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Optimal capacity expansion under uncertainty

Published online by Cambridge University Press:  01 July 2016

M. H. A. Davis ,
M. A. H. Dempster ,
S. P. Sethi  and
D. Vermes
M. H. A. Davis*
Affiliation:
Imperial College, London
M. A. H. Dempster*
Affiliation:
Dalhousie University
S. P. Sethi*
Affiliation:
University of Toronto
D. Vermes*
Affiliation:
University of Szeged
*
∗Postal address: Department of Electrical Engineering, Imperial College, London SW7 2BT, England.
∗∗ Postal address: Department of Mathematics, Statistics and Computing Science and School of Business Administration, Dalhousie University, Halifax, Nova Scotia, Canada B3H 1Z5.
∗∗∗ Postal address: Faculty of Management Studies, University of Toronto, Toronto, Ontario, Canada M5S 1V5.
∗∗∗∗ Postal address: Bólyai Institute, University of Szeged, Szeged, Hungary.
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Abstract

Capacity expansion is the process of providing new facilities over time to meet rising demand. A general mathematical model of this process is presented, incorporating uncertain future demand (including the possibility of ‘surprises’), non-zero lead times and random cost overruns. In this model the decision maker controls the rate of investment in the current expansion project. Optimization is studied by methods of stochastic control theory. Numerical algorithms are presented which determine the optimal policy in some simple cases.

Keywords

STOCHASTIC CONTROL THEORYPIECEWISE-DETERMINISTIC PROCESSESDYNAMIC PROGRAMMING
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 156 - 176
Copyright
Copyright © Applied Probability Trust 1987 

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References

Andersson, A. E., Hjorth, P., De Mare, L. and Thelander, A. L. (1979) Water resources planning and management in advanced economies: the case study of western Skåne, Sweden–the background report. Working Paper WP-79-23, International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
Bensoussan, A. and Lions, J. L. (1982) Contrôle impulsionnel et inéquations quasivariationelles. Dunod, Paris.Google Scholar
Bensoussan, A. and Tapiero, C. S. (1979) Impulsive control in management science: prospect and survey. Working Paper 79-34, European Institute for Advanced Studies in Management, Brussels.Google Scholar
Davis, M. H. A. (1984) Piecewise deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Statist. Soc. B 46, 353–388.Google Scholar
Davis, M. H. A. (1986) Control of piecewise-deterministic processes via discrete-time dynamic programming. In Proc 3rd Bad Honnef Symp. Stochastic Differential Systems, Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin.Google Scholar
De Leve, G., Federgruen, A. and Tijms, H. C. (1977) A general Markov decision method I: Model and techniques. Adv. Appl. Prob. 9, 296–315.CrossRefGoogle Scholar
Erlenkotter, D., Sethi, S. and Okada, N. (1981) Planning for surprise: water resources development under supply and demand uncertainty. I. The general model. Working Paper, International Institute for Applied Systems Analysis, Laxenburg, Austria.Google Scholar
Fleming, W. H. and Rishel, R. (1975) Deterministic and Stochastic Optimal Control. Springer-Verlag, New York.Google Scholar
Freidenfelds, J. (1980) Capacity expansion when demand is a birth-death random process. Operat. Res. 28, 712–721.Google Scholar
Grossman, D. and Marks, D. H. (1977) Capacity expansion for water resources facilities: a control theoretic algorithm for nonstationary uncertain demands. Adv. Water Resources 1, 31–40.CrossRefGoogle Scholar
Luss, H. (1982) Operations research and capacity expansion problems: a survey. Operat. Res. 30, 909–947.Google Scholar
Manne, A. S., (Ed) (1961) Investments for Capacity Expansion: Size, Location, and Timing-Planning. MIT Press, Cambridge, Mass. Google Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, Mass. Google Scholar
Nickell, S. (1977) Uncertainty and lags in the investment decisions of firms. Rev. Econom. Studies 44, 249–263.CrossRefGoogle Scholar
Segall, A., Davis, M. H. A. and Kailath, T. (1975) Nonlinear filtering with counting observations. IEEE Trans. Inf. Theory 21, 143–149.CrossRefGoogle Scholar
Tapiero, C. S. (1979) Capacity expansion of a deteriorating facility under uncertainty. RAIRO Rech. Operat. 13, 55–66.Google Scholar
Van Der Duyn Schouten, F. A. (1983) Markov Decision Drift Processes. Mathematical Centre Tract, Amsterdam.Google Scholar
Vermes, D. (1985) Optimal control of piecewise-deterministic processes. Stochastics 14, 165–208.CrossRefGoogle Scholar