PLANNING SECTORAL INVESTMENTS WITH ECONOMIES OF SCALE: A COMPUTATIONALLY EFFICIENT MIXED BIVALENT PROGRAMMING APPROACH

Year 1994, Volume: 12 , 49 - 60, 31.12.1994

Armağan Tarım Bilge Hacıhasanoğlu

Abstract

In this paper, a sectoral investment planning
model is examined from computaüonal point of view. It is a well known fact that
conventional mixed bivalent programming models with complex combinatorial
structures are generally intractable.
The paper exploits such a model to determine what capacity,
if any, should be maintained at the various geographical regions during the
planning period in order to meet regional demand and minimise total cost of the
entire system. A Lagrangean relaxation-basedprocedure
is developed to decompose the model into submodels by each geographical region
and planning year. Following that, computationally efficient algorithms to
solve the submodels are presented and computational results are discussed

Keywords

Planning, Integer Programming, Lagrangean Relaxation, Modelling

References

• Smith, C, "Survey on the Empirical Evidence on Economies of Scale", in Business Consentration and Price Policy, Princeton University Press; Princeton, 1955.
• Hacihasano¿lu, B., C)lçek Ekonomileri ve Sektörel Yahrtna Planlamasz, Hacettepe Ûniversitesif fictisadi ve Idari Bilimler Fakültesi Yaym No:13, Ankara, 1986.
• Geoffrion, A.M., "Lagrangean Relaxation for Integer Programming," Mathematical Programming", Mathematical Programming Study", Vol.2, 1974, pp.82-114.
• Fisher, M.L., "The Lagrangian Relaxation Methods for Solving Integer Programming Problems}' Management Science, Vol.27, 1981, pp.1-18.
• Fisher, M.L., "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, Vol.15, 1985, pp.10-21.
• Shapiro, J.F„ " A Survey of Lagrangean Techniques for Discrete Orgnization", Annals of Discrete Mathematics, vol.5, 1979, pp.113-118.
• Held, M., P.Wolfe, and H.DCrowder, "Validation of Subgradient Optimization," Mathematica Programming, vol.6, 1974, pp.62-68.