Abstract
This chapter considers linear programming problems (LPPs). We show the practical significance of LPPs through a number of examples and then analyze the geometric and algebraic features of LPPs. We also describe a well known solution algorithm, show how to perform a sensitivity analysis, and provide and discuss the dual form of an LPP.
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References
Bazaraa MS, Jarvis JJ, Sherali HD (2009) Linear programming and network flows, 4th edn. Wiley, New York
Bertsimas D, Tsitsiklis JN (1997) Introduction to linear optimization. Athena scientific series in optimization and neural computation, vol 6, third printing edn. Athena Scientific, Belmont
Brook A, Kendrick D, Meeraus, A (1988) GAMS – a user’s guide. ACM, New York. www.gams.com
Castillo E, Conejo AJ, Pedregal P, GarcÃa R, Alguacil N (2002) Building and solving mathematical programming models in engineering and science. Pure and applied mathematics series. Wiley, New York
Dantzig GB (1963) Linear programming and extensions. Princeton University Press, Princeton
Eaton JW, Bateman D, Hauberg S, Wehbring R (2016) GNU octave version 4.2.0 manual: a high-level interactive language for numerical computations. www.gnu.org/software/octave
Gurobi Optimization, Inc. (2010) Gurobi Optimizer Reference Manual, Version 3.0. Houston, Texas. www.gurobi.com
IBM ILOG CPLEX Optimization Studio (2016) CPLEX User’s Manual, Version 12 Release 7. IBM Corp. www.cplex.com
Luenberger DG, Ye Y (2008) Linear and nonlinear programming. International series in operations research & management science, vol 116, 3rd edn. Springer, New York
MATLAB (2016) The MathWorks, Inc., Natick, Massachusetts. www.mathworks.com/products/matlab
Vanderbei RJ (2001) Linear programming: foundations and extensions. Springer, New York
Wright SJ (1987) Primal-dual interior-point methods. Society for industrial and applied mathematics, Philadelphia, Pennsylvania
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Sioshansi, R., Conejo, A.J. (2017). Linear Optimization. In: Optimization in Engineering. Springer Optimization and Its Applications, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-56769-3_2
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DOI: https://doi.org/10.1007/978-3-319-56769-3_2
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