Questions tagged [operations-research]

Operations Research, sometimes known as Management Science or Decision Science, is the discipline of applying appropriate analytical methods to help those who run organisations make better decisions.

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Why should we minimize the sum of artificial variables in $2$ phase method? [closed]

In Phase $I$, if the LP is of the maximization type, why we do not maximize the sum of the artificial variables in Phase $I$?
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A profit-maximizing farmer [closed]

A farmer has several hectares of land on which, corn, tomatoes, or peas can be grown. The gross income resulting from planting 1 hectare of each crop is shown below, together with the hours labour, ...
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Converting primal to dual

\begin{align} &\text{minimize } &z = 7x_1 – 4.2x_2 – 2x_3 + x_4 \\ &\text{subject to } &x_1 + 2x_3 + 2x_4 &\leq 20 \\ &&x_1 + 2x_2 &= 18 \\ &&x_1 + 2x_3 – 3x_4 &...
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Is there a meaningful additive risk measure

An important property of coherent risk measures is subadditivity. But are there any additive risk measures that can be used in a meaningful way? (I would exclude the expectation for example)
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What are the sample points in sample space? What is the random variable?

As we know that interarrival time in queueing theory follows exponential distribution. I want to know what are the sample points and what is random variable corresponding to interarrival time? As ...
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I need to diving multiple sets of numbers by another set of numbers, as exactly as possible (as little waste as possible).

I'm working in Excel and I have 2 separate lists. On the first is final length of goods to be cut, and how many of a given length. And on the second is manufactured lengths of goods (the lengths we ...
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What is the steady state probability?

A lot of board games involve rolling dice and moving around a cyclical board. Monolopy is the most common example. On the 16 position board below, the player’s piece was on the bottom row as depicted ...
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1answer
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Maximizing Coverage of Area by Spreading Mobile Sensors Around

I have come across the paper that deals with spacial positioning of mobile sensors to optimally detect sound source, or position mobile cellphone towers to maximize the coverage. The region $Q$ is ...
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Need help formulating an event scheduling problem involving multiple clients and class types

I run training classes. A "B" class, a "C" class and an "Adv" advanced class. B classes run every saturday, take 3 hours, and have a maximum 4 clients. C classes follow B classes and take 2 hours. ...
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Finding Linear programming optimal solution.

Consider the following linear program: max $z = 4x_1+x_2+5x_3+3x_4$ subject to $x_1-x_2-x_3+3x_4 \le 1$ $5x_1+x_2+3x_3+8x_4\le55$ $-x_1+2x_2+3x_3-5x_4\le3$ It is claimed that the solution $x^*=(0,...
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Find simplex tableau using basis

Consider the following LP problem. $maximize$ $ 10x_1+12x_2+12x_3$ $subject$ $to$ $x_1+2x_2+2x_3+x_4=20$ $2x_1+x_2+2x_3+x_5 = 20$ $2x_1+2x_2+x_3+x_6=20$ $0\leq x_1,x_2,...x_6 $ Suppose we are ...
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Minimisation of the Number of Questions for 160 Papers [duplicate]

An exam centre is going to prepare question papers for 160 students where each paper has 9 questions from 9 different topics (one question per topic). They can allow upto 2 collisions, i.e. at most 2 ...
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Assignment problem cost matrix reconstruction justification

I have asked questions numerically on this topic, but here is a theoretical question that i want to ask, if the answer is affirmative, then only can i proceed with my problem. I have an assignment ...
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Integer program for minimizing maximum Lateness with precedence constraints

In studying for an upcoming exam the following problem came up: Write an integer program to: minimize the maximum Lateness for the one machine scheduling problem with precedence constraints and ...
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Confusion regarding worst case robust optimization

In a book, for an uncertain matrix $A(u)=A_0+u \cdot A_1$; where $u \in R$ is an uncertain scalar between $[-1,1]$, a robust form of the least square problem: $\sup_{-1\leq u \leq 1} ||A(u)x-b||_2$ ...
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Job Shop Scheduling Classification

I am searching for literature that might exist on my problem. I can't imagine that there is none. I think i am just not hitting the right search terms. Maybe someone knows what name my problem might ...
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Optimisation Algorithm

I am facing an optimisation problem, I would like to have you advices on the methods I could use. Let's suppose a town reprensented by a Polygone. The town contains n points (addresses) according two ...
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How to express this requirement in linear programming

I am trying to solve the following linear program. In this program, I am given a set $X$, and I have to minimize the costs of elements $x \in X$ using a real-valued function $f:X \rightarrow \mathbb{R}...
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3 Toast Problem From “Thinking Mathematically”: Solution Check

I am working through "Thinking Mathematically" by Mason, Burton and Stacey. One of the questions goes as follows: Three slices of bread are to be toasted under a grill. The grill can hold two slices ...
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Need help in formulating linear program

Can anyone explain the following passage? Both semiconductors and power generation industries also want to buy as many of the remaining units as possible How should I formulate the linear program ...
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this question is related to operation research .( facility location problem)

This is a conceptual facility location problem. I want advice on how one would approach it. We have 20 stands, each plotted on a 2d map. Each stand demands a certain # of apples per year. We are ...
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Problem solving a linear program using Excel

First of all, if you think this problem belongs on a different stack exchange, I am happy to move it. The exercise is as follows: ACI has decided to put an order for golf shoes twice every year and ...
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graphical method in game theory

Solve graphically the following game: $\begin{array}{ccc} &&B1&B2 \end{array} \\ \begin{array}{c} A1\\ A2\\ A3 \end{array} \left[ \begin{array} {cc} 3&-2 \\ -1&4 \\ 2 &2 \...
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Construct a linear programming problem to maximize the profit below

The question goes as follows- A company makes a specialty solvent at two levels of purity, which it sells in gallon containers. Product $A$ is of higher purity than product $B$, and profits are ...
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Linear Programming - Minimizing the maximum distance between a location and its closest school

I'm working on a linear programming project currently and I've run into some problems. The main idea of the project is to look at a section of a city and, using the schools that already exist in the ...
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Parallel machines problem and minimal machines

Given $n$ jobs where job $i=1..n$ starts at $a(i)$ and finish at $b(i)$ find the minimal machines that needed to finish all the jobs. Find the a rule for a solution and prove it's correctness. I came ...
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Dual of quadratic program

Given this problem $\min c^Tx + \frac{1}{2}x^tHx$ subject to $b \leq Ax \leq b+r$ $l \leq x \leq u$ by adding slacks the subject becomes: $Ax - w = b$ $x - g = l$ $x + t = u$ $w + p = r$ $g, w, ...
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Question Involving Golden Search Method and Fibonnaci Search Method theory

Hello, I am really struggling with this question. I (think) I have found the solution to the first constraint for a. Basically that the T(b-a) where 0 less than T less than 0.5 gives me the first ...
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Solving for an optimal policy in an infinite-horizon and finite-state-space MDP with expected average reward

I've just jumped into this area, and I was told that average reward criterion could make things slightly more difficult comparing to the usual discounted reward criterion. I will really appreciate if ...
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Vectorized Scalar | Is there such thing?

Ok, So I am trying to look for the branch of mathametics that deals with scalar property such as surface which shows vector like qualities. So for analogy I am looking for a scalar area such that any ...
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Handling Uncertainty with Budget Constraints in Robust Optimization

Let's say I have a linear optimization problem with some uncertain parameters Case 1: Uncertain Parameters are present independently in different constraints $$maximize\ x_1+x_2$$ $$ax_1+bx_2\leq 6 ...
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Within some points on a 2D-plane, find one point that is less than “P” away from each point.

If there are 10 given points on a 2d plane, how would one find a final point who's distance is less than P in distance away from each given point? Assuming such a final point exists, a final point ...
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Operations research : minimize the absolute value instead of square

I am working on an operations research problem In a previous work, they minimized the square of a-b : min sum (a-b)² I would like to work on a linear problem, by minimizing the absolute value of (a-b)...
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Maximin and savage's rule.

I'm struggling with this question, my lecture notes don't help me much, and when looking online the information is slightly confusing, so here's the question. Consider the situation described in ...
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How to solve the optimality equation? (Markov decision process)

I'm struggling with this problem I have to solve, I have attached the problem below. I have done some questions that are similar but I have given simple values for 'a' and 's'. If someone could help ...
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How to find the minimum $z$?

Solve: Minimize $z = 2x_1 + 3x_2$, such that $x_1 + x_2 ≤ 4$ $3x_1 + x_2 ≥ 4$ $x_1 + 5x_2 ≥ 4$ and such that $0 ≤ x_1 ≤ 3$, and $0 ≤ x_2 ≤ 3.$ My attempt : From $x_1 + x_2 ≤ 4$ ...
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Simplex Method Optimization

For part D of question 1: How do we know which column to pivot next? In my understanding I need to make all the numbers in top row positive, so I would go from the most negative number (-6), find the ...
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difference between intersecting, weakly and crossing supermodular functions

Am reading some texts on algorithms and I am confused with the differences between these definitions I read in several texts. Given a set $V$, we have these types of set functions $f:V \rightarrow \...
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How to find the optimal value of $z$?

Consider the linear programming Problem : Maximize $ z=5x +7y$ such that $x-y \le 1$ $2x+y \ge 2$ $x+ 2y \le 4$ $x \ge 0,$$ y \ge 0$ what is the optimal value of $z$ ?...
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How can I reward diversity in an objective function in integer programming?

I am building a staff scheduling model that has a set of binary variables $x_{[i,j]}$, subject to some set of constraints, where $x_{[i,j]}=1$ when person $i$ is assigned to job $j$. So far my ...
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Switching the solutions in linear programming.

Reduce the feasible solution $x_1=2,x_2=1,x_3=1$ for the linear programming problem $$ \begin{split} \max\ & x_1+2x_2+3x_3\\ \text{subject to }\ & x_1 - x_2 + 3x_3 &= 4\\ ...
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Find all degenerate basic feasible solution of the system

$$x_1 + x_2 + x_3 = 3$$ $$x_1 − x_2 + x_4 = 0$$ $$x_1, x_2, x_3, x_4 ≥ 0$$ How should I proceed it ? Should I convert it to 2-D like this $$x_1 + x_2 \leq 3$$ $$x_1 − x_2 \leq 0$$ ? What would be my ...
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Find the degenerate basic feasible solutions

Find the degenerate basic feasible solutions for the polyhedron $$x_1 + 4x_2 ≤ 8 ;$$ $$x_1 + 2x_2 ≤ 4 ;$$ $$x_1, x_2 ≥ 0.$$ Does degeneracy depend on the representation of the polyhedron?
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Number of solution of an LP with Lagrange

Consider the following problem: $$\min_{x \in \mathbb{R}^n}f(x)=c^Tx$$ Subject to $ Ax=b$, where $A$ is full rank. Without any positive requirements (for instance, $x\ge0$), I want to show the ...
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How to model restrictions for nurse scheduling problem to maximize days off in a fair way for all nurses?

I have the following problem. I want to plan a daily schedule of employs who provide services for some company and I want to organise it in such a way that the number of consecutive days off for each ...
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Aggregate production planning

I'm looking for a optimization model about production planning that takes the following into consideration: Single site Multi products One machine/resource Sequence dependent Fixed batch size ...
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Minimum cost in consulting company problem

I would like to know how could I solve this following problem, I am trying to find a solution but don't know what to begin with: A consulting company estimates its business for the next five ...
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Why are ties irrelevant in Weitzman's Optimal search for the best alternative

This question concerns the 1979 paper "Optimal search for the best alternative" by Martin Weitzman. The setup is as follows: There are $m$ boxes containing finite-expectation rewards $x_i \sim F_i$...
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2answers
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Understanding linear optimization better?

I'm taking a linear optimization class, and I'm having a difficult time formulating an 'integer program' from a problem. My main problem is taking given information (often tables), how do I declare ...
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How can I write this in proper mathematical equation?

I'm working on an optimization problem, but I'm not sure how to write this constraint correctly. I have several servers (e.g., S1, S2, S3, S4...) and some Virtual Network Functions (e.g., V1, V2, V3....

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