Modeling Trick!?

Hi everyone,

Say you wrote a model that might change product's price weekly, for
the time horizon considered in the model. But then, you don't want to
allow successive weekly price change!

Week Price
1 $12
2
3 $10
4
5 $5

So, if price changed to $12 in week1, it can't be changed in week2,
but week3 or week4 or week5.
If price changed in week3, it can't be changed in week4, but week
5and so on.

Assume you are using an algebraic modeler, is there something that
allow you to consider such constraint?

Thanks

Mike wrote:
Hi everyone,
>
Say you wrote a model that might change product's price weekly, for
the time horizon considered in the model. But then, you don't want to
allow successive weekly price change!
>
Week Price
1 $12
2
3 $10
4
5 $5
>
So, if price changed to $12 in week1, it can't be changed in week2,
but week3 or week4 or week5.
If price changed in week3, it can't be changed in week4, but week
5and so on.
>
Assume you are using an algebraic modeler, is there something that
allow you to consider such constraint?
>
Thanks

If you're willing to introduce binary variables, and if you can set an a
priori bound M on the largest change (in absolute value) in any one
week, it's not hard. Let p_i be the price in week i, y_i a binary
variable that takes value 1 if the price changes in week i. Add the
constraints

p_{i-1} - M*y_i <= p_i <= p_{i-1} + M*y_i

y_{i-1} + y_i <= 1

for each i.

/Paul