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Nonlinear goal programming theory and practice: A survey. (English) Zbl 0771.90087

Summary: Four major approaches of Nonlinear Goal Programming are reviewed and discussed; (1) simplex based; (2) direct search; (3) gradient search and (4) interactive approaches. The applications of Nonlinear Goal Programming are also discussed and classified into the following nine areas: (1) engineering design; (2) energy; (3) manufacturing/metal cutting; (4) marketing; (5) finance and accounting; (6) agriculture/farm planning; (7) routing and scheduling; (8) quality control and (9) R& D project selection.

MSC:

90C29 Multi-objective and goal programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
90C90 Applications of mathematical programming

Software:

PAGP
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References:

[1] Zionts, S., Methods for solving management problems involving multiple objectives, (Fandel, G.; Gal, T., Multiple Criteria Decision Making, Vol. 177 (1980), Springer: Springer Berlin), 540-558
[2] Chankong, V.; Haims, Y., Multiobjective Decision Making: Theory and Methodology (1983), North-Holland: North-Holland Amsterdam · Zbl 0622.90002
[3] Keeney, R.; Raiffa, H., Decision with Multiple Objectives: Preferences and Value Tradeoffs (1976), Wiley: Wiley New York · Zbl 0488.90001
[4] Goicoechea, A.; Hansen, A.; Duckstein, L., Multiobjective Decision Analysis with Engineering and Business Applications (1982), Wiley: Wiley New York · Zbl 0584.90045
[5] Hwang, C.; Masud, A., Multiple Objective Decision Making Methods and Applications (1979), Springer: Springer Berlin
[6] Steuer, R., Multiple Criteria Optimization: Theory, Computation and Application (1986), Wiley: Wiley New York · Zbl 0663.90085
[7] White, D., Multi-objective interactive programming, J. Ops Res. Soc., 31, 517-523 (1980) · Zbl 0426.90080
[8] Zeleny, M., Multiple Criteria Decision Making (1982), McGraw-Hill: McGraw-Hill New York · Zbl 0588.90019
[9] Shin, W.; Ravindran, A., An interactive MOMP method: a survey, Computers Ops Res., 18, 97-114 (1991)
[10] Klein, G.; Moskowitz, H.; Ravindran, A., Interactive multiobjective optimization under uncertainty, Mgmt Sci., 36, 58-75 (1990) · Zbl 0694.90089
[11] Charnes, A.; Cooper, W., (Management Models and Industrial Applications of Linear Programming, Vols 1 and 2 (1961), Wiley: Wiley New York) · Zbl 0107.37004
[12] Ijiri, Y., Management Goals and Accounting for Control (1965), North-Holland: North-Holland Amsterdam
[13] Lee, S., Goal Programming for Decision Analysis (1972), Auerbach, PA
[14] Ignizio, J., Goal Programming and Extensions (1976), Heath: Heath Lexington, Mass
[15] Arthur, J.; Ravindran, A., An efficient goal programming algorithm using constraint-partitioning and variable elimination, Mgmt Sci., 24, 867-868 (1978)
[16] Arthur, J.; Ravindran, A., PAGP: an efficient algorithm for linear goal programming problems, ACM Trans. Mathl Softw., 6, 378-386 (1980) · Zbl 0439.90083
[17] Lee, S.; Morris, R., Integer goal programming methods, (Starr, M.; Zeleny, M., Multiple Criteria Decision Making (1977), North-Holland: North-Holland Amsterdam), 273-289
[18] Garrod, N.; Moores, B., An implicit enumeration algorithm for solving zero-one goal programming problems, Omega, 6, 374-377 (1978)
[19] Lee, S., Interactive integer programming: methods and applications, (Zionts, S., Multiple Criteria Problem Solving (1978), Springer: Springer Berlin), 362-383
[20] Zanakis, S., A method for large scale integer goal programming with an application to a facility location/allocation problem, (Morse, J., Organizations: Multiple Agents with Multiple Criteria (1980), Springer: Springer Berlin), 490-498
[21] Arthur, J.; Ravindran, A., A branch and bound algorithm with constraint partitioning for integer goal programming, Europ. J. Opl Res., 4, 421-425 (1980) · Zbl 0436.90104
[22] Weistroffer, H., An interactive goal programming method for nonlinear multiple-criteria decision-making problems, Computers Ops Res., 10, 311-320 (1983)
[23] Ravindran, A.; Shin, W.; Arthur, J.; Moskowitz, H., Nonlinear integer goal programming models for acceptance sampling, Computers Ops Res., 13, 611-622 (1986) · Zbl 0615.90091
[24] Griffith, R.; Stewart, R., A nonlinear programming technique for the optimization of continuous processing systems, Mgmt Sci., 7, 379-392 (1961) · Zbl 0995.90610
[25] Miller, C., The simplex method for local separable programming, (Graves, R. L.; Wolfe, P., Recent Advances in Mathematical Programming (1963), McGraw-Hill: McGraw-Hill New York) · Zbl 0232.90060
[26] Wynne, A., Multicriteria optimization with separable and chance-constrained goal programming (1978), University of Nebraska-Lincoln, Unpublished PhD. dissertation
[27] Reeves, G., Quadratic goal programming, (Paper presented at the ORSA/TIMS joint national meeting (1977), San Francisco: San Francisco Calif)
[28] Beale, E., Numerical methods, (Abadie, J., Nonlinear Programming (1967), North-Holland: North-Holland Amsterdam) · Zbl 0168.40602
[29] Cooper, L.; Steinberg, D., Introduction to Methods of Optimization (1970), Saunders: Saunders Philadelphia · Zbl 0208.21401
[30] Reklaitis, G.; Ravindran, A.; Ragsdell, K., Engineering Optimization: Methods and Applications, ((1983), Wiley: Wiley New York)
[31] Bazaraa, M.; Shetty, C., Nonliner Programming: Theory and Algorithms (1979), Wiley: Wiley New York · Zbl 0476.90035
[32] Wolfe, P., Methods of nonlinear programming, (Graves, R.; Wolfe, P., Recent Advances in Mathematical Programming (1963), McGraw-Hill: McGraw-Hill New York) · Zbl 0178.22802
[33] Ringuest, J.; Gulledge, T., Quadratic goal programming: a multivariate value function approach, (Proc Am. Inst. Decis. Sci., 2 (1982)), 265-267
[34] Gupta, A.; Sharma, J., Integer quadratic goal programming, J. Inst. Engr. (India), 70, 43-47 (1989)
[35] Box, J., A new method of constrained optimization and a comparison with other methods, Computer J., 8, 42-52 (1965) · Zbl 0142.11305
[36] Monarchi, D., Nonlinear goal programming: formulation and example, (Management science report series, report No. 75-12 (1975), Graduate School of Business Administration, The University of Colorado)
[37] Nanda, J.; Kothari, D.; Lingamurthy, K., Economic-emission load dispatch through goal programming techniques, IEEE Trans. Energy Conver., 3, 26-32 (1988)
[38] Hooke, R.; Jeeves, T., Direct search of numerical and statistical problems, J. ACM, 8, 212-229 (1961) · Zbl 0111.12501
[39] Clayton, E.; Weber, W.; Taylor, B., A goal programming approach to the optimization of multiresponse simulation models, IIE Trans., 14, 282-287 (1982)
[40] Taylor, B.; Moor, L.; Clayton, E., R&D project selection and manpower allocation with integer nonlinear goal programming, Mgmt Sci., 28, 1149-1158 (1982)
[41] Taylor, B.; Moore, L.; Clayton, E.; Roscoe, K.; Pakes, T., An integer goal programming models for the deployment of state highway patrol units, Mgmt Sci., 31, 1335-1347 (1985)
[42] Lee, S.; Olson, D., A gradient algorithm for chance constrained nonlinear goal programming, Europ. J. Opl Res., 22, 359-369 (1985) · Zbl 0578.90062
[43] Zoutendijk, G., Methods of Feasible Directions (1960), Elsevier: Elsevier Amsterdam · Zbl 0097.35408
[44] Saber, H.; Ravindran, A., A partitioning algorithm for nonlinear goal programming, (Paper presented at the TIMS/ORSA joint national meeting. Paper presented at the TIMS/ORSA joint national meeting, Las Vegas, Nev. (1990)) · Zbl 0868.90102
[45] Abadie, J.; Carpentier, J., Generalization of the Wolfe reduced gradient method of the case of nonlinear constraints, (Fletcher, R., Optimization (1969), Academic Press: Academic Press New York), 37-47 · Zbl 0254.90049
[46] Lasdon, L.; Waren, A.; Jain, A.; Ratner, M., Design and testing of a generalized reduced gradient code for nonlinear programming, ACM Trans. Mathl Softw., 4, 34-50 (1978) · Zbl 0378.90080
[47] Saber, H., A partitioning gradient based (PGB) algorithm for solving nonlinear goal programming problems (1991), The University of Oklahoma, Unpublished Ph.D. dissertation
[48] Masud, A.; Hwang, C., Interactive sequential goal programming, J. Opl Res., 32, 391-400 (1981) · Zbl 0452.90069
[49] Dyer, J., Interactive goal programming, Mgmt Sci., 19, 62-70 (1972) · Zbl 0257.90023
[50] Monarchi, D.; Weber, J.; Duckstein, L., An interactive multiple objective decision-making aid using nonlinear goal programming, (Zeleny, M., Multiple Criteria Decision Making, Kyoto (1976), Springer: Springer Berlin) · Zbl 0335.90002
[51] El-Sayed, M.; Ridgely, B.; Sandgren, E., Nonlinear structural optimization using goal programming, Computers Struct., 32, 69-73 (1989) · Zbl 0688.73060
[52] Sandgren, E., Structural design optimization for latitude by nonlinear goal programming, Computers Struct., 33, 1395-1402 (1989) · Zbl 0703.73057
[53] Hwang, C.; Lee, H.; Tillman, F.; Lie, C., Nonlinear integer goal programming applied to optimal system reliability, IEEE Trans. Reliabil., 33, 431-438 (1984) · Zbl 0592.90043
[54] Ignizio, J.; Plamer, D.; Murphy, C., A multicriteria approach to super system architecture definition, IEEE Trans. Computers, 31, 410-418 (1982)
[55] McCammon, D. F.; Thompson, W., The design of Tonplitz piezoelectric transducers using nonlinear goal programming, J Acoust. Soc. Am., 68, 754-757 (1980)
[56] Van Crombrugge, M.; Thompson, W., Optimization of the transmitting characteristics of a Tonpilz-type transducer by proper choice of impedance matching layers, J. Acoust. Soc. Am., 77, 747-752 (1985)
[57] Lee, S.; Olson, D., Chance constrained aggregate blending, J. Construct. Engng Mgmt., 109, 39-47 (1983)
[58] Philipson, R.; Ravindran, A., Application of goal programming to machinability data optimization, Trans. ASME, 100, 286-291 (1978)
[59] Satyanarayana, B.; Rao, P.; Tewari, N., Application of nonlinear goal programming technique in metal cutting, (Proceedings of the 12th All India Machine Tool Design and Research Conference (1986), McGraw-Hill: McGraw-Hill New Delhi), 483-486
[60] Subbarao, P.; Jacobs, C., Application of nonlinear goal programming to machining variable optimization, (Proceedings of the 6th Manufacturing Engineering Transaction (1978), Metal Work Research Conference: Metal Work Research Conference Dearborn, Michigan), 298-303
[61] Takakuwa, S., Multiobjective optimization of manufacturing systems (1982), the Pennsylvania State University, Unpublished Ph.D. Dissertation
[62] Charnes, A.; Cooper, W.; Devoe, J.; Leaner, D.; Reineck, W., A goal programming model for media planning, Mgmt Sci., 14, 423-430 (1968)
[63] Charnes, A.; Cooper, W.; Learner, D.; Snow, E., Application of goal programming model for media planning, Mgmt Sci., 14, 431-436 (1968)
[64] Tawfik, M. S., An optimal international transfer pricing system: a nonlinear multiobjective approach (1982), The Pennsylvania State University, Unpublished Ph.D. dissertation
[65] De, P.; Acharya, D.; Sahu, K., A chance-constrained goal programming model for capital budgeting, J. Ops Res. Soc., 33, 635-638 (1982) · Zbl 0484.90077
[66] Ignizio, J., The development of cost estimating relationships via goal programming, Engng Econ., 24, 32-47 (1979)
[67] Keown, A., A chance-constrained goal programming model for bank liquidity management, Decis. Sci., 9, 93-106 (1978)
[68] Keown, A.; Martin, J., A chance-constrained goal programming model for working capital management, Engng Econ., 22, 153-174 (1977)
[69] Keown, A.; Taylor, B., A chance-constrained integer goal programming model for capital budgeting in the production area, J. Ops Res. Soc., 31, 579-589 (1980)
[70] Mitra, A.; Parankar, J., Warranty cost estimation: a goal programming approach, Decis. Sci., 19, 409-423 (1988)
[71] Stone, B.; Reback, R., Constructing a model for managing portfolio revisions, J Bank Res., 6, 48-60 (1975)
[72] Dash, G., Nonlinear goal programming via separable approximations in financial institution portfolio managment (1978), University of Colorado, Unpublished Ph.D. Dissertation
[73] Tayi, G.; Gangolly, J., Integration of auditor preferences and sampling objectives: a polynomial goal programming perspective, J. Ops Res. Soc., 36, 951-957 (1985) · Zbl 0573.90056
[74] Everitt, R.; Sonntag, N.; Puterman, M.; Whalen, P., A mathematical programming model for a renewable resource system: The Kemano II developing project, J. Fish. Res. Bd Canada, 35, 235-246 (1978)
[75] Chang, D., Optimum systems of rough rice handling, drying and storage (1981), Kansas State University, Unpublished Ph.D. dissertation
[76] Franz, L.; Rakes, T.; Wynne, A., A chance-constrained multiobjective model for mental health services planning, Socio-Econ. Plann. Sci., 18, 89-95 (1984)
[77] Rakes, T.; Franz, L.; Wynne, A., Aggregate production planning using chance-constrained goal programming, Int. J. Prod. Res., 22, 673-684 (1984)
[78] Tayi, G., A polynomial goal programming approach to a class of quality control problems, J. Ops Mgmt, 5, 237-247 (1985)
[79] Odom, P.; Shannon, R.; Buckles, B., Multi-goal subset selection under uncertainty, AIIE Trans., 11, 61-69 (1979)
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