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.
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?
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.
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