Abstract
In some dynamic problems it is possible to show that the optimal decisions during an initial positive time interval are either partially or wholly independent of the data from some future time onwards. In such cases, a forecast of the future data needs to be made only as far as that time to make optimal decisions in the initial time interval. The initial time interval is called the planning horizon and the time up to which data is required to make the optimal decisions during the planning horizon is called the forecast horizon. Whenever they exist, these horizons naturally decompose the problem into a series of smaller problems.
This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University, under Contract N00014-75-C-0621 NR 047-048 with the U.S. Office of Naval Research, and Grant A4619 from the Natural Sciences and Engineering Research Council of Canada. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ijiri, Y., and Thompson, G.L., Applications of Mathematical Control Theory to Accounting and Budgeting (The Continuous Wheat Trading Model), The Accounting Review 45 (1970) 246–258.
Kleindorfer, P.R., and Lieber, Z., Algorithms and Planning Horizon Results for Production Planning Problems with Separable Costs, Operations Research 27 (1979) 874–887.
Lieber, Z., An Extension to Modigliani and Hohn’s Planning Horizon Results, Management Science 20 (1973) 319–330.
Lundin, R.A., and Morton, T.E., Planning Horizons for the Dynamic Lot Size Model: Protective Procedures and Computational Results, Operations Research, 23 (1975) 711–734.
Mclntyre, J., and Paiewonsky, B., On Optimal Control with Bounded State Variables, in C. T. Leondes (ed.) Advances in Control Systems, Vol. 5 (Academic Press: New York, 1967) 389–419.
Modigliani, F., and Hohn, F., Production Planning Over Time, Econometrica 23 (1955) 46–66.
Morton, T.E., Universal Planning Horizons for Generalized Convex Production Scheduling, Operations Research, 26 (1978) 1046–1057.
Morton, Thomas E., “Forward Algorithms for Forward Thinking Managers,” Working Paper No. 7–78–79, Graduate School of Industrial Administration, Carnegie- Mellon University (1979).
Norstrom, C.J., The Continuous Wheat Trading Model Reconsidered. An Application of Mathematical Control Theory with a State Constraint, Working Paper No. 58–77–78, Graduate School of Industrial Administration, Carnegie-Mellon University, (1978)
Pekelman, D., Simultaneous Price-Production Decision, Operations Research 22 (1974) 788–794.
Pekelman, D., Production Smoothing with Fluctuating Price, Management Science 21 (1975) 576–590.
Pekelman, D., On Optimal Utilization of Production Processes, Operations Research 27 (1979) 260–278.
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mischenko, E.F., The Mathematical Theory of Optimal Processes ( Wiley: New York, 1962 ).
Sethi, S.P., Nearest Feasible Paths in Optimal Control Problems: Theory, Examples, and Counterexamples, Journal of Optimization Theory and Applications 23 (1977a).
Sethi, S.P., Teng, J.T., and Thompson, G.L., “Planning and Forecast Horizons for a Simultaneous Price-Production Decision Model,” Working Paper No. Graduate School of Industrial Administration, Carnegie-Mellon University, January, 1981.
Sethi, S.P., and Thompson, G.L., Applications of Mathematical Control Theory to Finance, Journal of Financial and Quantitative Analysis 5 (1970) 381–394.
Sethi, S.P., and Thompson, G.L., Optimal Control Theory: Applications to Management Science, Martinus Nijhoff, Boston, 1981.
Thompson, G.L., and Sethi, S.P., Turnpike Horizons for Production Planning, Management Science 26 (1980) 229–241.
Vanthienen, L., Simultaneous Price-Reduction Decision Making with Production Adjustment Costs, Proceedings XX International Meeting of TIMS held in Tel Aviv, Israel on June 24–29, 1973, Vol. 1 (Jerusalem Academic Press: Jerusalem, 1975) 249–254.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 D. Reidel Publishing Company
About this chapter
Cite this chapter
Sethi, S.P., Thompson, G.L. (1982). Planning and Forecast Horizons in a Simple Wheat Trading Model. In: Feichtinger, G., Kall, P. (eds) Operations Research in Progress. Theory and Decision Library, vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7901-7_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-7901-7_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7903-1
Online ISBN: 978-94-009-7901-7
eBook Packages: Springer Book Archive