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Algorithm for turnpike policies in the dynamic lot size model

100%

Bylka S.

Applicationes Mathematicae

1996-1997

tom 24

nr 1

57-75

This article considers optimization problems in a capacitated lot sizing model with limited backlogging. Nothing is assumed about the cost function in the case of finite restrictions of the size on the stock and backlogs. The holding and backlogging costs are functions assumed to be stationary or nearly stationary in time. In both cases, it is shown that there exists an optimal infinite inverse policy and a periodical turnpike policy. Some forward and backward procedures are adopted that determine an optimal infinite inverse policy and a strong turnpike policy relative to the class of standard or batch ordering type policies. Some remarks on the existence of planning and forecast horizons are also given.

Forecast horizon in dynamic family of one-dimensional control problems

89%

Rempała R.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Sufficient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 3. Definitions and hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. Properties of arcs and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 5. Dynamic family of optimal controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6. The maximum principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 7. Horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 8. Remarks to horizon theorems. An economic application . . . . . . . . . . . . . . . . . . . . 27 9. Discrete-time linear systems with stochastic parameters. Horizon theorems . . . . . 29 10. Proof of horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 11. Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Ograniczanie wyników

1 Applicationes Mathematicae

1 Bylka S.

1 Rempała R.

1 1996

1 1991

Wyniki wyszukiwania

Algorithm for turnpike policies in the dynamic lot size model

Forecast horizon in dynamic family of one-dimensional control problems