Re: [Fwd: GLPK doubt]

Dear Nicolas,

El jue, 08-02-2024 a las 01:39 +0300, Andrew Makhorin escribi=C3=B3:
> -------- Forwarded Message --------
>=20
> Date: Wed, 7 Feb 2024 16:17:04 -0300
> Subject: GLPK doubt
> To: [email protected]
> From: Nicolas Herculano Pires <[email protected]>
> > Dear esteemed GNU colleague,
> >=20
> > I hope this message finds you well. I am writing to address an issue I =
have encountered with GLPK, albeit it may seem trivial, it
> > remains a pertinent concern. I am currently grappling with GLPK in the =
context of solving an optimization problem, specifically
> > pertaining to portfolio project selection and scheduling.

You have a decision problem if and only if you have decision variables.=20

> >=20
> > My dilemma lies in the utilization of GLPK without employing decision v=
ariables. Allow me to elucidate further: I am employing GLPK to
> > tackle a portfolio project selection conundrum encompassing 200 project=
s over a planning horizon of 60 months. However, I have been
> > unable to find any resources or documentation on how to utilize GLPK wi=
thout employing decision variables.
> >=20
> > You may wonder, "What is the significance of reducing these variables t=
hrough GLPK?" The essence of my inquiry lies in the potential
> > reduction of variables. To illustrate, envision a scenario where each o=
f the 60 columns represents a month, and among these, only one
> > column is selected per project. This leaves the remaining 59 columns re=
dundant. Consequently, would it not be more efficient to
> > represent the selected month with a single indicator column, rather tha=
n allocating separate columns for each month?

Do you know in advance the column that represents each project? If the answ=
er is yes, then you can use only one column per project.

> >=20
> > For instance, if GLPK selects column 30 (corresponding to month 30), th=
e preceding columns (1 to 29) and subsequent columns (31 to 60)
> > would inherently hold values of zero, rendering them unnecessary. There=
fore, it seems logical to streamline the representation by
> > condensing the 60 columns into a single indicator column denoting the s=
elected month.

You said "if GLPK selects column 30" this means you have to have a variable=
 to indicate if a column is selected or no, isn't it?

> >=20
> > One might inquire, "But what if no month is selected?" In such instance=
s, I propose to designate a value of zero to indicate the absence
> > of a selected month, effectively reducing the total number of variables=
 from 12,000 to a mere 200.
> >=20
> > I am keen to explore any insights or guidance you may provide on this m=
atter. Your expertise and assistance in optimizing the
> > utilization of GLPK would be immensely appreciated.
> >=20
> > Warm regards,
> > N=C3=ADcolas Herculano

Manuel