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1500 questions
8
votes
1 answer

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, "yes/no" decisions can't be written as "if this…
V. Brunelle
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8
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Understanding why this MINLP formulation is infeasible

Algebraic Formulation - Note: All parameter values are subject to change, I have just used the numbers you see here as place holders for the time being. Additionally, there are a few other equations but I am highly confident that they are not…
GrayLiterature
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8
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2 answers

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 matter the values of $p$, $c$ and $j$, the max…
campioni
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8
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Extract info from Gurobi binary variables during run-time

Actually the question below is not specific to Gurobi, but that's the tool I am using. Consider a scheduling problem where a 2D array of binary variables $Z(i,v)$ is defined, where $i$ is index of time slot, and $v$ is index of operation, each…
user22363
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8
votes
3 answers

Maximize assigned tasks to each worker

In a scheduling problem I want to assign the maximum number of tasks to one worker before assigning it to another. For example, if I have $10$ tasks and $2$ workers, the best assignment would be $(10, 0)$ and the worst $(5, 5)$. I have tried the…
Stradivari
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8
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1 answer

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}\left(f_{k}+c_{0, j}^{k}\right) x_{0,…
A.Omidi
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8
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2 answers

Does the API affect the time Gurobi requires to find an optimum?

When working with Gurobi, CPLEX and the like the user can choose between many different APIs, for example Python, C++, R, Java, Matlab or C. Some of these API are more efficient than others. For example, in R the user does not need to declare any…
YukiJ
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8
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3 answers

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": Isn't any real world optimization problem…
Skander H.
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8
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1 answer

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}\hspace{6mm}\left\{t^{(l)}_{\rm…
KGM
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8
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1 answer

Understanding the AMPL Solver LIbrary within Pyomo

For anyone familiar with the Pyomo book, it occasionally makes reference to the AMPL Solver Library, and to my understanding, if you can manage to hook up to the solver library then you are able to use those particular solvers. However, I am…
GrayLiterature
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8
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1 answer

How to model 24 hours demand into a daily shift schedule?

I am working on a weekly staff scheduling optimization problem with 24/7 demand. The binary decision variable is: $X_{\text{staff},\,\text{day},\,\text{shift}}$ whether to assign the staff $s$ to day $d$ shift $\text{sh}$. There are several shift…
janicebaratheon
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8
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1 answer

Why is the Ellipsoid Method of polynomial complexity?

We know that the ellipsoid method is proven to be of polynomial complexity. However, as far as I can tell we may need to add exponentially many feasibility cuts in order to solve the LP (or prove no solution exists), which results in a…
Nikos Kazazakis
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8
votes
1 answer

Convergence rate value iteration

Value iteration is one of the most commonly used methods to solve Markov decision processes. Its convergence rate obviously depends on the number of states and actions. However, the convergence rate also largely varies between different MDPs with a…
Michiel uit het Broek
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8
votes
1 answer

Workforce Scheduling problem - Modelling to minimize resources

I am working on a scheduling program for a service desk. I want to decide the number of people required to come in at each shift. The data I have is: There are 4 overlapping shifts Arrival pattern at the hour level Each defect has a 24 hr to…
8
votes
1 answer

Strategy for filling a table only slightly dependant on the number of columns

I'm using the OR-Tools CP-SAT solver to fill a table with integers, with various constraints, as illustrated by the x in the following figure. | | A | B | C | D | E | | 1 | x | x | x | x | x | | 2 | x | x | x | x | x | | 3 | x | x | x | x | x | |…
Blackhole
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