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On the Status of Multistage Linear Programming Problems

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  • George B. Dantzig

    (The RAND Corporation, Santa Monica, California)

Abstract

In the first part special cases are presented. Typical of the multistage problems are those encountered in dynamic problems. If the time span is divided into periods, the initial inventory provides the input for activities that occur in the first period or first stage. The output from the first stage provides the inventory input for activities in the second period or stage, etc. [Dantzig, G. B. 1951. Programming of interdependent activities: Mathematical model, chapter II. T. C. Koopmans, ed. Activity Analysis of Production and Allocation. John Wiley and Sons, 19-33. Also Econometrica 17 (3-4) (1949).]. In the general case, the need to solve large scale systems is considered, followed by a discussion on solving general block triangular systems that cover a vast majority of practical problems.

Suggested Citation

  • George B. Dantzig, 1959. "On the Status of Multistage Linear Programming Problems," Management Science, INFORMS, vol. 6(1), pages 53-72, October.
    • Handle: RePEc:inm:ormnsc:v:6:y:1959:i:1:p:53-72
    DOI: 10.1287/mnsc.6.1.53
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    Cited by:

    1. Daphné Lorne & Stéphane Tchung-Ming, 2012. "The French biofuels mandates under cost uncertainty - an assesment based on robust optimization," Working Papers hal-03206367, HAL.
    2. Gerald Brown & Joseph Keegan & Brian Vigus & Kevin Wood, 2001. "The Kellogg Company Optimizes Production, Inventory, and Distribution," Interfaces, INFORMS, vol. 31(6), pages 1-15, December.

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