# 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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### Is there any way to use Lazy constraints in Pyomo?

I would like to know if there is any way to implement a Lazy constraint in the Pyomo package. (As far as I know, the only way to implement such a constraint is by ...
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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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### Gurobi - Is finding a feasible solution when optimizing a lot harder than finding a feasible solution?

The code is working fine but I feel as my intuition could be wrong. I first set up my problem as: $$\min_{f(x)\leq F} g(x)$$ and gurobi was unable to find a feasible solution. I then relaxed ...
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### Continuous optimization with a Euclidean TSP objective

I am trying to solve a problem of the form $$\min_{x_1,\dots,x_n} f(x_1,\dots,x_n)$$ subject to a constraint that $\mathrm{length}(\mathrm{TSP}(x_1,\dots,x_n))\leq c$, where $x_1,\dots,x_n$ are all ...
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I am playing around with some Quadratic Programs (QPs), and I want to check if my reasoning is right concerning a re-modeling from QP to MILP. So, let's consider the below QP: (QP) $\min c^T x + x^T Q ... 3 votes 0 answers 132 views ### Creating Disjunctions for MIP Model. Code taking too long to execute I am currently following this guide in the hopes of building a linear programming model in python and solving using gurobi. https://towardsdatascience.com/schedule-optimisation-using-linear-... 3 votes 0 answers 56 views ### Separating two LP solutions at the same time In a cutting plane algorithm for integer linear programming problems you would usually use an LP solver to get an extreme point of the polyhedron corresponding to the LP relaxation. Let's call that ... • 6,552 3 votes 0 answers 135 views ### When and where the cutting plane method should be applied? As the cutting plan algorithm is a method to strengthen the feasible space of the linear programming, specifically in the MILP problems to invoke the integer solutions, it may be a problem-based ... • 8,950 3 votes 0 answers 54 views ### PWL constraints efficiency So, I'm trying to optimize MILP, which has PWL constraints. I use gurobi, and when I'm optimizing model without those constraints, gurobi finds solution in a matter ... • 161 3 votes 0 answers 56 views ### Indeterminacy Reduction for MINLP I am considering a Mixed Interger NonLinear Program (MINLP), and using a solver to obtain admissible solutions. Is there a general method to reduce indeterminacy of solutions (e.g. by adding ... • 424 3 votes 0 answers 109 views ### Polynomial Time Solution For a Mixed-Integer Linear Programming Specific Case Consider the following mixed-integer linear programming (MILP): \begin{equation*} \begin{array}{ll@{}ll} \text{maximize} & 1 & \\ \text{subject to}& x_{i} \geq 0, &i=1 ,\dots, m\\ ... 3 votes 0 answers 124 views ### Mathematical model complexity Vs Time Complexity of the model As far as I know, when we talk about the term of complexity, it referred to the time complexity of the model in which how long does it take to solve a specific mathematical program by a specific ... • 8,950 3 votes 0 answers 97 views ### Extract/Inject Solutions (orig problem-space) during Search in MILP -> CoinOR Cbc Task / Goal I'm considering adding some customized problem-specific local-search component on top of a general-purpose MILP solver (= improvement heuristic). The basic idea is the following: All new ... • 527 3 votes 0 answers 139 views ### Harvest planning problem I need to model the following problem: For a planning horizon of$P$equal periods, one has$N$harvesting locations and$K$contractors who can harvest at those locations ($K < N$). Each ... 3 votes 0 answers 450 views ### In binary linear programming, what's the relationship between the dual solution and the lagrangian multipliers? In my optimization problem the objective function and all the constraints are linear. The decision variables are binary. [so, it's BLP] Some of the hard constraints are very time-consuming to be ... 3 votes 0 answers 96 views ### Resource scheduling problem with synchronization constraints: Weak LP relaxation I have a resource assignment/scheduling problem which involves assigning jobs to$m$workers. There are 2 sets of different jobs,$J^1$and$J^2$, and a set of periods$T$. Let$d_{jt}$be the number ... • 3,451 3 votes 0 answers 76 views ### Linearization of a quadratic model, what is the difference while using gurobi? I have a quadratic model of parking$N$cars in$S$separate lanes as follows. Each car has an arrival time and a departure time. Departure follow the last in first out principle. The objective is to ... • 521 3 votes 0 answers 53 views ### How to formulate a storage component? Letās say I have a drink for several customers, and I know their demand. Besides, I also have a storage tank for the drink during times when demand exceeds supply. The storage tank's size is not yet ... • 517 3 votes 0 answers 228 views ### Solving a nonlinear model with constraints of exponential functions and continuous variable multiplications I have a nonlinearly-constrained model and wonder if a nonlinear solver like Ipopt or Knitro can solve the problem. Briefly, my objective function is linear. I have the following variables with their ... • 1,249 3 votes 0 answers 89 views ### PuLP Python: How to linearize an inequality involving an integer variable I am working on a Copper payables problem where the objective function is to maximise the sum of copper payable over a time period, T. The total amount of payable tonnes i.e. what the customer will ... • 327 3 votes 0 answers 90 views ### Linearization of the shifted copy of a function Suppose in a model I have the expression$y_{1}(x) = 10 + 5 x^2$where$x \in [0,20]$is a continuous variable. In order to be able to use an MILP solver, I piecewise linearise$z_{1} = x^2$, by ... • 2,252 3 votes 0 answers 62 views ### Linearisation using SOS2 I am trying to linearise the following expresssion.$C(k) = B(k) e^{-d(k)}, B(k) \ge 0 , d(k) \ge 0 $I am trying to do this by using SOS2 sets. I set$X(k) = e^{-d(k)}$and I get$C(k) = B(k) X(...
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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 $c$ ...