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Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
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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 ...
3
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1answer
119 views

simplex method standard form

i am unable to understand algebraic formulation of simplex method.when we add slack variables, and solve for finding basic feasible solution we put free variables equal to zero. My question is why ...
2
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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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1answer
730 views

Introduction into Operations Research

I am a first year graduate student who advisor wants me to learn about operations research and to use stochastic integer programming in my research. He keeps giving me papers to read but they ...
2
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1answer
529 views

Reconstructing an optimal Simplex tableau from an optimal solution

I have here a bounded LP with infinite optimal solutions: ...
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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 ...
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1answer
36 views

How to model a multiobjective problem with a large dataset?

I have a large dataset of businesses (around 5k venues with distance from a predefined point, average price and service quality rating) and I need to create the objective functions to minimize the ...
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1answer
42 views

Primal of Dual of LP problem

Given that the following relation holds: $$\begin{align*} &\textbf{Primal problem} \\ &\max Z = c^Tx \\ &s.t. \\ &Ax \leq b \\ & x \geq 0\end{align*}$$ $\Longrightarrow$ ...
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151 views

A basic question related with the solutions of linear programming problems

I have to select one option from the problem statement given below. Which of the following statements is true in case of linear programming. $1$: An optimal solution exists at extreme points of a ...
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74 views

Operational Research. (Ressource Management)

I am looking for a solution that i know exists already in the field of "Operational Research"... I Just can't put my finger on the name of the thing. An heuristic to solve a very common and simple ...
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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 ...
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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 ...
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74 views

Assignment problem with multiple types, capacities and costs

I am trying to solve an optimization problem (variation of assignment problem). I'm stuck with how to represent this problem (as an LP or graph based). If it's formulated as a LP, I'm unsure of how to ...
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254 views

Is optimal solution to dual not unique if optimal solution to the primal is degenerate?

If optimal solution to the primal is degenerate, does it necessarily follow that optimal solution to dual not unique? That is, is uniqueness an unnecessary assumption? Spin-off from here. In my ...
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99 views

Nonlinear non-convex semi-infinite programming with norm equality constraint

In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a ...
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145 views

Prove an artificial variable that leaves the basis will never return.

Prove an artificial variable that leaves the basis will never return. Edit: This is for the simplex method (I think). I have no idea how to start this. Anyone know any books with these kinds of ...
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64 views

Linear programming of sperner lemma

How can you formulate the 2-D proof of Sperner lemma as a linear programming problem? I know that you have to divide the triangle up into smalled triangles with the original triangle having vertices ...
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146 views

Changing a queueing processes

Situation Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose service times are independent; both of these are allowed to have general ...
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21 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 ...
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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 ...
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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 ...
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848 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: ...
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50 views

Assignment problem with serval 'rounds' and additional constraints

Suppose we have an office with $n$ employees and we want to make a planning for the upcoming $T$ weeks. In each week there are $m_t, t\in \{1, 2, \ldots, T\},$ jobs to do. Each employee can give a ...
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125 views

Formulating linear programming treatment plan based on costs, periods, and condition

Note that this question is cross posted from OR-exchange Although we have a software that solves this for us, I'd like to understand the background behind the scenes as well as build a validation ...
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24 views

Need guidance on a Queuing problem

I can't really go into specifics, I'm more just looking for terms that I can research to get on the right track. Classes of model/processes etc. A close analogy to my problem: I need to optimally ...
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63 views

Sensitivity of coefficients in ODE

I am trying to formulate a mathematical model as part of an op-research problem, and I'm running into a roadblock concerning differential equations of a certain kind; I was hoping to understand if ...
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34 views

Highest (lowest) index of positive time-indexed variable

I have a simple problem involving a variable $x_{it}$ representing the amount of a resource allotted to a task $i$ in time $t$. The quantity of the (renewable) resource is constrained at a value $R$ ...
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988 views

Graphically solving a Linear Programming Problem?

I was given the following linear programming problem and have been asked to find all optimal solutions graphically. I am quite new to the subject, so please forgive my naivety. ...
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34 views

Complexity of Earlist Avaible Due Date for Scheduling Problem 1|ri, pi=1|Lmax

Let us consider the scheduling problem 1|ri,pi=1|Lmax (basically, this means there is one machine on which we have to schedule n jobs (all with identical procssing time 1) in such a way that the ...
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74 views

Infinite loop in column generation algortihm

I have to program the following: Input: I have k commodities that have to go from place i to j with a certain demand There are n nodes and the cost for traveling one piece between the nodes i and j ...
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17 views

Differential rents problem solving for transport problem

Sorry if question was asked, but I was unable to find the exact duplicate. Let's assume that we have transport problem. Will optimal plan for transport problem be the same regardless the method I ...
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12 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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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 ...
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29 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 $Q$? ...
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24 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 ...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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 ...
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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 ...
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0answers
24 views

Say optimal solution to the primal is degenerate. Does it hold that optimal solution to dual not unique?

I think it's supposed to be that existence of a degenerate and unique solution of the primal implies multiple solutions to the dual, according to this book (pages 141-145, proof of Theorem 4.5). In ...
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21 views

How to model the following banking question?

A group has 200 members. Each member settles up 100,000 S each month. The group runs a lottery every month and pays 10,000,000 $ to one member of the group i.e.,winner. The winner do not settle up ...
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26 views

Not every correlated equilibrium is equivalent to a Nash equilibrium?

This is a statement made under Theorem 3.4.13 on page 84 in the book by Yoav Shoham and Kevin Leyton-Brown, Multiagent Systems. Could someone explain this to a lay-man and also elaborate on why they ...
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20 views

Minimizing handling costs in the one-to-one TSPPD

Currently I'm reading about the Traveling Salesman Problem with Pickups and deliveries. This is similar to the classical TSP but there are $n$ requests and each request has a pickup location and a ...
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39 views

Simplex Method, which step is wrong?

Question: Maximize $z=2x_1-6x_2$, Subject to $-x_1-x_2-x_3\le-2$ and $2x_1-x_2+x_3\le1$. $x_1,x_2,x_3\ge0$. My work: $-2x_1+6x_2+z=0$ Then ${R_2\over2}\Rightarrow new R_2$, $new ...
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28 views

Is this variant of the Stable Roommate problem NP-hard?

I want to organize $2n$ people ${A, B, C, \dots}$ in pairs. Each people rates every other one with an integer number going from 0 to 10. The ratings may not be reciprocal (i.e., A may rate B a 10, and ...