Abstract
Operations Research (OR) is the branch of science dealing with tools or techniques for decision making to optimize the performance of systems, that is, to make those systems better. Measures of performance, of which there may be several, are numerical criteria that gauge the quality of some aspect of system’s performance, for example, annual profit or market share of a company, etc. They are of two types: (1) profit measures: (for these, the higher the value the better), (2) cost measures: (for these the lower the value the better).
OR deals with techniques for designing ways to operate the system to maximize profit measures or minimize cost measures as desired. Hence OR is the science to make systems better.
Linear Programming (LP) is an important branch of OR dealing with decision problems modeled as those of optimizing a linear function of decision variables subject to linear constraints that may include equality constraints, inequality constraints, and bounds in decision variables. In an LP, all decision variables are required to be continuous variables that can assume all possible values within their bounds subject to the constraints. LPs are special instances of mathematical programming. Besides LP, the subject mathematical programming includes network, integer, combinatorial, discrete, quadratic, and nonlinear programming.
The focus of this book is to study important aspects of LP and QP (quadratic programming) and their intelligent applications for decision making.
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References
Agha SR (2006) ‘Use of goal programming and integer programming for water quality management- A case study of Gaza Strip. Eur J Oper Res 174:1991–1998
Andreatta G, Filipi C, Romanin-Jacur G (1993) The linear balancing flow problem. Eur J OR 64:68–82
Bakshi HC, Bhatia HL, Puri MC (1979) Trade-off relations in assignment problems. Cahiers du Centre d’Etudes de Receherche Operationnelle 21:367–374
Berman O, Einav D, Handler G (1990) The constrained bottleneck problem in networks. Oper Res 38:178–181
Brooks PR, Dula JH (2008) Note on the L 1 projection onto a subspace. Virginia Commonwealth University
Charnes A, Cooper WW (1977) Goal programming and multiple objective optimization, Part I. Eur J Oper Res 1(1):39–54
Davis KR, Webster FE Jr (1968) Sales force management-text and cases. The Ronald Press
Geetha S, Nair KPK (1993) A variation of the assignment problem. Eur J Oper Res 68:422–426
Hwang CL, Masud AS (1979) Multiple objective decision making methods and applications: A state of the art survey. Springer, New York
Ignizio JP (1976) Goal programming and extensions. Lexington Books, Lexington, MA
Iverstine and Kinard (1977) Cases in production and operations management. Charles E. Merill Publishing Co., Columbus, Ohio
Kaplan W (1999) Maxima and minima with applications. Wiley, New York
Keeney RL, Raiffa H (1976) Decisions with multiple objectives. Wiley, New York
Khorramshshgol R, Okoruwa AA (1994) A goal programming approach to investment decisions: A case study of fund allocation among different shopping malls. Eur J Oper Res 73:17–22
Lanzenauer CHV (1975) Cases in OR. Holden-Day, San Francisco
Lee SM (1972) Goal programming for decision analysis. Auerbach, Philadelphia
Mehrotra V, Ozluk O, Salem CL (2006) An application of ORMS to not-for-profit financial management: Optimal assignment of operating costs to restricted funding sources. Working Paper, College of Business, San Francisco State University
Mukherjee K, Bera A (1995) Application of goal programming in project selection decision: A case study from the Indian coal mining industry. Eur J Oper Res 82:18–25
Murty KG (1983) Linear programming. Wiley, New York
Murty KG (1988) Linear complementarity, linear and nonlinear programming. Helderman Verlag, Berlin; Can be accessed on the web from Murty’s webpage at: http://www-personal.engin.umich.edu/ murty/
Murty KG (1995) Operations research: Deterministic optimization models. Prentice Hall, Englewood Cliffs, NJ
Nandalal KDW, Bogardi JJ (2007) Dynamic programming based operation of reservoirs, applicability and limits. Cambridge University Press, UNESCO
Rugg MM, White GP, Endres JM (1983) Using goal programming to improve the calculation of diabetic diets. Computers OR 1(4):365–373
Sawaragi Y, Nakayama YH, Tanino T (1985) Theory of multiobjective optimization, (vol. 176. Mathematics in science and engineering). Academic, Orlando, FL, ISBN 0126203709
Schniederjans MJ (1995) Goal programming : Methodology and applications. Kluwer, Boston
Singh P, Saxena PK (2003) The multiple objective time transportation problem with additional restrictions. Eur J Oper Res 14(6):460–476
Sponk J (1981) Interactive multiple goal programming: Applications to financial management. Martinus Nijhoff, Boston
Steuer RE (1986) Multiple criteria optimization: Theory, computations, and application. Wiley, New York
Steuer RE, Oliver RL (1976) An application of multiple objective linear programming to media selection. Omega 4(4):455–462
Vatter PA, Bradley SP, Frey SC Jr, Jackson BB (1978) Quantitative methods in management: Text and cases. Richard B. Irwin Inc., Homewood, IL
Zeleny M (1974) Linear multiobjective programming. Lecture notes in economics and mathematical systems, vol. 123. Springer Verlag, Berlin
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Murty, K.G. (2010). Formulation Techniques Involving Transformations of Variables. In: Optimization for Decision Making. International Series in Operations Research & Management Science, vol 137. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1291-6_2
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