Approximation Techniques and Optimal Decision Making for Stochastic Lanchester Models

Abstract

This thesis extends the analysis of stochastic Lanchester models beyond the stage of mere modeling. To this end, a frame-work of statistical decision theory is superimposed on a simplified combat situation. The commander must make decisions about the amount of force he will commit to a combat in reference to a suitable cost and reward structure. Problems of both the one- stage and the multi-stage variety are studied. The one-stage decision problem requires knowledge of the probability of victory and the expected number of survivors. A complete solution to this problem is given, based on the use of a martingale central limit theorem. The multi-stage decision problem requires the distribution of the force level configuration as a function of time. These distributions are approximated through the use of diffusion approximations. A two-stage problem is solved using these approximations and backward induction.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1978
Accession Number
ADA050416

Entities

People

  • Peter P. Perla

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • C4I
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Attrition
  • Computational Science
  • Data Science
  • Differential Equations
  • Equations
  • Equations Of State
  • Information Science
  • Mathematical Analysis
  • Mathematical Models
  • Operations Research
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistical Decision Theory
  • Statistics
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.