Michael, I'm sorry, but I didn't understand your explanation below- This is due to my limited LP/MIP understanding- sigh..
But, looking at the examples on http://www.aimms.com/aimms/download/manuals/AIMMS3OM_IntegerProgrammingTricks.pdfand doing some math led me to the following formulation: ---------------------------begin formulation-------------------------------------------------- not_a_and_b <= (1-a) not_a_and_b <= b not_a_and_b >= b-a not_b_and_a <= (1-b) not_b_and_a <= a not_b_and_a >= a-b d_if_not_a_and_b <= U*not_a_and_b d_if_not_a_and_b <= d d_if_not_a_and_b >= d -U*(1-not_a_and_b) d_if_not_a_and_b >= 0 e_if_not_b_and_a <= U*not_b_and_a e_if_not_b_and_a <= e e_if_not_b_and_a >= e-U*(1-not_b_and_a) e_if_not_b_and_a >= 0 d_if_not_a_and_b_or_e_if_not_b_and_a = d_if_not_a_and_b+e_if_not_b_and_a -----------------------------end formulation-------------------------------------------------- Is this close to what you were suggesting? Thanks Kretch On Tue, Oct 13, 2009 at 10:16 AM, Michael Hennebry < [email protected]> wrote: > On Mon, 12 Oct 2009, Yaron Kretchmer wrote: > > Thanks Michael >> Yes, the differences (and the variables themselves) are bounded. We can >> denote the the upper/lower limit for each variable/difference by the >> constants l(x) and u(x). >> > > First, I made a mistake: > The sets have seven extreme points each, > one for one value of (a,b) and two each for the others. > > What would the formulation be in that case? >> > > I think I'll let you do the math. > Each constraint will be tight at three of the extreme points. > That gives you three equations in four variables. > Scaling is allowed, so one of the variables may be fixed. > Check to make sure that the other extreme points satisfy the constraint. > If some slacks are positive and others negative, > the "facet" you have been deriving is invalid. > If all are nonpositive and three are zero, then the direction is wrong. > > Note that you do not have to use constant bounds. > If the bounds depend on (a,b) that is just fine. > The narrower the bounds, the tighter the linear relaxation will be. > Narrowing bounds might be worth considerable effort. > > ][Michael Hennebry wrote:] > >> the feasible sets of (a,b,c-d) and (a,b,c-e) >>> have four extreme points. >>> Their convex hulls are tetrahedra. >>> >>> ]Yaron Kretchmer wrote: > >> Now I'd like to be able to model conditional non-binary variables. Does >>> >> > ]]][Yaron Kretchmer wrote:] > > anybody know how to formulate this in mathprog? >>>>> >>>>> ----------Begin Description ------------------- >>>>> *) a,b are binary >>>>> *) c,d,e is continuous. >>>>> *) I'd like c to be >>>>> - 0 if a=b=0 >>>>> - d if a=0,b=1 >>>>> - e if a=1,b=0 >>>>> - 0 if a=b=1 >>>>> ----------End Description >>>>> >>>> > -- > Michael [email protected] > "Pessimist: The glass is half empty. > Optimist: The glass is half full. > Engineer: The glass is twice as big as it needs to be." >
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