Abstract
In this paper the well known “wheat trading” problem is generalized to allow for general non-linear holding cost functions. A forward algorithm in the spirit of the Modigliani-Hohn and Arrow-Karlin algorithms is given. Furthermore the conditions for the existence of weak decision and forecast horizons are relaxed. In particular, it is shown that the price may on some intervals exceed the price shield introduced by Sethi and Thompson without violating the optimality of the solution in the first interval.
Zusammenfassung
In dieser Arbeit wird das bekannte „Weizenhandels“-Problem auf den Fall nichtlinearer Lagerhaltungskosten verallgemeinert und mit Hilfe eines Vorwärtsalgorithmus' im Stile der Modigliani-Hohn und Arrow-Karlin-Algorithmen gelöst. Weiters werden die Bedingungen für die Existenz von schwachen Entscheidungs- und Prognosehorizonten gelockert. Dabei wird gezeigt, daß der Preispfad auch auf ganzen Intervallen den von Sethi-Thompson eingeführten PreisSchild überschreiten darf, ohne die Optimalität der Lösung im ersten Intervall zu verletzen.
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References
Arrow KJ, Karlin S (1958) Production over time with increasing marginal costs. In: Arrow KJ, Karlin S, Scarf H (eds) Studies in the mathematical theory of inventory and production. Stanford Univ Press, Stanford, pp 61–69
Feichtinger G, Hartl RF (1986) Optimale Kontrolle ökonomischer Prozesse: Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften. De Gruyter, Berlin
Hartl RF (1984) A survey of the optimality conditions for optimal control problems with state variable inequality constraints. In: Brans JP (ed) Operational research '84. North-Holland, Amsterdam, pp 423–433
Ijiri Y, Thompson GL (1970) Applications of mathematical control theory to accounting and budgeting (the continuous wheat trading model). Accounting Rev 45:246–258
Jacobson DH, Lele MM, Speyer JL (1971) New necessary conditions of optimality for control problems with state-variable inequality constraints. J Math Analysis & Applications 35:255–284
Maurer H (1979) Differential stability in optimal control problems. Appl Math & Optimiz 5: 283–295
Modigliani F, Hohn F (1955) Production planning over time and the nature of the expectation and planning horizon. Econometrica 23:46–66
Rempala R (1980) On the multicommodity Arrow-Karlin inventory model. Proc First Int Symp on Inventories, Hungarian Acad of Science, Budapest, pp 491–499
Rempala R (1982) On the multicommodity Arrow-Karlin inventory model — part II: Horizon and horizontal solution. Proc Second Int Symp on Inventories, Hungarian Acad of Science, Budapest, pp 785–792
Seierstad A, Sydsaeter K (1977) Sufficient conditions in optimal control theory. International Economic Review 18:367–391
Sethi SP, Thompson GL (1982) Planning and forecast horizons in a simple wheat trading model. In: Feichtinger G (ed) Operations research in progress. Reidel, Dordrecht, pp 203–214
Sprzeuzkouski AY (1967) A problem in optimal stock management. J Optim Theory & Applications 1:232–241
Stöppler S (1985) Der Einfluß der Lagerkosten auf die Produktionsanpassung bei zyklischem Absatz — Eine kontrolltheoretische Analyse. OR-Spektrum 7:129–142
Teng J-T, Thompson GL, Sethi SP (1984) Strong decision and forecast horizons in a convex production planning problem. Opt Control Applications & Methods 5:319–330
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This research was supported by a grant S 3204 on “Dynamics of the Firm.” from Fonds zur Förderung der wissenschaftlichen Forschung.
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Hartl, R.F. A forward algorithm for a generalized wheat trading model. Zeitschrift für Operations Research 30, A135–A144 (1986). https://doi.org/10.1007/BF01919174
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DOI: https://doi.org/10.1007/BF01919174