Mixed Integer

This book deals with stochastic combinatorial optimization problems in supply chain disruption management, with a particular focus on management of disrupted flows in customer-driven supply chains. The problems are modeled using a scenario based stochastic mixed integer programming to address riskneutral, risk-averse and mean-risk decision-making in the presence of supply chain disruption risks. The book focuses on integrated disruption mitigation and recovery decision-making and innovative, computationally efficient multi-portfolio approach to supply chain disruption management, e.g., selection of primary and recovery supply portfolios, demand portfolios, capacity portfolios, etc.

This book presents a comprehensive description of theory, algorithms and software for solving nonconvex mixed integer nonlinear programs (MINLP). The main focus is on deterministic global optimization methods, which play a very important role in integer linear programming, and are used only recently in MINLP.

Interest in constrained optimization originated with the simple linear pro­ gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models.

This book presents scheduling with a medium- and short-term focus, which makes it possible to capitalize on fleeting market opportunities while simultaneously working to reconcile economic and environmental priorities.

Stefan Rocktäschel introduces a branch-and-bound algorithm that determines a cover of the efficient set of multiobjective mixed-integer convex optimization problems. He examines particular steps of this algorithm in detail and enhances the basic algorithm with additional modifications that ensure a more precise cover of the efficient set. Finally, he gives numerical results on some test instances.