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97 views

Are any tools or techniques available to solve the “placement of safety points” problem?

Definition 0. Given a metric space $X$ and subsets $H$ and $S$ thereof, define: $$d(H,S) = \sup_{h \in H} \inf_{s \in S}d(h,s)$$ (This as an asymmetric version of the Hausdorff distance.) Here's ...
3
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194 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 ...
3
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0answers
66 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 ...
3
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152 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 ...
3
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78 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 ...
2
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10 views

Is there a known optimal solution for searching an ordered list with non-uniform query cost?

Let $D$ be the set of integers from $1$ to $n$ inclusive for $n \geq 1$, and let $$f(i) = \begin{cases} 0& i \leq k \\ i - k& i > k \end{cases}\,\,\,\forall\, i \in D$$ for some $k \...
2
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23 views

Linear programming: choosing entering variable

maximize 10𝑥1 + 12𝑥2 +12𝑥3 subject to 𝑥1 + 2𝑥2 + 2𝑥3 + 𝑥4= 20 2𝑥1 + 𝑥2 + 2𝑥3+𝑥5= 20 2𝑥1 + 2𝑥2 + 𝑥3 +𝑥6= 20 𝑥1, … , 𝑥6 ≥ 0 This is my first step for simplex tableau x1 x2 ...
2
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51 views

How to model task scheduling with constraints

I am trying to model a task scheduling with constraints, in order to understand which model or algorithm is better suited to compute an optimal solution. Suppose I have $n$ jobs with CPU loads ...
2
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37 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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52 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 that'...
2
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1k 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: ...
2
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97 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 ...
2
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76 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 ...
2
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305 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 ...
2
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121 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 ...
2
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172 views

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

This is in the context of the Big M Method in the simplex algorithm in linear programming. Prove an artificial variable that leaves the basis will never return. I have no idea how to start this. ...
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11 views

Why does the Dantzig cut require the constraint data to be integral?

Given the following integer linear program, (ILP) $\min c'x$ subject to $Ax \ge b, x \in \mathbb{N}_0$ where all elements of $A$ and $b$ are integral, and assuming its linear-program relaxation (...
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36 views

Transform an assignment problem to use the Hungarian algorithm

I have this assignement problem: There are three machines to perform four tasks. The costs of assigning to a machine each of the tasks are given by the following matrix: $$\begin{pmatrix} ...
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32 views

Model linearly: Determine amount of units for production

A company produces 2 products in a week. Let $x_i$ denote the number of units of product $i$ to produce. Each product requires liters of Chemical X to make. Info is given below: \begin{array}...
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82 views

What programs or websites solve linear integer or goal programming problems?

I don't think I can use Excel. My solver doesn't work so I can't even use Excel for regular linear programming. Something like this but for integer or goal programming. This seems to allow integer ...
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51 views

Develop a model for determining the optimal production schedule in a manufacturing facility

I have to formulate (linearly) the following problem mathematically: What I tried: 1. Variables Let $x_{ijk} = 1$ if, in month k, product i should be made in production line j, where $i=...
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40 views

Strict inequalities in an LP problem

So I have to formulate an LP problem out of this scenario converting 3 variables into just 2 variables in order to use the graphical method. I guess I do that by using the demand constraint: I ...
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41 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 ...
1
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34 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 $f(\beta_0,\beta_1)=\log(1+\...
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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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128 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 ...
1
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0answers
27 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 ...
1
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0answers
470 views

How do I convert max min problem into a linear programming problem?

Let $A$ be a given $m \times n$ matrix, $c$ a given $n$-vector, and $b$ a given $m$-vector. Show that this problem $$\max \min (c^T x - y^T Ax + b^Ty) \text{ such that } x,y \ge 0$$ can be reduced ...
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71 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 ...
1
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38 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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1k 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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35 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 ...
1
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0answers
80 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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18 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 ...
0
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10 views

References request: two-queue, one-server model with pre-emptive queue priority and finite buffers

Sorry of the title is a mouthful. I'm developing a queue model with the following characteristics: Two queues: One contains an infinite number of people (Queue A) while the other (Queue B) is ...
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29 views

Properties of polyhedron solving constrained max problem

This is a question for people who don't have trouble to think in more than two dimensions. Don't hesitate to ask clarifying questions! Let us suppose we have $n$ random variables $X_i$ that are iid ...
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21 views

Formulating a linear transportation problem as a stochastic linear program

[Question provided in picture]http://i.imgur.com/avoARFG.jpg[/img] I am having trouble with part b of this question. For part a, I have the following: let xij = number of units produced by plant i ...
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0answers
8 views

Reduced cost in linear programming maximization sensitivity analysis?

My sensitivity report of maximization problem shows negative reduced cost although my optimal values of variables are not zero. So, what does it mean by the negative values of reduced cost? Here is ...
0
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0answers
8 views

Correct definition of the co-occurrence graph of a pseudo-Boolean function

In section 4.6 of Pseudo-Boolean Optimization, Boros and Hammer have defined the co-occurrence graph of a pseudo-Boolean function as follows. If a pseudo-Boolean function $f : \mathbb{B}^n \mapsto ...
0
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0answers
31 views

If the primal is unbounded, then the dual is infeasible.

In the context of duality in linear programming, prove that If the primal is unbounded, then the dual is infeasible. My book says that this is a corollary to complementary slackness. What's ...
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22 views

Travelling Salesman Variation

Is there a name for this variation and a recommended algorithm for solving this problem: You have a large boat with many leaks on it. As soon as you patch a leak, it resets, and slowly begins ...
0
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0answers
38 views

Weights in goal programming

I'm not quite convinced about assigning weights in goal programming. Here is an example formulation problem. What I tried: Let $x_j$ be the number of minutes for ad $j = R, T$ We want to ...
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0answers
15 views

Linear programming exercise verification

I am working on this exercise (translation mine): A Motel provides a 24 hour service and needs a minimum number of workers depending on the time slot: ...
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28 views

How to find extreme directions?

objective:min $−3x_1−2x_2−x_3$ The set is : $X=\lbrace (x_1,x_2,x_3):2x_1+x_2-x_3\le2; x_1,x_2,x_3\ge0 \rbrace$ Attempt: $2d_1+d_2-d_3\le0$ (a) $d_1+d_2+d_3=1$ and $d_1,d_2,d_3\ge0$ Since from (...
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6 views

Parallel series systems defined in OR? Isomorphism to SP-graphs in graph theory?

The series parallel graph definition is inductive with respect to series operation and parallel operation in graph theory. In comparison to series parallel systems in OR (Operations Research) and ...
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54 views

What values make the solutions in the optimal? infeasible? degenerate? etc

Note that $c_i$'s in the $z_j-c_j$ row are not coefficients of the $x_i$'s. I use instead: $r_1, r_2, r_3$. I'm assuming there's a non-negativity constraint. we need to state necessary ...
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26 views

Need optimal tableaus be unique assuming unique solution?

If so, why? If not, do they differ by some ERO/s? That is, they are row equivalent? This is the problem (taken from Chapter 2 here): My classmate gave an optimal tableau that is different ...
0
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25 views

RINS: start - incumbent and relaxation solution have all different values

RINS: Relaxation induced neighborhood search; introduced by Danna et.al in 2010 this paper. I wanted to design an example how the RINS algorithm works to make sure that I have it completly understood ...
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28 views

Use graphical analysis to solve a parameterised LP problem

For $c < 0$, we have no feasible solutions and hence no optimal solutions. For $c=0$, our only feasible solution is $z=0$ obtained by $(0,0)$. For $c > 0$, well... I graphed the constraints ...