Production Planning with Capacitated Resources and Congestion

This book presents a comprehensive overview of recent developments in production planning. The monograph begins with an introductory chapter reviewing the need for these models of production planning that operate by determining time-phased releases of work into the facility or supply chain, relating these to the Manufacturing Planning and Control (MPC) and Advanced Planning and Scheduling (APS) frameworks that form the basis of most academic research and industrial practice.  The extensive body of work on Workload Control is also placed in this context, and the need for improved models motivated by a discussion of the difficulties these approaches encounter.
The next two chapters present a detailed review of the state of the art in optimization models based on exogenous planned lead times, examining the cases where these can take both integer and fractional values. The difficulties arising in estimating planned lead times that are consistent with factory behavior are highlighted, noting that many of these lead to non-convex optimization models. Attempts to address these difficulties by iterative multimodel approaches that combine simulation and mathematical programming are also discussed in detail. The next three chapters of the volume address the set of techniques developed using clearing functions, which represent the expected output of a resource in a planning period as a function of the expected workload of the resource during that period.
The chapters on this subject propose a basic optimization model for multiple products, discuss the difficulties of this model and some possible solutions, review prior work, and discuss a number of alternative formulations of the clearing function concept with their respective advantages and disadvantages. Applications to lot sizing decisions and a number of other specific problems are also described. The volume concludes with an assessment of the state of the art described in the volume, and several directions forfuture work.