Qualitative analysis of a one-step finite-horizon boundary for event-driven controllers

The classical proofs for the existence of a stationary (s, S) inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite-horizon models. This note presents a simpler alternative. Since optimal stationary (s, S) policies are relatively simple to characterize, it is easy to construct a solution to the optimality equation which is satisfied by an (s, S) policy or an equivalent variant thereof. For the discounted model, the proof characterizes an (s, S) policy that is optimal for all initial inventory positions. This policy can be generated by a simple existing algorithm. For the average-cost model, the optimality proof is completed with some additional arguments, which are simple but novel, to overcome the normal difficulties encountered in models with unbounded one-step expected costs.

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A simple proof for optimality of (s, S) policies in infinite-horizon inventory systems

Journal of Applied Probability ◽

10.2307/3214683 ◽

1991 ◽

Vol 28 (4) ◽

pp. 802-810 ◽

Cited By ~ 68

Author(s):

Yu-Sheng Zheng

Keyword(s):

Simple Proof ◽

Average Cost ◽

Cost Model ◽

Infinite Horizon ◽

Finite Horizon ◽

Inventory Systems ◽

Inventory Policy ◽

Optimality Equation ◽

One Step ◽

Equivalent Variant

The classical proofs for the existence of a stationary (s, S) inventory policy that minimizes the total discounted or average cost over an infinite horizon are lengthy because they depend heavily on the optimality results for corresponding finite-horizon models. This note presents a simpler alternative. Since optimal stationary (s, S) policies are relatively simple to characterize, it is easy to construct a solution to the optimality equation which is satisfied by an (s, S) policy or an equivalent variant thereof. For the discounted model, the proof characterizes an (s, S) policy that is optimal for all initial inventory positions. This policy can be generated by a simple existing algorithm. For the average-cost model, the optimality proof is completed with some additional arguments, which are simple but novel, to overcome the normal difficulties encountered in models with unbounded one-step expected costs.

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An Interactive Minicomputer Program for the Indexing and Simulation of Electron Diffraction Patterns

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100092670 ◽

1976 ◽

Vol 34 ◽

pp. 542-543

Author(s):

R.P. Goehner ◽

W.T. Hatfield ◽

Prakash Rao

Keyword(s):

Electron Diffraction ◽

Real Time ◽

Pattern Analysis ◽

Flow Diagram ◽

Hard Copy ◽

Time Analysis ◽

Real Time Analysis ◽

Transmission Electron ◽

One Step ◽

Diffraction Patterns

Computer programs are now available in various laboratories for the indexing and simulation of transmission electron diffraction patterns. Although these programs address themselves to the solution of various aspects of the indexing and simulation process, the ultimate goal is to perform real time diffraction pattern analysis directly off of the imaging screen of the transmission electron microscope. The program to be described in this paper represents one step prior to real time analysis. It involves the combination of two programs, described in an earlier paper(l), into a single program for use on an interactive basis with a minicomputer. In our case, the minicomputer is an INTERDATA 70 equipped with a Tektronix 4010-1 graphical display terminal and hard copy unit.A simplified flow diagram of the combined program, written in Fortran IV, is shown in Figure 1. It consists of two programs INDEX and TEDP which index and simulate electron diffraction patterns respectively. The user has the option of choosing either the indexing or simulating aspects of the combined program.

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Nutrient-regulated gene expression in eukaryotes

Biochemical Society Symposium ◽

10.1042/bss0730085 ◽

2006 ◽

Vol 73 ◽

pp. 85-96 ◽

Cited By ~ 8

Author(s):

Richard J. Reece ◽

Laila Beynon ◽

Stacey Holden ◽

Amanda D. Hughes ◽

Karine Rébora ◽

...

Keyword(s):

Gene Expression ◽

Rna Polymerase ◽

Rna Polymerase Ii ◽

Transcriptional Control ◽

Direct Interaction ◽

Signalling Pathways ◽

A Cell ◽

One Step ◽

Higher Eukaryotes ◽

Regulated Gene Expression

The recognition of changes in environmental conditions, and the ability to adapt to these changes, is essential for the viability of cells. There are numerous well characterized systems by which the presence or absence of an individual metabolite may be recognized by a cell. However, the recognition of a metabolite is just one step in a process that often results in changes in the expression of whole sets of genes required to respond to that metabolite. In higher eukaryotes, the signalling pathway between metabolite recognition and transcriptional control can be complex. Recent evidence from the relatively simple eukaryote yeast suggests that complex signalling pathways may be circumvented through the direct interaction between individual metabolites and regulators of RNA polymerase II-mediated transcription. Biochemical and structural analyses are beginning to unravel these elegant genetic control elements.

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