# Questions tagged [mixed-integer-programming]

For questions about mathematical optimization problems involving both continuous and binary or general integer variables.

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### which method has been used to automatically reformulate logical constraints in a standard MIP solver?

There are many of the formulations to linearize logical constraints by introducing new auxiliary binary or any appropriate variables and adding the corresponding constraints to the model. It can be ...
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### Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
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### For subset selection regression as a mixed integer program, how tightly should the bounding box be set?

When solving best subset regression as a mixed integer program, how do you decide how tightly to bound the range of values of the $X$ values? When the box is tight, the solver finds a solution ...
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### MIP formulation for graph planarity test

In this question, it was asked wether a MIP formulation exists to test for a graph's planarity. The inputs are the graph's nodes and edges, and the output would be a certificate which guarantees that ...
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### Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
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### Modelling a simple ordering problem to have balanced delivery days

Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
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### Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
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### Issue of Dense columns in the formulation

I'm working on a price-selection model where we need to identify price point for each time-period (could be day/week). Objective of the model is to figure out optimal price-point for each time-point ...
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### Water quality component optimization

I have an optimization problem that I'm attempting to tackle. As you can see in the image below, there's a graph network through which water flows. I've drawn out the problem in the image to explain ...
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### What are useful plots/statistics/metrics when analyzing the solution sensitivity in multi-objective optimization?

Consider an optimization problem with $n>3$ objectives. For handling this there exists often two approaches: a) some weighting of the objectives, b) fix an order of objectives and then optimize ...
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### cvxpy: Code that works for default solver doesn't work for cp.GLPK_MI

The following code works: ...
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### Publishing paper that uses LP solver to solve equation

I was reading this paper by Cerna et al. (2018)1. In the paper there are only CPLEX-solvable equations given by the authors and the results. How valuable is this paper, and what is its quality? Can ...
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### Integer variable optimization - decreasing execution time

I have a variable declared as follows in AMPL: ...
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### Discrete optimization in transport economics

I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ ...
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### Modelling Question

Let $W^C_t$, $W_t$ be binary variables and $p$ an integer variable with $1 \leq p \leq 3$ The variables are related through the following equation: $$W^C_t = \sum_{\theta=1}^{p} W_{t-\theta}$$ I can ...
Suppose, there exists a scheduling problem $S$, in this case a single resource, with the following descriptions:  \text{conv(S)} = \{x \in \mathbb{R}^n \ | \ \forall \lambda_{i} \in \mathbb{R}^{n+}, ...
I am working on the directed graph by using the Networkx package and what I need is to use its predecessors' method on an optimization model. Let's say, there exists a directed graph with just $12$ ...