Let's start with the obvious part: if $z=\max(x,y)$ then $$z\ge x$$ and $$z \ge y.$$In fact, adding those two constraints will be sufficient

*if*the nature of the model ensures that the smallest feasible value of $z$ will always be chosen Typically this means that (a) $z$ has a positive coefficient in an objective function being minimized, or a negative coefficient in an objective function being maximized, and (b) $z$ does not connect to other variables, through constraints, in a way that might allow an inflated value of $z$ to cause other variables to change enough that their improved objective contribution would more than pay for the damage done by inflating $z$.

There are also occasional cases where inflation of $z$ is not actually a concern: you need $z$ to be at least as big as both $x$ and $y$ (which the constraints ensure), but a larger than necessary value of $z$ will not affect the objective function or the values of other variables, and can be corrected manually once a solution is found.

The (slightly) tricky case is when you cannot be sure that the "pressure" of the objective function will prevent inflated values of $z$ from occurring, and you really do need the value of $z$ to be correct. To handle this case, we will need finite bounds for $x$ and $y$, so from here on I will assume that $L_x \le x \le U_x$ and $L_y \le y \le U_y$. We have to introduce a new binary variable $w$, which will switch values depending on whether $x$ or $y$ is the larger of the two. In addition to the two previous constraints, we add the following:$$z \le x + (U_y - L_x)w$$and$$z \le y + (U_x-L_y)(1-w).$$The combined effect of the constraints is that $w=0\implies z=x\ge y$ and $w=1\implies z=y\ge x$.

Can you shed me a light on this subject regarding my problem? I need to find PoverBudget, which is PoverBudget = (summation_t=1:24) Pbattery - Pbudget . I want the PoverBudget to be zero, if the resulting value is negative or else keep the value if its positive. I am confused how to formulate it, as a constraint or as an objective function. Actually, I need to minimize (Cost_battery * PoverBudget) in the objective function, and I cannot find ways to model that in CPLEX.

ReplyDeleteAny help will be greatly appreciated.

Assuming that Cost_battery > 0, the solver will want to give it the smallest value possible (given the rest of the solution). That means you can declare PoverBudget to be a nonnegative variable and then constrain it to be >= the summation you gave. If the sum is negative, the solver will set it to zero, the smallest feasible solution (given the sign restriction).

Deletetelasmosquiteira-sp.com.br

ReplyDeletetelas mosquiteira

telas mosquiteiro

As telas mosquiteira sp , telas mosquiteiro sp garantem ar puro por toda casa livrando-a completamente dos mosquitos e insetos indesejáveis. As telas mosquiteira garantem um sono tranquilo a toda família, livrando e protegendo-nas dos mais diversos insetos. Muitos destes insetos são transmissores de doenças e a tela mosquiteira é indispensável no combate a mosquitos transmissores de doenças.

A dengue, por exemplo, já matou centenas de pessoas só na capital de São Paulo e um pequeno investimento em nossas telas mosquiteiras podem salvar vidas. As telas mosquiteiras também impedem a entrada de insetos peçonhentos como as aranhas e os escorpiões, estes insetos também oferecem risco, pois seu veneno em poucos minutos podem levar uma criança a morte.

telas mosquiteira jundiai

telas mosquiteiro jundiai

telas mosquiteira aplhaville

telas mosquiteiro alphaville

telas mosquiteira granja viana

telas mosquiteiro granja vinana

telas mosquiteira cotia

telas mosquiteiro cotia

telas mosquiteira tambore

telas mosquiteiro tambore

A chegada da temporada Primavera/Verão traz consigo a elevação da temperatura e a maior ocorrência de chuvas. Mas não é só isso. As estações mais quentes do ano causam muita dor de cabeça e muitos zumbidos indesejáveis em função das pragas urbanas – pernilongos, baratas, cupins e outros insetos -, que afetam todas as regiões brasileiras.

Nossa missão é oferecer telas mosquiteiras de qualidade a um preço acessível, fazendo com que as telas mosquiteiras sejam uma opção viável para muitas pessoas.

telas mosquiteiras Jundiaí

telas mosquiteiro Jundiai

telas mosquiteiras jundiai

telas mosquiteiro industria

telas mosquiteira restaurante

telas mosquiteiro restaurante

telas mosquiteira empresa

telas mosquiteiro empresa

This comment has been removed by the author.

ReplyDeleteVery useful !

ReplyDeleteIt seems to work for several variables :

z0=max(a,b)

z1=max(z0,c)

z2=max(z1,d)

....

a,b,c have same bounds

Isn't it ?

Regards

Yes, you can "chain" max operations as you described, adding one binary variable for each $z_j$. You can equivalently start with one binary variable for each original variable ($w_a$ corresponding to $a$, $w_b$ corresponding to $b$, ...) with the constraint $w_a + w_b + ... = 1$ (exactly one variable is picked to be maximal), and similar upper bound constraints as before (where the original $w$ would now be $w_y$ and $1-w$ would be $w_x$). The lower bounds $L_a$ etc. would be as before, while the upper bounds would change so that, for example, $U_y$ in the first upper limit constraint would be replaced by the largest upper bound of any variable other than $x$, while $U_x$ would be replaced by the largest upper bound of any variable other than $y$. Either approach should work.

Delete