Production Planning by Mixed Integer Programming
This book is about modeling and solving multi-item, single/multi-machine, single/multi-level, production planning problems with time-varying demands by mixed integer programming. Sincethebeginningsofoperationsresearchandmanagementscience,m- els for production planning have been an important object of study with the Harris EOQ formula or Wilson’s (Q,r) model, and Wagner–Whitin’s dynamic lot-sizing model, the cornerstones for the treatment of stationary and ti- varying (dynamic) demand, respectively. The introduction of Materials Requirement Planning (MRP) systems in the 1970s was a major step forward in the standardization and control of p- duction planning systems, but MRP and its successors were ?rst and foremost information systems necessary but not su?cient for the e?cient planning of the factory or enterprise. Much criticism was leveled at the inability of such systems to deal e?ectively with lead times and capacity constraints. Even in today’s Enterprise Resource Planning (ERP) systems and Advanced Pl- ning and Scheduling (APS) systems, the planning modules are still seen as unusable, or unable to handle the complexity of the underlying capacitated planning problems. Starting in the 1960s and 1970s, the ?rst serious e?orts were made to describemixedintegerprogramming(MIP)modelsforsingle-andmulti-stage planning problems of the type that arise regularly in practice, and that MRP and APS systems are designed to tackle. viii Preface Unfortunately MIP systems at the time were only able to solve “toy” - stances, and so e?orts were mainly concentrated on simple and rapid heur- tics.
First to collect the large number of mathematical (polyhedral combinatorics) results on lotsizing and single product planning problems developed over the last twenty yearsAuthors are world leaders in mixed integer programming Tutorial style approach very accessible No competition