is a discipline to apply analytical methods for better decisions. It has many synonyms such as management science, decision science and system science.

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2
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1answer
18 views

Graphs with weighted edges and vertices

I am considering a route planning problem, which I try to model with a graph. I understand that 1. to find a shortest path in a graph, we need to know the weights on the edges. 2. as some places are ...
0
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0answers
11 views

Reliability Theory Problem , Operations Research

Suppose the time to failure of a device follows Uniform distribution on (0,2) (in years). Find the conditional probability that the device will fail in 1.05 years given that it worked 1 year.
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0answers
20 views

Primal/Dual Simplex methods clarification

I have several questions regarding these methods. Primal Simplex Method Does the pivot element always have to be a positive entry in the table? Does the RHS always have to be positive in the pivot ...
0
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0answers
22 views

What is a Hungarian forest: definition

I have a doubt in the definition of the Hungarian forest. This is from the book Matching theory by Lovasz. Let $G$ be a bipartite graph with partite sets $A,B$ and let $M$ be a matching of $G$. Let ...
0
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1answer
44 views

How to configure simplex method to start from a specific point

If I have a linear programming problem e.g. $$\max 2x_1 + x_2$$ with these constraints $$x_1-2x_2 \leq 14$$ $$2x_1-x_2\leq 10$$ $$x_1-x_2 \leq 3$$ And I want to solve the problem starting from a ...
0
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1answer
27 views

Canonical form simplex method

In 2-phases simplex method what kind of operations must be done to get the canonical form tableau? In this step(phase 2 of 2-phases method) after the remotion of artificial variables columns of ...
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0answers
26 views

Do corner points optimise a linear function over a bounded convex region?

This proof says if $Z_P \ne Z_Q$, then $Z$ is maximised (or minimised, I guess) at one of the endpoints -- of what exactly? $\overline{PQ}$? So the maximum value of $Z$ occurs at either $P$ or $Q$? ...
0
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0answers
22 views

Do we need nonnegativity in this proof on convexity of a feasible region in an LP problem?

Is the $\color{red}{\text{non-negativity constraint (see red box)}}$ used at all in the proof? If so, where? If not, does the proof then hold for a standard LP problem without the non-negativity ...
-1
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1answer
14 views

Optimization Problem Maximize $z= 60x_1+20x_2$

Restate the absolute value constraint as a combination of two linear constraints: I know how to find the optimal solution (std form, canonical form, simplex algorithm ...etc) I don't know how to put ...
0
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1answer
42 views

Polytopes defined by $x_i >=0, Ax = b$ are generic ? (Understanding simplex method)

Consider polytopes in $R^n$ defined by $x_i >= 0, Ax = b$, for $b > 0$. Assume $A$ is of full rank $r$ and $Ax=b$ has solutions. The following properties seems to be correct. I would be ...
0
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1answer
113 views

Normalized objective function in optimization problem

I have fairly standard linear optimization model with two objectives \begin{align*} \text{max}\, (f_1 &= 4x_1+5 x_2\,,\,f_2 = 1x_1 + 0x_2 ) \\ \text{subject to}& \\ 1x_1 + 1x_2 ...
4
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1answer
45 views

Exercise 2.27 from Bazaraa (LP)

Consider the system $Ax=b$ where $A=[a_1,a_2,...,a_n]$ is an $m \times n$ matrix of rank $m$. Let $x$ be any solution of this system. Starting with $x$, construct a basic solution. There is a hint ...
0
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1answer
31 views

Linear Programming Free Variables

I am using a book called Introduction to Operations Research. I'm not sure how to deal with free variables that are not constrained i.e. they could be positive or negative. I understand how any ...
0
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0answers
19 views

selecting N integers with constraints

I need to write a program which takes 4 inputs as follows N = The number of integers to be generated ($10 <$ N $< 10000$) Start = The minimum value of the integers ($100 <$ Start) End ...
1
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1answer
57 views

MILP optimization constraint formulation

I'm trying to find a sensible way to add constraint for my optimization problem. Lets assume we have binary decision variables $x_i\in\{0,1\}$ and two constraints \begin{align*} \sum\limits_{i=1}^n ...
0
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1answer
36 views

Travelling salesman problem as an integer linear program

So the travelling salesman problem is a problem wherein a salesman has to travel through all cities in a way that the total travelling distance is minimal. You can rewrite this as an integer linear ...
0
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1answer
26 views

The order of derivatives implies reversed order of minimizers

Suppose that $f_1$ and $f_2$ are both differentiable functions defined on $\mathbb{R}$ that have finite minimizers, $S_1$ and $S_2$, respectively, and that $f_1' \le f_2'$. Show that if $S_1$ and ...
0
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1answer
38 views

How to read Linear Program from an optimal tableau

Suppose we are given an optimal tableau and the objective function. How can we determine the RHS of constraints or if possible the constraint equations? For example consider the given tableau with ...
0
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1answer
48 views

How to solve this operation research problem using dual simplex method?

Maximize $$ z = 2x_1 -x_2 +x_3$$ Subject to constraints $$2x_1 + 3x_2 -5x_3 \ge 4$$ $$-x_1 +9x_2 -x_3 \ge 3$$ $$4x_1 ...
0
votes
2answers
42 views

Scheduling Algorithms

I Need to send a number of packets from A to B. A and B are connected by different paths of different lengths (all disjoint). Paths have different capacities too (like I can't overfill them). I have ...
1
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0answers
5 views

Stochastic withdrawals from finitely-lived stock

Suppose an energy source has n quanta of energy in storage, all of which are available now (t=0) until t = T, at which time the energy source disappears (or is no longer available). Suppose there are ...
0
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2answers
95 views

How can I linearize the distance from two points?

I'm studying Operations Resarch and the professor give us the following problem: • There is a 10*10 matrix in which there are 20 villages on random coordinates. • We have to drop two supply packages ...
0
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0answers
30 views

Sequential linear programming

I need some help starting this problem. I'm not sure how to put this in SLP form from the general form. And, how do I use the X^0 vector in this? For the optimization problem below, put the problem ...
1
vote
1answer
58 views

Particle swarm optimization

I don't know where to start. Like, I don't know how to plug the info into the algorithm. Show two iterations of particle swarm optimization (neighborhood approach) method. Mathematically show two ...
0
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1answer
33 views

Progressive Solving of Linear Programming Problem

Suppose you solve a linear optimisation problem: **Maximize:** 2a + 3b + 4c **Subject to:** 3a + 5b + 2c <= 5 8a + 3b + 1c <= 8 C = 0 And then remove the C ...
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1answer
49 views

Linear Programming Problem Exercise.

A firm has to transport $1200$ packages using large vans which can carry $200$ packages each and small vans which can take $80$ packages each.The cost for engaging each large van is Rs $ 400$ and each ...
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0answers
13 views

Finding which components of a function have the largest effect?

Say I have a function such as: $$y = \left({x_1 + x_2 \over x_3 + \frac{x_4}{x_5}} \right)\left({1 \over 1 - x_6} + x_7 + x_8 + x_9(x_{10} + x_{11}) + \frac{x_{12}}{x_{13}}(x_{14} + x_{15})\right)$$ ...
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0answers
24 views

Linear Programming with Supply Demand restraints

A tech firm needs to buy 1700 computers and has a choice of 3 vendors. Each vendor sells the computer at a different price, and delivers for a flat fee. Each vendor requires a minimum of 200 computers ...
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0answers
33 views

Please show that $f(\beta_0,\beta_1)=\log(1+\operatorname{exp}(-y_1(\beta_0+\beta_1 x_1)))+\log(1+\operatorname{exp}(-y_2(\beta_0+\beta_1 x_2)))$

I would like to show that the following result is indeed true. I am very new with this subject, so I ask for a hint to get me started please. Please show that ...
0
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1answer
43 views

Find absolute maxima and minima of f(x,y,z)=xyz subject to g(x,y,z)=x^2+y^2+z^2-12 and h(x,y,z)=x+y+z-4

I had no problem getting these equations: $yz=2\lambda x + \mu$ $xz=2\lambda y + \mu$ $xy=2\lambda z + \mu$ $x^2+y^2+z^2=12$ $x+y+z=4$ The part that I can not figure for the life of me is how to ...
0
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0answers
25 views

how do I select a multiple combination of multi-level variables that meets a set of constraints (totals?)

I have left-censored, tabled survey data, random rounded to base 3, where any count of less than 6 is censored, however true 0s are included as 0. The variables, factors in statistical terms, used ...
0
votes
2answers
99 views

operations research decision variables sequence

I have $6$ decision variables $(x_1, x_2, x_3, x_4, x_5, x_6)$ in my problem. All of them are integer and $\ge 0$ and they represent a sequnce. I want to put constraints on them that if a variable is ...
0
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1answer
49 views

optimizing contractor schedules - operations research linear programming

I am facing the below problem I know for each week how many workers that I need. I need to ensure that for a given week I have workers more than or equal to what I need. ...
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0answers
25 views

What is the submodular function and what is its uses

I am reading a scientific paper and I find a notion that I have never seen it before, it is the submodular function. I understand the basic definition but I need ...
0
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0answers
28 views

What is meant by “deterministic error”?

I am reading a scientific paper in computer science and I have found the term of deterministic error. I googled to find any meaning to this notion but I did not find anything. So is there anyone to ...
0
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0answers
10 views

Pay off of adding new service station

I have to solve the following problem: In a factory they do reperations of a certain type of machine. The machines that need reparations arrives at the factory with a frequency of 4 every hour, such ...
3
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1answer
55 views

Assignment Problem Using Branch-And-Bound Method

The department chair intends to assign classes to 3 professors to teach. There are 6 classes in total, so each professor gets assigned 2 classes each. Each professor ranks the classes that they want ...
0
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1answer
63 views

Objective function: linear programming

The following simultaneous nonlinear equations are to be solved: $$y=e^x$$ $$y=x(1+x)$$ Define an objective function that can be maximized to obtain a solution to these equations. Sketch x vs ...
3
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2answers
54 views

Faster Algorithms for Convex Hulls

I was interested in the following: Given two polyhedra $P_1, P_2$ specified in the form: $$ P_1 = {x : A_1x \le b_1 } $$ $$ P_2 = {x : A_2x \le b_2 } $$ Whereas $ x \in R^n$ and $b_1, b_2$ are ...
0
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1answer
22 views

Question about least square allocation of an amount to different buckets.

Suppose we have to allocate $x$ amount to $k$ desired amounts. Is there algorithm to do this that minimizes the squared distance between the actual $k$ allocated values and the $k$ desired amounts? ...
1
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1answer
110 views

Probabilistic dynamic programming question

A gambler has 2 dollars. He is allowed to play a game four times and his goal is to maximize his probability of ending with at least 6 dollars . If the gambler bets $b$ dollars then with ...
0
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1answer
91 views

Optimization problem in flight scheduling

I found this question here The question is I wrote the LP problem as this: Let $x_{ij}$ be the maximum no.of flights between city i and city j. Let $a_0$ be the artificial link and $x_0$ be the ...
2
votes
1answer
32 views

optimization network models

This is a question from Wane Winston 's Book. I don't understand how to do this. I tried to do it this way but it doesn't seem to work. Let $C_{ij}$ be the cost of using box of i $ i>=j$ Then ...
2
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0answers
48 views

Find Solution regarding 2-Norm

I try to understand that, but I have no clue what do to and how to do it. $A$ is a $m \times n$ matrix with $rg(A)=m$. Find the solution for $Ax = b$, which is regarding to the $2$-norm (I guess ...
1
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1answer
52 views

Operations Resarch Optimal Scheduling

Consider the following problem: A car manufacturing company needs to transport car frames, which are $10$ cubic units each, and wheels, which are $2$ cubic units each, across the Atlantic ocean. ...
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0answers
838 views

Primal and dual problem (Optimal solution) - Operations research

I'm currently studying operations research and I want to know and understand how we find an optial solution to the dual problem with minimum effort. Lets say we have this primal and dual problem: ...
1
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1answer
70 views

Operation research - postoptimality analysis - find all solutions to problem

I'm currently learning Operations Research from "Introduction to Operations Research - Hillier". I know that somethimes a problem has many optimal solutions. For example in a two dimensional problem ...
2
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1answer
135 views

What would be the objective functions for this problem?

I have the following data (this is just a sample of my entire dataset): # Distance PriceIndex Rating 1 400 3 5 2 420 2 4 3 500 1 2 Considering the ...
2
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0answers
79 views

What subjects properly belong in operations research as their “owning” discipline?

Warning: This is a soft question, hence I would make it a wiki-community post if I could. Operations Research involves a broad swath of disciplines, ranging from probability and statistics/stochastic ...
0
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1answer
50 views

If the entries of an invertible matrix N are between -1 and 1, is its operator norm less than 1?

For Euclidean norm. If so, why? If not, might $(I-N)^{-1}$ exist some other way? This spins-off from here.