Thesis

STUDIES OF INVENTORY CONTROL AND CAPACITY PLANNING WITH MULTIPLE SOURCES

A Dissertation Presented to The Academic Faculty

By

Frederick Craig Zahrn

In Partial Fulfillment Of the Requirements for the Degree Doctor of Philosophy in Industrial Engineering

Georgia Institute of Technology August 2009

STUDIES OF INVENTORY CONTROL AND CAPACITY PLANNING WITH MULTIPLE SOURCES

Approved by: Dr. Shi-Jie Deng, Advisor School of Industrial and Systems Engineering Georgia Institute of Technology Dr. John H. Vande Vate, Advisor School of Industrial and Systems Engineering Georgia Institute of Technology Dr. Hayriye Ayhan School of Industrial and Systems Engineering Georgia Institute of Technology Dr. Mark E. Ferguson College of Management Georgia Institute of Technology Dr. Anton J. Kleywegt School of Industrial and Systems Engineering Georgia Institute of Technology

Date Approved: July 6, 2009

ACKNOWLEDGMENTS

I thank my advisors, Dr. Shi-Jie Deng and Dr. John H. Vande Vate, for their guidance of my research. I am particularly indebted to them—Prof. Vande Vate especially— for technical and expository advice in the portion of the dissertation on capacity planning. I also thank Dr. R. Gary Parker for his support of my graduate studies.

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TABLE OF CONTENTS

Acknowledgments Summary Chapter 1: Average optimal control in an inventory model with multiple sources 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Inventory control with a convex ordering cost function . 1.2.2 Inventory control under average cost criteria . . . . . . . 1.3 Formal problem statement and proof strategy . . . . . . . . . . 1.4 Technical arguments . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Preliminary analytical results . . . . . . . . . . . . . . . 1.4.2 Relaxed model, finite-horizon discounted setting . . . . . 1.4.3 Relaxed model, infinite-horizon discounted setting . . . . 1.4.4...