Here is a much-needed attempt to reconcile optimization with apportionment in just-in-time (JIT) sequences. It argues that apportionment theory and optimization based on deviation functions provide benchmarks for a process, and examines recent developments.

Preliminaries.- The Theory of Apportionment and Just-In-Time Sequences.- Minimization of Just-In-Time Sequence Deviation.- Optimality of Cyclic Sequences and the Oneness.- Bottleneck Minimization.- Competition-Free Instances, The Fraenkel's Conjecture, and Optimal Admission Sequences.- Response Time Variability.- Applications to the Liu—Layland Problem and Pinwheel Scheduling.- Temporal Capacity Constraints and Supply Chain Balancing.- Fair Queueing and Stride Scheduling.- Smoothing and Batching.

Proportional Optimization and Fairness is a long-needed attempt to reconcile optimization with apportionment in just-in-time (JIT) sequences and find the common ground in solving problems ranging from sequencing mixed-model just-in-time assembly lines through just-in-time batch production, balancing workloads in event graphs to bandwidth allocation internet gateways and resource allocation in computer operating systems. The book argues that apportionment theory and optimization based on deviation functions provide natural benchmarks for a process, and then looks at the recent research and developments in the field. Individual chapters look at the theory of apportionment and just-in-time sequences; minimization of just-in-time sequence deviation; optimality of cyclic sequences and the oneness; bottleneck minimization; competition-free instances, Fraenkel’s Conjecture, and optimal admission sequences; response time variability; applications to the Liu-Layland Problem and pinwheel scheduling; temporal capacity constraints and supply chain balancing; fair queueing and stride scheduling; and smoothing and batching.

From the reviews:“This book explores the usefulness of apportionment methods in just-in-time sequencing. … Examples and exercises provide further insight into each topic. This book can be recommended to engineers, computer scientists and experts in number theory, that have to find ‘smooth’, ‘fair’ or otherwise optimal solutions to sequencing and scheduling problems, where the characteristics of each item depend on the model it belongs to.” (Mechthild Opperud, Mathematical Reviews, April, 2013)“The book is a very solid piece of work with a thorough introduction to the field followed by a detailed presentation of several important topics. It is composed of 11 chapters complemented by an extensive bibliography and an index. … Summing up, the book contains an up-to-date presentation of different approaches addressing the problem of fair and just-in-time scheduling. Written by the expert in the field, it is a must for those interested in the above area.” (Jacek Blazewicz, Zentralblatt MATH, Vol. 1169, 2009)

Presents the latest research on just-in-time (JIT) sequencing and the efforts to apportion resources fairly within the process Extends JIT sequencing to fields like computer science, communications and the social sciences Presents novel approaches to solving the Liu-Layland problem and bottleneck minimization