Integer programmingAn integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Program evaluation and review techniqueThe program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project. First developed by the United States Navy in 1958, it is commonly used in conjunction with the critical path method (CPM) that was introduced in 1957. PERT is a method of analyzing the tasks involved in completing a given project, especially the time needed to complete each task, and to identify the minimum time needed to complete the total project.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Markov decision processIn mathematics, a Markov decision process (MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via dynamic programming. MDPs were known at least as early as the 1950s; a core body of research on Markov decision processes resulted from Ronald Howard's 1960 book, Dynamic Programming and Markov Processes.
Time perceptionThe study of time perception or chronoception is a field within psychology, cognitive linguistics and neuroscience that refers to the subjective experience, or sense, of time, which is measured by someone's own perception of the duration of the indefinite and unfolding of events. The perceived time interval between two successive events is referred to as perceived duration. Though directly experiencing or understanding another person's perception of time is not possible, perception can be objectively studied and inferred through a number of scientific experiments.
Markov chainA Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
Nuclear weapons of the United KingdomIn 1952, the United Kingdom became the third country (after the United States and the Soviet Union) to develop and test nuclear weapons, and is one of the five nuclear-weapon states under the Treaty on the Non-Proliferation of Nuclear Weapons. The UK initiated a nuclear weapons programme, codenamed Tube Alloys, during the Second World War. At the Quebec Conference in August 1943, it was merged with the American Manhattan Project.
Problem solvingProblem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles.
Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
