Hey everyone,

im trying to solve a vendor selection problem and want to implement a chance constraint that ensures that a supplier is only awarded if the probability that his transit time is below transittime_max is above a certain value.

(e.g. P(t*x = alpha )*

when t is normal distributed this equals meanx + inverrorf(1-alpha) * sqr((st.dev*x)^2)

(s. full model below)

my problem: there s no inverse error function in GAMS. Erwin solves this by doing a little model just do calculate the inverse. but i dont think this is applicable to my model.

anyone any ideas? i appreciate any kind of help

## cheers,

Nadine

\

scenario_builder_chance_constraint.gms (7.18 KB)

Nadine:

What about adding a variable and constraint

Variable inve inverse error function value

Equation invedef;

## Invedef… Errorf(Inve ) =E= 1-alpha;

And then use the variable inve as the inverse error function inside the rest of the model.

Remember to provide good initial values!

Good luck

Arne

\

Arne Stolbjerg Drud

ARKI Consulting & Development A/S

Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark

Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: adrud@arki.dk

From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of ShawnStein

Sent: Tuesday, July 08, 2014 10:53 AM

To: gamsworld@googlegroups.com

Subject: using inverse error function

Hey everyone,

im trying to solve a vendor selection problem and want to implement a chance constraint that ensures that a supplier is only awarded if the probability that his transit time is below transittime_max is above a certain value.

(e.g. P(t*x = alpha )

when t is normal distributed this equals mean*x + inverrorf(1-alpha) * sqr((st.dev*x)^2)

(s. full model below)

my problem: there s no inverse error function in GAMS. Erwin solves this by doing a little model just do calculate the inverse. but i dont think this is applicable to my model.

anyone any ideas? i appreciate any kind of help

cheers,

## Nadine

\

To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.

To post to this group, send email to gamsworld@googlegroups.com.

Visit this group at http://groups.google.com/group/gamsworld.

For more options, visit https://groups.google.com/d/optout.

–

To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.

To post to this group, send email to gamsworld@googlegroups.com.

Visit this group at http://groups.google.com/group/gamsworld.

For more options, visit https://groups.google.com/d/optout.

Nadine,

One idea is to use the relationship between the CDF of the standard normal and the error function: they are essentially the same, differing only in translation and scaling. An inverse CDF for the normal distribution is available as a GAMS extrinsic function (see Appendix J of the GAMS User’s Guide, “Stochastic Library”) so I’d guess that starting with the inverse CDF of the normal you can get the inverse for the error function.

-Steve

On Tue, Jul 8, 2014 at 4:52 AM, ShawnStein wrote:

Hey everyone,

im trying to solve a vendor selection problem and want to implement a chance constraint that ensures that a supplier is only awarded if the probability that his transit time is below transittime_max is above a certain value.

(e.g. P(t*x = alpha )*

when t is normal distributed this equals meanx + inverrorf(1-alpha) * sqr((st.dev*x)^2)

(s. full model below)

my problem: there s no inverse error function in GAMS. Erwin solves this by doing a little model just do calculate the inverse. but i dont think this is applicable to my model.

anyone any ideas? i appreciate any kind of help

## cheers,

Nadine

\

Steven Dirkse, Ph.D.

GAMS Development Corp., Washington DC

Voice: (202)342-0180 Fax: (202)342-0181

sdirkse@gams.com

http://www.gams.com