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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Operations research book to start with

for somebody having a quite strong background in Mathematics, which are some good books for the domain of Operations research? I guess there are textbooks covering topics like linear and nonlinear ...
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1answer
104 views

Mathematical formulation in operations research

Does anyone know how I would enforce the following constraints using a mathematical formulation? Any help or feedback is appreciated. a) If person A is given project 1, then person D must be given ...
3
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1answer
334 views

The Hungarian Algorithm

In reading the proof of the Hungarian algorithm for the assignment problem in a weighted bigraph, I could not understand why the algorithm terminates. In the algorithm we choose a cover (namely labels ...
3
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2answers
59 views

Determine the equations needed to solve a problem

I am trying to come up with the set of equations that will help solve the following problem, but am stuck without a starting point - I can't classify the question to look up more info. The problem: ...
3
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2answers
198 views

Functions minimized at the median of their arguments

I am doing research on problems of location of a public facility on a network which lead me to the following question. Is there an interesting way to characterize the class of functions $f : ...
3
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2answers
1k views

Financial Linear Programming Problem

I'm very new at linear programming and I'm trying to figure out a way to approach this problem below: ...
3
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1answer
77 views

Software for Binary Integer Linear Programs

I am aware that there is good software out there to solve integer linear programs (ILPs). However, is there (preferably free or low cost) software I could use to solve large binary integer linear ...
3
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1answer
66 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 ...
3
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0answers
60 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 ...
3
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1answer
1k views

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 ...
2
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1answer
342 views

Unimodular matrix definition?

I'm a bit confused. Based on Wikipedia: In mathematics, a unimodular matrix M is a square integer matrix having determinant +1, 0 or −1. Equivalently, it is an integer matrix that is invertible ...
2
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1answer
61 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 ...
2
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1answer
433 views

How to solve this LP problem as a Dynamic Programming problem?

The standard form LP problem is $$\min -3x_1-7x_2-10x_3 \text{ s.t. }$$ $$x_3\leq 2$$ $$40x_3+40x_2+20x_1\leq 180$$ $$x_1,x_2,x_3\geq 0$$ My last lecture covered the Bellman equation ...
2
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0answers
54 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 ...
2
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0answers
135 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 ...
2
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0answers
404 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
75 views

Integral Polyhedra: Integer on each face

The general topic is unimodular matrices and integral polyhedra. I am really new to this field and I am studying for an exam in an advanced operations research course. In this case we are always ...
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2answers
39 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
25 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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1answer
51 views

In Courty and Li (2000) “Sequential Screening”, what justifies the last equation in Lemma 3.2?

Regarding the article "Sequential Screening," in Review of Economic Studies, 2000 by Courty and Li: In Lemma 3.2, the last equality states that ...
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1answer
310 views

Meaning of the bar over $\bf{c}'$ in $\bf{\bar{c}}'=\bf c' -\bf c'_B \bf B^{-1} \bf A\geq \bf 0$?

I am trying to understand the page 87 Bertimas about Linear Programming. The author uses bolding and bars -- now I am starting to think that the bar means something else to vector, bolding apparently ...
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1answer
25 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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1answer
85 views

Application of queueing theory

Jake's Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder. The grinding time required by a machine operator ...
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1answer
1k views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
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1answer
581 views

Cost-to-go form of Dynamic Programming algorithm?

My lecture of Mat-2.3148 (Finnish) defines dynamic-programming-algorithm so that$J_N(x_N)=g_N(x_N)$ and $J_k(x_k)=\min_{u_k}\left\{g_k(x_k,u_k)+J_{k+1}(f_k(x_k,u_k))\right\}$ where the state ...
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1answer
62 views

How do you call the operation of counting the number of euclidian division until the denominator is lower than the remainder?

I was looking for the minimum size of a base35 secret_key to be able to generate at least 1,000,000 secret key. The result is 35*35*35*35 = 1500625 How do you ...
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1answer
725 views

Warehouse Location Problem as an integer progam instead of a mixed-integer program

Given a set of costumers $M = \{1, \dots , m \}$ and a set of of factories $N = \{1, \dots , n\}$ we have $c_{ij} \geq 0$ costs to deliver to costumer $i \in M$ from factory $j \in N$ $F_j \geq 0$ ...
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1answer
888 views

A question about the operation research and simplex method

For the simplex method, we need to add slack variables. My question is how to determine how many slack variables should be considered in the LP problem? I don't quite get why in the cases to find out ...
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0answers
48 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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0answers
13 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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0answers
19 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
32 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
30 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
47 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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0answers
50 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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0answers
27 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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1answer
71 views

Travelling Salesman on Subset of Points

I'd like to solve the travelling salesman problem, except that the salesman only needs to travel to a subset of the locations. Each location has exactly one client, and each client has a "type". For ...
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0answers
723 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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0answers
26 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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0answers
62 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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1answer
495 views

Reduced cost in the Phase II of the two-phase Simplex?

My lecture slides outline how the two-phase simplex works: this table shows the end result of the phase I for the standard-form problem and the auxliary table of the phase I here. I understood until ...
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0answers
462 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 ...
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1answer
89 views

exchanging operators in max-max function

I am trying to determine if the following holds. $\max_{i\in I}\max_{a_j \in P_j}\{\sum_j a_{ij}x_j - b_i\}=\max_{a_j \in P_j}\max_{i\in I}\{\sum_j a_{ij}x_j - b_i\}$ $P_j$ is a closed convex set, ...
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0answers
15 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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1answer
19 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 ...
0
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1answer
88 views

How to enforce a constraint that a decision variable can only take 1 of $k$ integer values?

How would you enforce the constraint that $x$, a decision variable, can only take values -3, 7, or 19? I think I probably need to introduce a binary variable here but not sure where to start. Thanks. ...
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1answer
112 views

Partial linear relaxation yields an integer solution

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
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1answer
1k views

Example about the Reduced cost in the Big-M method?

I want to gather examples about the reduced cost in different cases, now for the Big-M method. I hope this makes the methods more accesible. So How does the Big-M method work with the below? ...
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1answer
18 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 ...
0
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1answer
37 views

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 ...