We can use mathematical models to study the cost-efficient use of a supply chain to distribute goods between manufacturers, suppliers, and warehouses. We use these models to evaluate current business processes with the goal of minimizing distribution costs. Models describe goods either as entities at discrete time instances (discrete event simulation), or as a dynamic flow (continuous approach). In large systems, however, a discrete event simulation is often not feasible, since computing time increases exponentially with the size of the system. A continuous approach based on differential equations, on the other hand, does not necessarily have these shortcomings. Here, individual goods are aggregated into goods per time unit, and become parts of a dynamic flow.

This well-organized book focuses solely on the continuous approach. It describes different simulation and optimization techniques, using ordinary and partial differential equations.

The book contains eight chapters. After a brief introductory chapter, the authors discuss conservation laws and numerical techniques that allow their discretization. Chapters 3 through 6 discuss continuous supply chain models, such as queueing models, models based on ordinary differential equations, models based on partial differential equations, and continuum discrete (mixed) models. Chapter 7 moves on to optimization problems and the relationship between discrete events and continuous optimizations. The book concludes in chapter 8 with computational results for the presented simulation and optimization models.

This well-written book is suitable for students and researchers who are familiar with the theory of ordinary and partial differential equations and basic optimization techniques. Readers who are mainly interested in applications, however, may want to look elsewhere. The book lacks concrete examples, and, as such, is not suited for practitioners, but rather for mathematicians working on the theory of supply chain simulations and optimizations. An instructor of an advanced graduate course could use this book as a textbook. I wholeheartedly recommend it as a reference for researchers.