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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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 ...
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54 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 ...
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30 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 ...
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42 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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40 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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116 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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46 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 ...
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1answer
110 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 ...
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37 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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36 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.
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2answers
70 views

Under what conditions does $(I-N)^{-1}$ exist?

Given an nxn matrix N and $I=I_n$, under what conditions does $(I-N)^{-1}$ exist? On one hand $(I-N)(I + N + N^2 + ...) = (I + N + N^2 + ...) - (N + N^2 + ...) = I?$ On the other hand, $(I-N)(I + N ...
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59 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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11 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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1answer
22 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
46 views

An LP problem from David G. Luenberger's Linear and Nonlinear Programming book

Could someone help me to solve the following problem? A class of piecewise linear functions can be represented as $f(x) = Maximum (c_{1}^Tx+ d_{1}, c_{2}^Tx, \cdots, c_{p}^Tx + d_{p})$. For such a ...
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51 views

Setting up the Bellman equations for dynamic programming

I have the following question I want to understand. The owner of a chain of three grocery stores has purchased five crates of fresh strawberries. The estimated probability distribution of ...
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19 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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21 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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14 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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2answers
48 views

Prove linear program is unbounded

So I need help on my homework (I feel like a 10 year old). The exercise goes like this: Prove algebraically that the following program is unbounded: Max: $x_1 - x_2$ Constraints: $-2x_1 + x_2 ...
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1answer
79 views

What gambling/board game or real life thing can (surprisingly) be modelled as a linear programming problem?

So I've taken Linear Programming 101. I've read my textbook, took the test and all that, and - besides all the theory, the nice algebraic interpretations, etc - I've encountered a lot of textbook ...
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44 views

Can a basic variable be the entering variable in Simplex method?

I have got from my teacher that "the entering variable in a maximization problem is the non-basic variable having the most negative coefficient in the Z- row" I think X1,X2 are non basic and ...
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35 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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23 views

Consider the maximum flow problem with n nodes and m arcs. You are writing a formulation with f as the maximum flow.

Consider the maximum flow problem with n nodes and m arcs. You are writing a formulation with f as the maximum flow. How many terms the objective function will have?
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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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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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24 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 ...
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138 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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60 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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46 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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1answer
52 views

Removing a max function in the constraints

Can the following problem be transformed into a linear programming problem: Find $x_1,..,x_N$ which maximizes the objective function $$\sum_{i=1}^{N}x_{i}\sum_{j=1}^{n_{i}}c_{ij}$$ subject to the ...
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44 views

Difference between CPM and PERT

What is the difference between Critical Path Method and Program Evaluation and Review Technique?
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84 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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1answer
204 views

Prove optimal solution to dual is not unique if optimal solution to the primal is degenerate

How do I prove an optimal solution to dual is not unique if an optimal solution to the primal is degenerate? I have no idea how to start this. Anyone know any books with these kinds of questions (and ...
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118 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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2answers
69 views

Stationary probability in an M/M/$1$ queue with a lazy server

Customers arrive to a single server queue according to a Poisson process with rate $\lambda$. Each customer requires Exponential($\mu$) service time. In the beginning when there are $0$ ...
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1answer
38 views

Duality - linear programming

I have to find a respective dual programme for the given LP $$ \max \ 2 x_1 + 2x_2$$ s.t. $ -x_1 - x_2 \ge -5 \\\phantom{-}x_1,\phantom{,,}x_2 \ge 0$ I got this: $$\min \ 5y_1$$ s.t. $y_1 \ge 2 ...
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60 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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30 views

Poisson Distribution Research Question in R

I am working on doing a Poisson distribution based upon the number of potholes and accidents on a given road. The problem I currently have is that I am basing a general linear model off of only the ...
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1answer
31 views

discuss convexity of the following set?

discuss convexity of the following set ? $$M= \{(x,y)∈\Bbb R^2 : x^2+y^2≥a^2 ,x^2+y^2≤b^2 ,x>0,y>0\} $$
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1answer
23 views

Need help using the neighborhood search heuristic

I need help using the following neighborhood search heuristic on the set S that is partitioned into A and B where A = {1, 2} and B = {3, 4}. This set partition is our initial solution x_0, and the ...
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23 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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2answers
77 views

an interior point of a convex set

How can we prove a point is an interior point of a convex set, considering we don't have all of the extreme points of the given convex set ? or How can we find an interior point of a convex set, ...
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1answer
49 views

Relative Interiors of polyhedra

***Source article: Magnanti, T. L., & Wong, R. T. (1981). Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research, 29(3), 464-484
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1answer
657 views

simplex M-method minimization problem

Solve using the simplex method. Identify the solution of the dual in the final simplex tableau Minimize: $$z=12x_{1}+4x_{2}+2x_{3}$$ **Constraints:**$$ x_{i}\ge 0$$ $$-6x_{1}+3x_{2}\ge 9$$ ...
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33 views

How to distribute groups over activities in rounds

I typed out my problem in a Latex file and I will add an image of it here: If anyone could help me how to solve this problem that would be amazing. Thank in advance. Boris
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Is “nonanticipating” a measurability property of a function or something more?

I have been reading some operations research papers that throw in the term "nonanticipating" at key points in the exposition, but I can't figure out precisely what they mean. My best guess is that ...
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33 views

maximization problem with inequalities restriction

I have a function $g(x,y,z)$, and $x+y+z=1, x\geq0,y\geq0,z\geq0$. Now I want to maximize $g$. If I ignore the inequalities, then I can use lagrangian and can solve this thing for maximum. But I am ...
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44 views

Scheduling Algorithm for a multi-server queue problem

I have 4 servers, n customers and m reports. At any time, a customer may request one of m reports. There are only 4 servers which are capable of generating reports. Each server can only process one ...
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What is the system equation $f$ in Hamilton equation in $H=g+p^Tf$?

I am studying the Donald Kirk's book Introduction to Dynamic Programming. Suppose some integral $\int g dt$ that must be minimised. Then you are given some constraints. Hamilton equation is $H=g+p^T ...