基本説明
This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems.
Full Description
This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations.
Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised...There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)
Contents
Production Planning and MIP.- The Modeling and Optimization Approach.- Production Planning Models and Systems.- Mixed Integer Programming Algorithms.- Classification and Reformulation.- Reformulations in Practice.- Basic Polyhedral Combinatorics for Production Planning and MIP.- Mixed Integer Programming Algorithms and Decomposition Approaches.- Single-Item Uncapacitated Lot-Sizing.- Basic MIP and Fixed Cost Flow Models.- Single-Item Lot-Sizing.- Lot-Sizing with Capacities.- Backlogging and Start-Ups.- Single-Item Variants.- Multi-Item Lot-Sizing.- Multi-Item Single-Level Problems.- Multi-Level Lot-Sizing Problems.- Problem Solving.- Test Problems.
