This review is of the third edition of the book “Inventory Control” by Sven Axsäter published by Springer.

The book provides a predominantly mathematical treatment of many aspects of inventory management, both for distribution and manufacturing purposes. It is written in such a manner as to be suitable for use as a university textbook. It contains plenty of exercises to enable students to consolidate their understanding. There are many references to published papers and, as a result, it is a good starting point for research. Although the book is, primarily, theoretical, the author displays thorough familiarity with practical considerations.

Readers need to have a basic mathematical background including a basic knowledge of calculus and probability.

About half of the book is concerned, primarily with distribution and the rest of the book is concerned, primarily, with manufacturing.

Unlike much of the literature on inventory management, a normal distribution of lead time demand is not assumed throughout the book. Consequently, the theory covered is suitable for slow moving items as well as fast moving ones.

The chapter on forecasting covers the following topics:

• Constant model

• Trends and seasonality

• Forecasts based on other factors

• Model choice

• Moving average

• Exponential smoothing

• Regression analysis

• Sporadic demand

• Box-Jenkins techniques

• Forecast errors (including use of mean absolute deviation (MAD) and variance)

• Standard deviation as a function of demand

• Forecast errors for other time periods, e.g. over the lead time

• Use of sales data instead of demand data

• Monitoring forecasts

• Manual forecasts

The chapter on costs and concepts covers:

• Holding costs

• Ordering or setup costs

• Shortage costs or service constraints

• Other costs and assumptions

• Ordering systems and policies

• Optimality of ordering policies

• Updating of order quantities and reorder points

There is a chapter on demand models (constant, normal, gamma, Poisson, compound Poisson, logarithmnic compounding, geometric compounding and a model for smooth discreet demand). Both the normal and compound Poisson distributions of demand are considered throughout much of the book.

The chapter on deterministic lot sizing in single echelon systems covers economic order (or batch) quantities, finite production rate, quantity discounts, backorders, time varying demand (including the Wagner-Whitin algorithm and the Silver-Meal heuristic and a heuristic which balances holding and ordering costs.

The chapter on the setting of reorder points deals with all of the demand models mentioned above. This is important because the normal distribution, which is assumed by many authors for modelling demand, is unsuitable for slow moving items. Distribution of the inventory level and inventory position are dealt with for a continuous review (R, Q) policy with both the normal and compound Poisson distributions of demand.

The relationships between service levels and shortage costs are dealt with extensively and consider both lost sales and backordering. This is important in relation to making optimisation both possible and practical. This is something which I will elaborate on in some of the articles in this blog.

The newsboy problem is dealt with.

Methods of handling stochastic lead times are covered.

There is a chapter on optimising (R, Q) and (s, S) policies.

There is a chapter on coordinated replenishments and there are three chapters on multi-eschelon inventory systems from manufacturing through distribution to retail.

I would strongly recommend this book to anyone who is interested in inventory management theory.