# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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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 ...
264 views

### To which area does constraint programming belong?

The problem I solved is a flow-shop scheduling problem with parallel machines. I solved it with the IBM ILOG CPLEX Optimization framework. There I used the constraint programming (CP). The question ...
609 views

### A variant of the Shortest Path Problem

Consider a layerwise directed acyclic graph DAG, $G=(V,E)$ and two vertices $s$ and $t$. $s$ is connected to all vertices in $L_0$, $L_0$ is connected to all vertices in $L_1$ and so forth. Consider ...
203 views

### Could reserving a hotel room potentially lead to a suboptimal allocation of rooms?

Suppose you have a standard hotel with a set of rooms. If you have booked a room for a fixed period of time, would allocating a specific room in advance potentially cause a conflict when trying to ...
132 views

### Partial derivative of LP solution $(x_1 , \ldots, x_n)$ w.r.t. $x_i$ or $a_i$

Suppose I have an optimal solution and I want to know how the solution would (likely) change if one of the coefficients in the objective function changes, or if I add a constraint that forces $x_i$ ...
186 views

### Profit Maximization vs Cost Minimization for Employee Scheduling

I wanted to write two objective functions for an employee scheduling problem (MIP) until it occurred to me, that one objective function may be redundant. Is there a difference between the cost ...
1k views

### Reading an LP/MPS file using Pyomo software

I would like to know is it possible to read an LP/MPS file into the Pyomo software and solve the problem? If so, how can I do that?
151 views

### When should I use a solver for IP and MIP and can I just use a library from Python, R, Matlab, etc…?

Are there any rules of thumb for figuring out when you need to use a solver like Gurobi or CPLEX, and when you can just solve you problems directly with a Python, R, or Matlab package? Is it just a ...
396 views

### Finding minimum time for vehicle to reach to its destination

Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
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### How to classify and model this problem?

I was given the task to model the following problem and find a solution for it, but as I do not have any experience in this field, I already have trouble classifying it. There are a number of ...
83 views

### Calculating robustness of layout plans

We have tried to design a manufacturing cell which will produce specific families of products. We figure out three layout plans for implementation. For practical reasons, we need to calculate the ...
1k views

### How to formulate problems in the language of mathematical programming?

The question says it all. I am having difficulties formulating general problems (meaning no numbers just variables). When I read the solution, I understand but I can't figure how to formulate myself ...
2k views

### How to convince people that OR can help them?

When talking to people who are not familiar with what OR is and what it is about, and you want to convince them that it might be useful for them/their industry, what do you tell them in order to ...
1k views

### Open source MILP solver for quick “good enough” solution

I have a problem that I have already posted elsewhere in OR.stack, but the question is focused around a large binary MILP (about 1 million decision variables). Ultimately, I am more time constrained ...
622 views

### Bin packing variant

I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
299 views

### How can I transform this MILP into an LP problem?

I have a MILP problem with one of the constraints is given below. Sometimes, even for a small-sized problem, the solver takes a very long time to find a solution. What could be an efficient ...
179 views

### Difference between “Optimization” and “Constrained Optimization”?

(Another OR noob question) As I'm trying to learn about OR and Optimization methods for work, I'm having a hard time understanding the difference between "Optimization" and "Constrained Optimization"...
726 views

### Difference between exploration and exploitation in Simulated Annealing algorithm

In evolutionary algorithms, two main abilities maintained which are Exploration and Exploitation. In Exploration the algorithm searching for new solutions in new regions, while Exploitation means ...
414 views

### Is there a greedy heuristic approach to the MILP problem?

I have the following optimization problem which is an MILP. I can solve it with an MILP solver. \begin{alignat}{1}\max_{x_n,t}\,&\quad t\quad\\\text{s.t.}&\quad\sum_{n=1}^{N} x_n \,&= M\\...
230 views

### Standard cumulative distribution function with optimization model variable

We all know that expressions in mathematical optimization models can't contain "black boxes" around a decision variable since everything has to be written using mathematical expressions. For example, "...
773 views

### Excel Solver linear programming - Is it possible to use average of values as a constraint without #DIV/0! errors or sacrificing linearity?

I'm trying to create an assignment optimization model where the areas are assigned to either the south or north school districts so that the total distance is minimized. Each school must have at least ...
592 views

### Travelling salesman problem with given number of locations to visit

There's a great example here of how to find a solution to the travelling salesman problem: ...
1k views

### How to linearize a constraint with max

I would like to linearize a constraint with max. I have the following constraint: $$\max_{pcj}X_{pwcj}\leqslant L_{wk}.$$ With this constraint, I would like to ensure that for $\forall w \in W$, no ...
180 views

### Can Gurobi or CPLEX handle nonlinearly constrained problems?

Though my title is quite general (please feel free to edit), indeed, I wonder if the following models can be solved in Gurobi or CPLEX. Model 2 is just an alternative one to Model 1. Although we ...
222 views

### GLPK: meaning of the "marginal' column in the solution output

I'm using GLPK to solve an LP. I use it through its standalone solver, that I call with the glpsol command, and I get the solution detail written in a file using ...
169 views

### Specific filter on the set using Python

I'm trying to write an optimization model using an open-source solver's Python API. I'm new to use Python. The model objective function is as follows: \begin{equation} \sum_{k=1}^{K} \sum_{j=1}^{n}\...
252 views

### Disciplined convex programming representation of $x\cdot\min x$

How can I reformat the problem below to follow DCP rules? DCP rules are Disciplined Convex Programming Rules that allow convex programs to be solved. DCP Is there a way to reformat the problem ...
160 views

### Modeling Linear Program to decide if an inequality is facet

Suppose you have a set of points $v_1,\ldots,v_n$, which are the vertices of the polytope $P=\operatorname{conv}\{v_1,\ldots,v_n\}$ and a linear inequality $a^\top v \leq b$. What would be a linear ...
320 views

### if-else condition for the objective variable using big M notation

Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$. Now, how can I impose the following? if $\beta_{i,j}>0$ then $\beta_{j,i}=0$ Big M notation can be ...
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### What are Operations Research applications for 'morally discussable causes'?

Out of curiosity, since I read this question What are Operations Research applications for 'good causes'? and thought it might be a good addition to it. What are Operations Research ...
297 views

### How to resolve this issue in multi-objective optimization?

I have the following multiobjective optimization problem. The objectives are non-conflicting. The Optimization Problem: \underset{\large{a^{(l)}_{c,u},f^{(l)}_{c,u},z_{l,t},l\in\mathcal{L}}}{\max}\...
147 views

### Heuristic Search Planning Tree Leading to Worse TSP Solutions than Naive Greedy

I'm doing a Traveling Salesman Problem (TSP) homework for a coursera optimization course. My first attempt was a regular naive greedy approach, from each point, moving to the closest node (that hadn't ...
I have this problem described in natural language, and I was wondering whether it is relatable to any known problem. I have a directed acyclic graph. Each node can host a "probe". If node $i$ hosts ...
I am minimizing $f(x_1,x_2) = 100(x_2-x_1^2)^2 + (1-x_1)^2$, where I try many algorithms to compare with each other. All of the algorithms find the optimal solution $(1,1)$ quickly, so I am not ...