Re: [Fwd: GLPK doubt]

[Manuel Muñoz Márquez]

Dear Nicolas,

El jue, 08-02-2024 a las 01:39 +0300, Andrew Makhorin escribió:
> -------- Forwarded Message --------
> 
> Date: Wed, 7 Feb 2024 16:17:04 -0300
> Subject: GLPK doubt
> To: help-glpk@gnu.org
> From: Nicolas Herculano Pires <rgm47164@comp.uems.br>
> > Dear esteemed GNU colleague,
> > 
> > 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. 

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

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

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

> > 
> > One might inquire, "But what if no month is selected?" In such instances, 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.
> > 
> > I am keen to explore any insights or guidance you may provide on this 
> > matter. Your expertise and assistance in optimizing the
> > utilization of GLPK would be immensely appreciated.
> > 
> > Warm regards,
> > Nícolas Herculano

Manuel