Questions tagged [operations-research]

Operations Research, sometimes known as Management Science or Decision Science, is the discipline of applying appropriate analytical methods to help those who run organisations make better decisions.

803 questions
222
votes
16 answers

Optimizing response times of an ambulance corp: short-term versus average

Background: I work for an Ambulance service. We are one of the largest ambulance services in the world. We have a dispatch system that will always send the closest ambulance to any emergency call. There is a belief that this results in the fastest…
44
votes
4 answers

What is the best rest position for two elevators in a 10-story building?

Situation My apartment block has ten stories. The first ground level is 1, the highest story is 10. There are two equivalent elevators, spanning all stories. Current configuration: One elevator always rests at level 1, the other at level…
28
votes
3 answers

What is a principal minor of a matrix?

I was going through the book on operation research by Hamdy A.Taha. It referred to principal minor of a hessian matrix. Can someone explain what is meant by a principal minor? Is it different from 'minor of a matrix'?
18
votes
6 answers

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 optimization, convex optimization and quadratic…
14
votes
1 answer

How can I mathematically model and analyze an incremental game like Cookie Clicker?

Recently, I've been interested in the optimization of the infamous incremental game Cookie Clicker. From Wikipedia: The user initially clicks on a big cookie on the screen, earning one cookie per click. They can then spend cookies on buildings,…
13
votes
3 answers

Variable leaving basis in linear programming - when does it happen?

In the simplex algorithm in linear programming, what are conditions for a variable to leave a basis (not necessarily basis for the/an optimal solution)? I'm supposed to list as many sufficient and necessary conditions as possible for some basic…
9
votes
2 answers

Introduction to Operations Research

I am a first year graduate student and my 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 regularly go over my head with their use of notation…
8
votes
2 answers

The Berlin Airlift

I am trying to learn more about the Berlin Airlift transport problem. Two links I could find are here: http://drmohdzamani.com/notes/file/Simplex%20Method.pdf http://www.cabrillo.edu/~mladdon/math13/LP%20Dantzig%20Berlin%20Problem.pdf Problem…
8
votes
2 answers

How can I calculate the optimal frequency of moving funds between two compound interest accounts?

The Problem I have two compound interest accounts, Account A, which has 0.5% yearly interest, but I have to keep \$30,000 there to unlock some bonus; and Account B, which has 2% yearly interest. Transferring between the two accounts costs \$0.5. I…
8
votes
1 answer

How to minimize studying using mathematics?

A friend asked me this question earlier today, and it made me wonder how to come up with a general solution (where each variable is an integer): I have a vocabulary test tomorrow at school. On it, there will be $W$ terms listed, and I will have…
Cisplatin
  • 4,835
  • 7
  • 34
  • 60
8
votes
1 answer

Definition of capacity of cut in a flow network

In the flow network below, an S-T cut is made. The net flow across the cut is $12-4+11=19$. The capacity of the cut is $12+14=26$. The "backwards" edge $(v_3,v_2)$ is not counted when calculating capacity. Why isn't the capacity of a cut defined to…
8
votes
2 answers

Linear Programming Formulation of Traveling Salesman (TSP) in Wikipedia

I am confused by Wikipedia's Linear Programming formulation of the Traveling Salesman Problem, in say the objective function. Question: If there are n cities indexed 1,...,n, what is city with index 0? This can be seen in the objective function…
8
votes
0 answers

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 some slightly dodgy intuition about why this…
8
votes
2 answers

Convert a piecewise linear non-convex function into a linear optimisation problem.

Update: Problem and solution found here (p. 17, 61), although my prof's solution (formulation) is different. Convert $$\min z = f(x)$$ where $$f(x) = \left\{\begin{matrix} 1-x, & 0 \le x < 1\\ x-1, & 1 \le x < 2\\ \frac{x}{2}, & 2 \le x \le…
7
votes
1 answer

Multidimensional Assignment: Is it really NP-Hard? Why? What's the Intuition?

I recently learned about the multidimensional version of the assignment problem (the 1:1 version was studied in the Kuhn-Murkes Hungarian algorithm for bipartite graphs). The article I was reading was about 1:1:1 or three-sided matches and above --…
1
2 3
53 54