large body of work exists in process industry supply chain optimisation. We describe the state of the art of research in infrastructure design, modelling and analysis and planning and scheduling, together with some industrial examples. We draw some conclusions about the degree to which different classes of problem have been solved, and discuss challenges for the future. © 2005 Published by Elsevier Ltd.

There has been significant progress in the area of short-term scheduling of batch processes, including the solution of industrial-sized problems, in the last 20 years. The main goal of this paper is to provide an up-to-date review of the state-of-the-art in this challenging area. Main features, strengths and limitations of existing modeling and optimization techniques as well as other available major solution methods are examined through this paper. We first present a general classification for scheduling problems of batch processes as well as for the corresponding optimization models. Subsequently, the modeling of representative optimization approaches for the different problem types are introduced in detail, focusing on both discrete and continuous time models. A comparison of effectiveness and efficiency of these models is given for two benchmarking examples from the literature. We also discuss two real-world applications of scheduling problems that cannot be readily accommodated using existing methods. For the sake of completeness, other alternative solution methods applied in the field of scheduling are also reviewed, followed by a discussion related to solving large-scale problems through rigorous optimization approaches. Finally, we list available academic and commercial software and briefly address the issue of rescheduling capabilities of the various optimization approaches.

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This contribution gives an overview on the state-of-the-art and recent advances in mixed integer optimization to solve planning and design problems in the process in-dustry. In some case studies specific aspects are stressed and the typical difficulties of real world problems are addressed. Mixed integer linear optimization is widely used to solve supply chain planning prob-lems. Some of the complicating features such as origin tracing and shelf life constraints are discussed in more detail. If properly done the planning models can also be used to do product and customer portfolio analysis. We also stress the importance of multi-criteria optimization and correct modeling for optimization under uncertainty. Stochastic programming for continuous LP problems is now part of most optimization packages, and there is encouraging progress in the field of stochastic MILP and robust MILP. Process and network design problems often lead to nonconvex mixed integer nonlinear programming models. If the time to compute the solution is not bounded, there are already a commercial solvers available which can compute the global optima of such problems within hours. If time is more restricted, then tailored solution techniques are required.

The optimal scheduling of crude-oil operations in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming (MILP) or mixed integer nonlinear programming (MINLP) formulations. This paper presents a new continuous-time formulation, called single-operation sequencing (SOS) model, which can be used to solve the crude-oil operations problem introduced by Lee et al. 1. It is different from previous formulations as it requires to postulate the number of priority-slots in which operations take place instead of specifying the number of time intervals or event points to be used in the schedule. This MINLP model is also based on the representation of a crude-oil schedule by a single sequence of transfer operations. It allows breaking symmetries involved in the problem, thus tremendously reducing the computational expenses (all instances can be solved within 2 minutes). A simple two step MILP- NLP procedure has been used to solve the non-convex MINLP model leading to an optimality gap lower than 5 % in all cases.

We consider a complex scheduling problem in the chemical process industry involving batch pro-duction. The application described comprises a network of production plants with interdependent production schedules, multi{stage production at multi{purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic al-gorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource speci¯c parameters such as batch sizes, and setup and cleanup times. The collabora-tive planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater °exibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom{built utilities for manual changes to the production schedule, investigation of various what{if scenarios, and marketing queries.

We consider a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm (GA) based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries.

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In this chapter we present some of the applications of MINLP and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixed-integer nonlinear op-timization we refer the reader to the work by Belotti et al.[1]. Bonami et al.[2] review convex MINLP al-gorithms and software in more detail. Tawarmalani and Sahinidis[3] describe global optimization theory,

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