Discrete Optimization Methods and their Role in the Integration of Planning and Scheduling

摘要

The need for improvement in process operations, logistics and supply chain management has created a great demand for the development of optimization models for planning and scheduling. In this paper we first review the major classes of planning and scheduling models that arise in process operations, and establish the underlying mathematical structure of these problems. As will be shown, the nature of these models is greatly affected by the time representation (discrete or continuous), and is often dominated by discrete decisions. We then briefly review the major recent developments in mixed-integer linear and nonlinear programming, disjunctive programming and constraint programming, as well as general decomposition techniques for solving these problems. We present a general formulation for integrating planning and scheduling to illustrate the models and methods discussed in this paper.