forall (s1 in scenarios, c in classes, o in options) {
      Revenue1[s1][c][o] - priceOptions[1][c][o]*Seats1[s1][c][o] <= 0;
      priceOptions[1][c][o]*Seats1[s1][c][o] - Revenue1[s1][c][o] + priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= priceOptions[1][c][o]*demand[1][s1][c][o];
   }

this they also not included

Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0;

I want to know why this is happening means how this linearization working even when it not able to satisfy my inequality condition (PriceLevel1[c][o] = 0 -> Revenue1[s1][c][o] = 0)

please help me to clarify how yield management model is working correctly?

Is any other thing in yield management taking care of this (Revenue1[s1][c][o] - priceOptions[1][c][o]*demand[1][s1][c][o]*PriceLevel1[c][o] <= 0; ) or PriceLevel1[c][o] = 0 -> Revenue1[s1][c][o] = 0 condition, which i am lacking?

please help me