ormsfact.txt

0-1 integer programming is one of the 21 problems Richard Karp showed to be NP-Complete in 1972 http://j.mp/tgXFw5
The Karush-Kuhn-Tucker conditions are necessary for an optimal solution of a nonlinear program http://j.mp/sT4FSn
When operations researchers say "programming" they're referring to optimization problems, not computer programming http://j.mp/vthdSt
"OR is the science of decision making, the science of choice." (Saul Gass and Arjang Assad)
Video lectures from Econ 159: Game Theory at Yale http://j.mp/tzDb9P
Operations research, control theory, and machine learning intersect in the study of reinforcement learning http://j.mp/s0n6uN
Linear programs have the strong duality property; that is, the optimal values of the primal and dual problems are equal
Poisson process http://j.mp/snxTcP
The impact that variability of service and inter-arrival times have in queueing systems. http://j.mp/KFkj0z
Harry Markowitz won the Nobel Prize in Economics for his portfolio theory involving a nonlinear optimization problem http://j.mp/rLB7Jt
M/M/1 queue http://j.mp/vVHl63
Frederick Winslow Taylor developed "scientific management" in the early 20th century to improve labor productivity http://j.mp/sdL5lP
A M/M/c queue can be represented by a birth and death process http://j.mp/ufl2Vf
Queueing theory is the mathematical study of waiting in lines http://j.mp/w3CKwe
Kendall's notation for queueing models http://j.mp/scpGvy
Dynamic programming is a method for solving problems by splitting them into smaller subproblems http://j.mp/twPPlW
Branch and Bound algorithm for combinatorial optimization problems was proposed by Land and Doig in 1960 http://j.mp/th5WRR
[pdf] A proof of Little's law http://j.mp/vF1KCI
Agner Krarup Erlang: father of queueing theory http://j.mp/vvjAbv
"It is usually very difficult to obtain analytical results for a... model that assume a nonhomogeneous Poisson arrival process" (S. Ross)
Stephen Boyd: Lectures on Convex Optimization http://bit.ly/vKK1Cl
The Power of Mathematics for industrial engineering and operations research http://j.mp/OzLGdi
A Markov decision process is a discrete time stochastic control process http://j.mp/rCwZ1f
Karush proved the KKT conditions in his masters thesis in 1939, thirteen years before Kuhn and Tucker published the same result!
The max-flow min-cut theorem http://j.mp/sqZ7QO
Carrots, Oatmeal, Operations Research http://stiglerdiet.com/blog/2012/Jan/09/carrots-oatmeal-operations-research/
A stochastic process has the Markov property if the conditional probability of the future is independent of the past http://j.mp/vndZdQ
PHPSimplex is a free, online linear programming solver http://j.mp/LIYIRt
Diagram of distribution relationships by @JohnDCook j.mp/LJ3RJw
The Bellman equation is a necessary condition for optimality of a dynamic program http://j.mp/uzIQeW
Kruskal and Prim published polynomial time algorithms for finding minimal spanning trees in 1956 and 1957, respectively.
[free textbook] Warehouse & Distribution Science by Bartholdi and Hackman http://bit.ly/xgl5LR
A Dynamic Programming Model For Baseball http://bit.ly/xJqn4p
Brief description of Lagrange duality http://bit.ly/z9H16n via @AnalysisFact
[youtube] Newton's Method http://j.mp/rND7um
Dantzig and Beale introduce stochastic programming in their 1955 paper "Linear Programming Under Uncertainty."
The first OR degree program was at The Case Institute of Technology in Cleveland. The first masters student graduated in 1955.
Linear fractional programs, where the objective is a rational function and constraints are linear, can be converted into linear programs
The Traveling Salesman Problem http://j.mp/rAKJdo
A Markov Process is a stochastic process with the Markov property http://j.mp/rMHOeJ
There is no polynomial time approximation scheme for the bin packing problem unless P=NP
Frank and Lillian Gilbreth developed motion study to improve productivity... and are the stars of Cheaper by the Dozen http://j.mp/sWmhfU
The Bayesian Optimization Algorithm uses Bayesian networks to explore the candidate solution space of a given problem http://j.mp/Irjr9d
Narendra Karmarkar developed the interior point method for linear programming at AT&T Bell Labs in 1984 
Cutting plane methods are used to reduce the size of the LP relaxation polyhedron of a mixed integer program http://j.mp/tzuwqY
Little's law: the average number of customers in a stable queue is the arrival rate times the average time in the system http://j.mp/ulvHx0
Quadratic programming problems have linear constraints and a quadratic objective function http://j.mp/w3e0DD
Dantzig used Stigler's diet problem (a 9x77 linear program) to see if the simplex method could handle a "large-scale" problem.
Minimax Theorem http://j.mp/sat5Rs
Simulation of different airplane boarding strategies http://j.mp/HTw9T4
[youtube] Optimizing Your Diet: What Linear Programming Can Tell You! http://j.mp/tkKUkE
For an optimization problem, the duality gap is the difference between the primal and dual optimums; for LP, it's zero http://bit.ly/zXnCMo
Nonhomogeneous Poisson processes model arrival processes where the arrival rate changes with time. http://bit.ly/AsOdRe
Ordering by earliest due date minimizes the maximum lateness in the single machine scheduling problem
The ellipsoid method for linear programming is guaranteed to converge in a finite number of steps http://bit.ly/yaDjNZ
Economic order quantity is the order quantity that minimizes total inventory holding costs and ordering costs http://j.mp/IeRRA3
Simplex method moves from a primal feasible solution to dual feasibility; dual simplex moves from dual feasibility to primal feasibility.
My Hobby: Embedding NP-Complete Problems in Restaurant Orders on @xkcd http://j.mp/m0BMut via @fbahr 
Professor Leon Lasdon on the Importance of Operations Research  http://j.mp/IAfci3
Queuing at Disney World on Vimeo http://j.mp/IFY21a
Convex minimization studies the problem of minimizing convex functions over convex sets http://j.mp/JbvoB7
The assignment problem consists in finding a maximum weight matching in a weighted bipartite graph. It can be solved in polynomial time.
Shifting bottleneck heuristic  http://j.mp/JtbWmA
A stochastic process is a collection of random variables indexed by a totally ordered set T; usually, T is "time."
The ellipsoid method was the first polynomial time algorithm for LP. Simplex is exponential in the worst case but is often fast.
Tabu search is a neighborhood search metaheuristic that uses memory of points recently visited in attempt to not get stuck in local minima
Quadratically constrained quadratic programming is, in general, NP-Hard. http://j.mp/NliGXP
Nobel Prize Winners who have published in Management Science http://j.mp/Q8eFVL via @mlesz1
Finding good solutions to the traveling salesman problem with neural networks http://j.mp/Nuo7CN
What is the optimal way to find a parking spot? http://j.mp/STiawo by @lamclay
RT @seanjtaylor: If you get a degree in operations research you should be allowed to call yourself an optimalogist.
Finding an optimal seating chart for a wedding http://j.mp/SCKHpA
NP Or Not NP? That Is The Question http://ibm.co/UHoet7
RT @tdhopper: If spherical horses arrived according to an exponential distribution, physicists and queueing theorists would rule the world.
Markov's idea that changed the world http://hvrd.me/SDUK3C
Behavioral approaches to operational problems at Disney World http://bit.ly/WrfkYa
The Mathematics of Queues using Mathematica http://t.co/4zddmIzIRH
Visualizing path finding algorithms http://bit.ly/12cxWdh
Binary Integer Programming With Python http://bit.ly/18wSa6T via @fperez_org
How to pair socks from a pile efficiently? http://bit.ly/15pFnQ6
Classes of Metaheuristics http://j.mp/16a9oHW