# Questions tagged [mixed-integer-programming]

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

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### Is there a name for this variation of the generalized assignment problem?

All the input variables are positive float (x > 0). We have $M$ agents with limited amount of time $t_1,\dots,t_M$, $N$ tasks $task_1,\dots,task_N$ associated with duration $d_1,\dots, d_N$. Cost ...
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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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### MIP Model with relaxed integer constraints takes longer to solve than normal model, why?

I am currently working on my undergrad thesis which is a mathematical optimization problem of the territory design family of problems. I am using the mathematical formulation of the problem to solve ...
1 vote
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### Assistance in formulating implication constraints for inequalities

I would like to seek some advice on modeling the following logical implications, where $\delta$ is a binary variable, $D_{j}$ and $A_{j}$ are nonnegative discrete variables, and $p_{j}$ are ...
1 vote
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### Plant Network model

I am looking for some help in Plant Network Optimization- as an example scenario would be to optimize the Plant network based on the below inputs and figure out best possible plants to use to service ...
1 vote
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### Traffic lights optimization (part 2)

This is a follow up question of this thread, in which it is asked how to model a circular layout of a given set of cliques of a graph, which represent simultaneous movements at an intersection. @...
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### Knapsack Constraint

Is the following expression a knapsack constraint? $\sum_i a(i) y(i) \ge W$, where $y(i)$ binaries, $a(i),W$ reals. What confuses me is the $\ge$ sign. Alternatively, do solvers generate cuts out of ...
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### How to identify which node is serving each customer?

I have a linear programming problem. There are two questions: Consider 2 centers (1,2) that should serve clients [s,b,c,t], What it the minimum distance cost. The formulation is straight forward. The ...
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### How to formulate an MIP so that a binary variable is 0 or 1 depending on whether another variable is nonzero?

I have a binary indicator variable $i \in \{ 0, 1 \}$ and an integer variable $c \in \mathbb{Z}$. I am trying to come up with a formulation in which $i = 0$ if $c = 0$ and $i = 1$ if $c \neq 0$. ...
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### Small negative decision variable returned in Gurobipy model

I have a multi-period model in gurobipy with 7 types continuous decision variables and 1 type of binary (Thousands indexed total). The model solves properly and the solution has passed many validation ...
1 vote
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1 vote
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### How to tackle online scheduling problems?

In scheduling problems, one usually has different options as objective functions (makespan, tardiness, etc). However, for any such type of scheduling problem one can consider an online version of it ...
1 vote
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### Fixing binary variables in an Binary Integer Program

I have a Binary Integer Program with two binary decision variables and additionally have an expected solution. At the time of execution of this program I expect the parameters to change slightly. I am ...
1 vote
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### Solver for Flexible Job Shop Scheduling Problem

I have a FJSSP that I would like to solve. However, the jobs in this problem have deadlines and in addition there are setup times between two jobs. Because of this, my objective function is not just ...
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### The linearization of the logical constraints

I know the logical constraints can be linearized by either the logical representation of whose relation, (for pure binary variables e.g. CNF/DNF) or for general form by using Big-M formulation. As I ...