linear programming

Principles of Corporate Finance

by Richard A. Brealey, Stewart C. Myers and Franklin Allen  · 15 Feb 2014

this package. As we will show in the next section, the only practical and general way to do so is to use the technique of linear programming. When we have to choose between projects F and G, it is easiest to compare the net present values. But if your heart is set

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satisfy the constraints and then calculate the net present value. But it is smarter to recognize that linear programming (LP) techniques are specially designed to search through such possible combinations. Uses of Capital Rationing Models Linear programming models seem tailor-made for solving capital budgeting problems when resources are limited. Why then are they

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then are they doing maximizing NPV?14 We might be tempted to suppose that if capital is not rationed, they do not need to use linear programming and, if it is rationed, then surely they ought not to use it. But that would be too quick a judgment. Let us look at

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procedure fails when capital is rationed in more than one period or when there are other constraints on project choice. The only general solution is linear programming. Hard capital rationing always reflects a market imperfection—a barrier between the firm and capital markets. If that barrier also implies that the firm’s

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be solved by hunting and pecking—but only in principle. To solve the capital rationing problem, we can employ linear programming; to solve the portfolio problem, we would turn to a variant of linear programming known as quadratic programming. Given the expected return and standard deviation for each stock, as well as the correlation

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consequences of the assumptions and policies specified by the financial manager. Optimization models for short-term financial planning are also available. These models are usually linear programming models. They search for the best plan from a range of alternative policies identified by the financial manager. Optimization helps when the firm faces complex

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on. Firms use computerized financial models to help in this process. These models range from simple spreadsheet programs that merely help with the arithmetic to linear programming models that search for the best financial plan. Short-term financial planning focuses on the firm’s cash flow over the coming year. But the

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planning model would be a natural tool for deriving these figures. 18The Second Law is presented in Section 10-1. 19It is possible to build linear programming models that help search for the best strategy subject to specified assumptions and conditions. These models can be more effective in screening alternative financial strategies

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partners have limited liability and general partners have unlimited liability. Limit order Order to buy (sell) securities within a maximum (minimum) price (cf. market order). Linear programming (LP) Technique for finding the maximum value of some objective function subject to stated linear constraints. Line of credit Agreement by a bank that a

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population survives to a particular age. Lookback option Option whose payoff depends on the highest asset price recorded over the life of the option. LP Linear programming. LYON Liquid yield option note. M MACRS Modified accelerated cost recovery system. Mail float Time spent by a check in the mail. Maintenance margin Minimum

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an operating company. Q q Ratio of the market value of an asset to its replacement cost. QIBs Qualified institutional buyers. Quadratic programming Variant of linear programming whereby the equations are quadratic rather than linear. Qualified Institutional buyers (QIBs) Institutions that are allowed to trade unregistered stock among themselves. Quanto swap Differential

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budgeting Capital leases, 643 Capital markets. See also Financial markets historic performance of, 160–167, 197 Capital rationing, 119–122 defined, 119 example, 119–122 linear programming in, 121, 195 profitability index in, 107, 119–120 quadratic programming in, 195 Capital structure. See also Debt financing; Debt policy; Equity financing; Restructuring capital

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, 456, 592 Limited liability companies (LLCs), 6 Limited liability partnerships (LLPs), 6 Limited partnership, 355, 846–847 Lindahl, F. W., 339, 339n Lindt & Sprüngli, 706 Linear programming (LP), 121, 195 LinkedIn, 387, 871 Lintner, John, 198, 198n, 406n Liquidation value, 78, 487 Liquidity cash management and, 787 defined, 735 value of, 887

Artificial Intelligence: A Modern Approach

by Stuart Russell and Peter Norvig  · 14 Jul 2019  · 2,466pp  · 668,761 words

lakes). The difficulty of constrained optimization problems depends on the nature of the constraints and the objective function. The best-known category is that of linear programming problems, in which constraints must be linear inequalities forming a convex set4 and the objective function is also linear. The time complexity of

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linear programming is polynomial in the number of variables. Linear programming is probably the most widely studied and broadly useful method for optimization. It is a special case of the more general problem

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developed, including simulated annealing, which returns optimal solutions when given an appropriate cooling schedule. •Many local search methods apply also to problems in continuous spaces. Linear programming and convex optimization problems obey certain restrictions on the shape of the state space and the nature of the objective function, and admit polynomial-time

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)); entomology (ant colony (Dorigo et al., 2008), bee colony (Karaboga and Basturk, 2007), firefly (Yang, 2009) and glowworm (Krishnanand and Ghose, 2009) optimization); and others. Linear programming (LP) was first studied systematically by the mathematician Leonid Kantorovich (1939). It was one of the first applications of computers; the simplex algorithm (Dantzig, 1949

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obey a variety of astronomical, precedence, and power constraints. The best-known category of continuous-domain CSPs is that of linear programming problems, where constraints must be linear equalities or inequalities. Linear programming problems can be solved in time polynomial in the number of variables. Problems with different types of constraints and objective functions

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on one of four different colors.) Infinite-domain CSPs—for example, with integer- or realvalued variables—require quite different algorithms, such as bounds propagation or linear programming. Consider the following example. We define triangle(X,Y,Z) as a predicate that holds if the three arguments are numbers that satisfy the triangle

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constraint-solving algorithms for the constraints allowed in the language. For example, a system that allows linear inequalities on real-valued variables might include a linear programming algorithm for solving those constraints. CLP systems also adopt a much more flexible approach to solving standard logic programming queries. For example, instead of depth

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Tetris MDP. 16.2Algorithms for MDPs In this section, we present four different algorithms for solving MDPs. The first three, value iteration, policy iteration, and linear programming, generate exact solutions offline. The fourth is a family of online approximate algorithms that includes Monte Carlo planning. 16.2.1Value Iteration The Bellman equation

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be reached by a good policy. There’s no sense planning for the results of an action you will never do. 16.2.3Linear programming Linear programming or LP, which was mentioned briefly in Chapter 4 (page 139), is a general approach for formulating constrained optimization problems, and there are many industrial

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for every state s and every action a. This creates a connection from dynamic programming to linear programming, for which algorithms and complexity issues have been studied in great depth. For example, from the fact that linear programming is solvable in polynomial time, one can show that MDPs can be solved in time polynomial

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and Atkeson, 1993; Andre et al., 1998; Wingate and Seppi, 2005). The formulation of MDP-solving as a linear program is due to de Ghellinck (1960), Manne (1960), and D’Épenoux (1963). Although linear programming has traditionally been considered inferior to dynamic programming as an exact solution method for MDPs, de Farias and Roy

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(2003) show that it is possible to use linear programming and a linear representation of the utility function to obtain provably good approximate solutions to very large MDPs. Papadimitriou and Tsitsiklis (1987) and Littman et

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al. (1995) provide general results on the computational complexity of MDPs. Yinyu Ye (2011) analyzes the relationship between policy iteration and the simplex method for linear programming and proves that for fixed γ, the runtime of policy iteration is polynomial in the number of states and actions. Seminal work by Sutton (1988

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), the optimal choice at the root is the highest (or lowest) intersection point of the remaining hyperplanes. Finding this choice is an example of a linear programming problem: maximizing an objective function subject to linear constraints. Such problems can be solved by standard techniques in time polynomial in the number of actions

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that are similar to the ones used in the zero–sum case. For two players these equations are linear and can be solved with basic linear programming techniques, but for three or more players they are nonlinear and may be very difficult to solve. 17.2.3Repeated games So far, we have

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1. But in general we can solve extensive games by converting to normal form and then finding a solution (usually a mixed strategy) using standard linear programming methods. That works in theory. But if a player has I information sets and a actions per set, then that player will have aI pure

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than exponential. Rather than represent strategies, it represents paths through the tree; the number of paths is equal to the number of terminal nodes. Standard linear programming methods can again be applied to this representation. The resulting system can solve poker variants with 25,000 states in a minute or two. This

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second. Within such a logic, one can prove, for example, that Satisfiability of sets of probability assertions can be determined in the propositional case by linear programming (Hailperin, 1984; Nilsson, 1986). Thus, we have a “probability logic” in the same sense as “temporal logic”—a logical system specialized for probabilistic reasoning. To

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Clamp, S. E. (1981). Geographical variation in disease presentation. Medical Decision Making, 1, 59–69. de Farias, D. P and Roy, B. V. (2003). The linear programming approach to approximate dynamic programming. Operations Research, 51, 839–1016. de Finetti, B. (1937). Le prévision: ses lois logiques, ses sources subjectives. Ann. Inst. Poincaré

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, C. A. (1989). Adaptive importance sampling. In Proc. Fifth International Conference on Structural Safety and Reliability. Karmarkar, N. (1984). A new polynomial–time algorithm for linear programming. Combinatorica, 4, 373–395. Karp, R. M. (1972). Reducibility among combinatorial problems. In Miller, R. E. and Thatcher, J. W. (Eds.), Complexity of Computer Computations

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, 14, 151–165. Manna, Z. and Waldinger, R. (1985). The Logical Basis for Computer Programming: Volume 1: Deductive Reasoning. Addison-Wesley. Manne, A. S. (1960). Linear programming and sequential decisions. Management Science, 6, 259–267. Manning, C. and Schutze, H. (1999). Foundations of Statistical Natural Language Processing. MIT Press. Manning, C., Raghavan

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., 356, 1104 Lindsten, F., 517, 1104 linear-Gaussian, 440, 473, 497, 656, 779 linear algebra, 1076–1077 linear constraint, 167 linear function, 694 linearization, 942 linear programming, 139, 159, 161, 167, 562, 603 linear quadratic regulator (LQR), 962, 982 linear regression, see regression (in machine learning) linear resolution, 326 linear separability, 700

Capital Ideas: The Improbable Origins of Modern Wall Street

by Peter L. Bernstein  · 19 Jun 2005  · 425pp  · 122,223 words

Prize in economic sciences in 1975 for his work in this area. Koopmans developed an analytic method known as linear programming or activity analysis that falls under the general heading of operations research. Linear programming solves problems that involve combinations of inputs and outputs. Assume, for example, that an airline has a limited number

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economizing on crew time its most important objective? Or if it wanted to make as many landings as possible in the New York City area? Linear programming identifies the combinations of inputs and outputs that are achievable, defines the combinations that minimize the inputs and maximize the outputs, and then identifies the

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and developed a systematic means to avoid it. Markowitz’s reflections on diversification and risk led him to explore the subject more thoroughly in a linear programming course he was taking under Koopmans. Koopmans had asked the class to describe a resource allocation problem and state whether or not it was a

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linear programming problem. Markowitz took the occasion to analyze the choices facing an investor who must decide between seeking high returns and attempting to hold down risk

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at the same time. He concluded that the solution to this problem was even more complex than linear programming. Koopmans gave him an A on his paper and noted, “The problem does not seem that hard. Why don’t you solve it?”10 That

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between risk and reward in selecting a portfolio; this is the subject matter of his 1952 article and is closely related to the techniques of linear programming that Markowitz learned from Koopmans. The second track tells how each investor should go about selecting the single portfolio that most closely conforms to the

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an envelope. The task is simpler if you have access to a computer. Markowitz combined his skill with the computer with Koopmans’s achievements in linear programming to make the task at least manageable. Still, the audience for such technical matters was still limited in the 1950s. The Naval Research Logistics Quarterly

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up residence in the Los Angeles area at a think tank called RAND—an acronym for R&D, or research-and-development—to work on linear programming applications for industrial firms. RAND had been established during World War II, primarily to do research for the armed forces. Its sphere of interest has

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the Dutch economist Tjalling Koopmans. Koopmans was then working in New York for a Dutch shipping company, where he was applying his new technique of linear programming to the company’s scheduling problems. Modigliani then launched forth on a varied teaching career. He began at the New Jersey College for Women. In

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breakdowns. Analysts were developing long-run forecasts to implement the dividend discount model. Computer-based portfolios were up and running, with risk-controlled procedures and linear programming to combine the holdings into the optimal portfolio. In 1970 further impetus came unexpectedly from outside. Keith Schwayder, a young man who had just completed

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’Brien Rubinstein Associates, Inc. (LOR) Leland-Rubinstein Associates Leverage Leveraged buyouts Liquidity management market money Preference theory stock “Liquidity Preference as Behavior Toward Risk” (Tobin) Linear programming Loading charges: see Brokerage commissions London School of Economics (LSE) London Stock Exchange Macroeconomics Management Science Marginal utility concept “Market and Industry Factors in Stock

Television disrupted: the transition from network to networked TV

by Shelly Palmer  · 14 Apr 2006  · 406pp  · 88,820 words

(early morning, daytime, family time, prime time access, etc.) Pay Per View • On-demand • Subscription • Ad-supported Distribution Traditional network television was developed to deliver linear programming using a fairly efficient one-to-many system. Alternatively, networked television systems offer one-to-one and optionally, non-linear distribution. Linear Distribution Methodology • Broadcast

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, Near-VOD) • Consumer-based time-shifted (personal video recorder, TiVo®, Media Center) Technically speaking, all of the linear methodologies could be used to distribute non-linear programming as well. But in common practice, only cable, IPTV and the Internet are used to do so. Copyright © 2006, Shelly Palmer. All rights reserved. 1

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IPTV systems. The unique attribute of linear television is that it is scheduled for you by the network or station programmers. Marketers sometimes refer to linear programming as “destination television” because you are supposed to watch the program when it is presented. (Of course, consumers don’t always do what they’re

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subscription, pure subscription, pay-per-view, rental and purchase. • The major components of the television business are form factors, packaging and distribution. • Linear programming is scheduled for consumers, Non-linear programming is on-demand. • There are highly evolved business rules and negotiable currencies used in the traditional television business, and these must evolve for

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network advertising executives. Of course, you can use the enhancements to help call attention to the advertisements just as easily as you can with the linear programming content. This actually works and, for the limited number of people who enjoy playing enhanced television games, is more effective than its pure linear counterpart

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7:21 AM Page 58 58 C H A P T E R 4 Existing Wireless Networks consumers want or need a way to watch linear programming on a mobile phone. But, this won’t stop content owners from making every possible piece of branded content available in the format. The “cool

Algorithms to Live By: The Computer Science of Human Decisions

by Brian Christian and Tom Griffiths  · 4 Apr 2016  · 523pp  · 143,139 words

continuous versions of these problems: There are certain kinds of continuous optimization problems that can be solved in polynomial time; the most prominent example is linear programming problems, in which both the metric to be optimized and the constraints on the solution can be expressed as a linear function of the variables

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involved. See Khachiyan, “Polynomial Algorithms in Linear Programming,” and Karmarkar, “A New Polynomial-Time Algorithm for Linear Programming.” However, continuous optimization is no panacea: there are also classes of continuous optimization problems that are intractable. For example, see Pardalos

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precursors, however, also exist—for instance, Lorie and Savage, “Three Problems in Rationing Capital”; Everett III, “Generalized Lagrange Multiplier Method”; and Gilmore and Gomory, “A Linear Programming Approach to the Cutting Stock Problem, Part II.” For an overview and reflections see Fisher, “The Lagrangian Relaxation Method for Solving Integer Programming Problems,” as

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Coulston. Pierre-Simon Laplace, 1749–1827: A Life in Exact Science. Princeton, NJ: Princeton University Press, 2000. Gilmore, Paul C., and Ralph E. Gomory. “A Linear Programming Approach to the Cutting Stock Problem, Part II.” Operations Research 11, no. 6 (1963): 863–888. Gilovich, Thomas. How We Know What Isn’t So

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Metaphysik der Sitten. Riga: Johann Friedrich Hartknoch, 1785. ______. Kritik der praktischen Vernunft. Riga: Johann Friedrich Hartknoch, 1788. Karmarkar, Narendra. “A New Polynomial-Time Algorithm for Linear Programming.” In Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, 1984, 302–311. Karp, Richard M. “An Introduction to Randomized Algorithms.” Discrete Applied

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, John L. “A New Interpretation of Information Rate.” Information Theory, IRE Transactions on 2, no. 3 (1956): 185–189. Khachiyan, Leonid G. “Polynomial Algorithms in Linear Programming.” USSR Computational Mathematics and Mathematical Physics 20, no. 1 (1980): 53–72. Khot, Subhash, and Oded Regev. “Vertex Cover Might Be Hard to Approximate to

Masterminds of Programming: Conversations With the Creators of Major Programming Languages

by Federico Biancuzzi and Shane Warden  · 21 Mar 2009  · 496pp  · 174,084 words

just no substitute for years of hard work. So here you are in the middle of some project and you decide you need to understand linear programming to solve your problem; probably what you’ll get from the Internet will not be helpful, and if you have to solve this problem within

How I Became a Quant: Insights From 25 of Wall Street's Elite

by Richard R. Lindsey and Barry Schachter  · 30 Jun 2007

, if not all, such restrictions. Could a computer allocate the funds in a more efficient manner? This seemed to be an ideal opportunity for a linear programming application: Maximize expected return while meeting all regulatory restrictions. The results demonstrated that manual adherence to each restriction with cushions was expensive in terms of

Statistics in a Nutshell

by Sarah Boslaugh  · 10 Nov 2012

, NJ: Wiley. This handy pocket guide describes numerical operations useful in business, including index numbers, interest and mortgage problems, forecasting, hypothesis testing, decision theory, and linear programming. Gordon, Robert J. 1999. “The Boskin Commission Report and its aftermath.” Paper presented at the Conference on the Measurement of Inflation, Cardiff, Wales. http://faculty

The Art of Computer Programming: Fundamental Algorithms

by Donald E. Knuth  · 1 Jan 1974

. Representation of matrix A2), with nodes in the format List heads appear at the left and at the top. LEFT UP ROW COL VAL solving linear programming problems by the simplex method. A pivot step is the following matrix transformation: / Pivot row Any other row • • Before pivot step After Any Pivot other

Commodity Trading Advisors: Risk, Performance Analysis, and Selection

by Greg N. Gregoriou, Vassilios Karavas, François-Serge Lhabitant and Fabrice Douglas Rouah  · 23 Sep 2004

outputs of the DMU. Following Banker, Charnes, and Cooper (BCC) (1984) we can measure the output-oriented efficiency of the ith DMU by solving this linear programming problem:17 Max fi Subject to N ∑ λ j yrj j =1 N ∑ λ j xsj j =1 N ∑ λj ≥ φi yri r = 1, 2

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an inefficient DMU fi > 1. On the other hand, an input-oriented measure of efficiency can be obtained for the ith DMU by solving the linear programming problem: 16The concept of efficiency used here is that of technical efficiency. It is used in the context of an expanded efficient frontier with n

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