In 1958, Stanford University Press published "Studies in the
Mathematical Theory of Inventory and Production" (edited by Kenneth
J. Arrow, Samuel Karlin, and Herbert Scarf), which became the
pioneering road map for the next forty years of research in this
area. One of the outgrowths of this research was development of the
field of supply-chain management, which deals with the ways
organizations can achieve competitive advantage by coordinating the
activities involved in creating products--including designing,
procuring, transforming, moving, storing, selling, providing
after-sales service, and recycling. Following in this tradition,
"Foundations of Stochastic Inventory Theory" has a dual purpose,
serving as an advanced textbook designed to prepare doctoral
students to do research on the mathematical foundations of
inventory theory and as a reference work for those already engaged
in such research.
The author begins by presenting two basic inventory models: the
economic order quantity model, which deals with "cycle stocks," and
the newsvendor model, which deals with "safety stocks." He then
describes foundational concepts, methods, and tools that prepare
the reader to analyze inventory problems in which uncertainty plays
a key role. Dynamic optimization is an important part of this
preparation, which emphasizes insights gained from studying the
role of uncertainty, rather than focusing on the derivation of
numerical solutions and algorithms (with the exception of two
chapters on computational issues in infinite-horizon models).
All fourteen chapters in the book, and four of the five appendixes,
conclude with exercises that either solidify or extend the concepts
introduced. Some of these exercises have served as Ph.D. qualifying
examination questions in the Operations, Information, and
Technology area of the Stanford Graduate School of Business.
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