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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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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5 views

Difference between CPM and PERT

What is the difference between Critical Path Method and Program Evaluation and Review Technique?
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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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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 ...
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70 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
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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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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33 views

Graphical method for Maximisation, using 3 equations

Solve graphically the below LPP Maximize profit Z=30x1 + 20x2 Subject to 3x1+2x2<=60....(1) 6x1+2x2<=60....(2) 8x1+ x2<=60....(3) X1,x2>=0. I did the above ...
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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 ...
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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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1answer
23 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
17 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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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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38 views

Operations Research: Problems of choice with delayed effects

A company buys a manufacturing plant at a cost of $ 500,000. The manufacturing plant has a term of 5 years, with a value of elimination equal to $ 200,000 The manufacturing plant only requires a ...
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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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32 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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13 views

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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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 ...
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27 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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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 ...
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38 views

Euler equation for $\int_0^{\infty}e^{-rt}(x^2+2x+\dot x^2) \ \mathrm dt$? Is $\infty$ in the boundary open or closed?

I am pondering this problem here, the course Mat-2.3148 Dynamic Optimization in Aalto University, i.e. Find the function $x(t)$ such that $\int_0^{\infty}e^{-rt}(x^2+2x+\dot x^2)\ \mathrm dt$ has ...
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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 ...
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38 views

Line that passes between two vectors

I encountered the following in a text book I'm reading and I can't seem to understand why this is true (I'm translating this into English so excuse me if I'm not using the correct english terms): ...
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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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72 views

Suppose I have the tableau below for a maximization problem. For the tableau to be optimal what are values for c1, c2, and b?

Suppose I have the tableau below for a maximization problem. For the tableau to be optimal what are values for c1, c2, and b? z x1 x2 x3 x4 x5 x6 RHS 1 c1 c2 0 0 0 0 10 ...
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32 views

Proving equivalence between basic feasible solution and vertex

I stumbled upon this proof of the Bertimas book on Linear optimization and I don't see what the "key ingredient" is that makes it work. Baxic feasible solution $\implies$Vertex Let $x^*$ be a ...
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1answer
14 views

What if objective function $Z$ is also in the constraints?

What if objective function $Z$ is in the constraints? To construct the dual form for this problem? how do I approach to this problem? Maximize $\;\;\;\;\;\;\; z$ subject to $$\;\;\;z - ...
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21 views

Partial dependencies in PERT

Assume that there are 6 activities in a Project: $A$, $B$, $C$, $D$, $E$ and $F$. ...
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1answer
107 views

Network simplex method, leaving and entering variables

Could someone give me a hint on this question, which is a past exam question: Under what circumstances will an entering variable in the network simplex method be the same as the leaving variable? ...
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48 views

Good MIP formulation of a timetabling problem

I am trying to formulate a university timetabling problem as a mixed-integer program. The choice variables are binary variables of the form $x(c,s,r)$ which is $1$ if a class of course $c$ is held in ...
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102 views

Probability Density Function and Proof

Given the Probability Density Function: $f(x)=kx(2-x), 0\leq x\leq 1$ Prove that $k=\frac 3 2$ Looks like it should be a Beta Distribution, but all examples of a beta distribution use the format: ...
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41 views

operation research revised simplex

in revised simplex when be compute inverse of basis matrix, it is told in the book that only one column changes(obviously because of entering basic variable)but i could not understand how does it make ...
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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 ...
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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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158 views

The difference between Dynamic Optimization, Stochastic Programming, Optimal control and Markov Decision Processes

I've seen the following terms thrown around somewhat interchangeably, and I'm confused. What are the distinctions between them, and what are some representative problems that each deals with? ...
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45 views

Double summation of linear function?

I am doing an assignment in operations research and I seem to struggle with some basic arithmetics. I need to formulate an objective function of the form $$\sum^3_{i=1}\sum^8_{j=1}(cij+c'ij)xij$$ ...
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485 views

Minimizing shipping cost under given constraints

I have a question that has been bugging me for about a day now. A manufacturing company receives orders for engines from two assembly plants. Plant I needs at least 45 engines and Plant II needs at ...
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602 views

Minimize LPP using graphical method [ operational research ]

Question: Minimize z = 2x + 6y Subject to 2x + y >= 2; 3x + 4y <= 12 x,y >=0 Is min z = 2 the right answer ? if not how do i solve this ?
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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
68 views

Relation between arg min of two functions

When is $u_F(x) = \underset{u}{\text{argmin}}(F_1(x),\cdots,F_u(x),\cdots,F_U(x))$ $\le$ $\underset{u}{\text{argmin}}(G_1(x),\cdots,G_u(x),\cdots,G_U(x)) = u_G(x)$ where $u \in \{1,2,\cdots,U\}, x \in ...
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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
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
70 views

How to solve a linear program with OR constraints

I have $n$ people. I want assign them to $c$ jobs. A job may be not assigned at all or there must be a minimum and maximum number of people assigned to it. $n$ is about 4000 and $c$ is about 1000. ...
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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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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 : ...
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132 views

How to answer this linear algebra question, which is related to operations research?

I have the following question: Let $A$ be an $(m \times n)$-matrix and $b$ a vector in $\mathbb{R}^m$. The system of inequalities $Ax \leq b$ has a solution $x \geq 0$, if and only if $yb \geq 0$ for ...
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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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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. ...