Josef Kallrath

Planning and scheduling in the process industry

Abstract. Since there has been tremendous progress in planning and scheduling in the process industry during the last 20 years, it might be worthwhile to give an overview of the current state-of-the-art of planning and scheduling problems in the chemical process industry. This is the purpose of the current review which has the following structure: we start with some conceptional thoughts and some comments on special features of planning and scheduling problems in the process industry. In Section 2 the focus is on planning problems while in Section 3 different types of scheduling problems are discussed. Section 4 presents some solution approaches especially those applied to a benchmark problem which has received considerable interest during the last years. Section 5 allows a short view into the future of planning and scheduling. In the appendix we describe the Westenberger-Kallrath problem which has already been used extensively as a benchmark problem for planning and scheduling in the process industr y.

Optimal planning in large multi-site production networks

Abstract This contribution describes a general mixed-integer linear programming model based on a time-indexed formulation covering the relevant features required for the complete supply chain management of a multi-site production network. While the actual application is taken from the chemical industry, the model provides a starting point for many applications in the chemical process industry, food or consumer goods industry. In many real world problems certain features just need to be eliminated from this general model in order to describe a current situation. The model combines aspects related to production, distribution and marketing and involves production sites (plants) and sales points. Besides standard features of lot sizing problems (raw materials, production, inventories, demands) further aspects, e.g., different time scales attached to production and distribution, the use of periods with different lengths, the modeling of batch and campaign production need to be considered. There are also new conceptual aspects in this paper, e.g., how to define the capacity of a multi-site, multi-product production network, or how to approach complex planning problems. We give a complete description of features ready for implementation, and the experience we have with the current implementation in our company. A long-term implication of this contribution might be that it will initiate further research efforts aiming to derive special cuts improving the formulation.

Global optimization in the 21st century: Advances and challenges

This paper presents an overview of the research progress in global optimization during the last 5 years (1998–2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixedinteger nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box/black-box/nonfactorabl e models, and (e) bilevel nonlinear optimization. Our research contributions part focuses on (i) improved convex underestimation approaches that include convex envelope results for multilinear functions, convex relaxation results for trigonometric functions, and a piecewise quadratic convex underestimator for twice continuously differentiable functions, and (ii) the recently proposed novel generalized BB framework. Computational studies will illustrate the potential of these advances.

Eclipsing binary stars : modeling and analysis

Introduction.- The Data Base and Methods of Acquisition.- A General Approach to Modeling Eclipsing Binaries.- Determination of Eclpsing Binary Parameters.- Light Curve Models and Software.- The Wilson-Devinney Program and WD95.- The Structure of Light Curve Programs and the Outlook for the Future.- Appendix A: A Brief Review of Mathematical Optimization.- Appendix B: Estimation of Fitted Parameter Errors: the Details.- Appendix C: Geometry and Coordinate Systems.- Appendix E: Subroutines of the Wilson-Devinney Program.- Appendix F: Graphics Utilities and Visualization.- Appendix G: Glossary of Symbols.- Bibliography.- Subject Index.

Mixed Integer Optimization in the Chemical Process Industry: Experience, Potential and Future Perspectives

Proper organization, planning and design of production, storage locations, transportation and scheduling are vital to retain the competitive edge of companies in the global economy.Typical additional problems in the chemical industry suitable for optimization are process design, process synthesis and multi-component blended-flow problems leading to nonlinear or even mixed integer nonlinear models. Mixed integer optimization (MIP) determines optimal solutions of such complex problems; the development of new algorithms, software and hardware allow the solution of larger problems in acceptable times. This tutorial paper addresses two groups. The focus towards the first group (managers and senior executives) and readers who are not very familiar with mathematical programming is to create some awareness regarding the potential benefits of MIP, to transmit a sense of what kind of problems can be tackled, and to increase the acceptance of MIP. The second group (a more technical audience with some background in mathematical optimization), might rather appreciate the state-of-the-art view on good-modelling practice, algorithms and an outlook into global optimization. Some real-world MIP problems solved by BASFs mathematical consultants are briefly described, among them discrete blending and multi-stage production planning and distribution with several sites, products and periods. Finally, there is a focus on future perspectives and sources of MIP support are indicated from academia, software providers and consulting firms.

Combined strategic and operational planning - an MILP success story in chemical industry

Abstract. We describe and solve a real world problem in chemical industry which combines operational planning with strategic aspects. In our simultaneous strategic & operational planning (SSDOP) approach we develop a model based on mixed-integer linear (MILP) optimization and apply it to a real-world problem; the approach seems to be applicable in many other situations provided that people in production planning, process development, strategic and financial planning departments cooperate.The problem is related to the supply chain management of a multi-site production network in which production units are subject to purchase, opening or shut-down decisions leading to an MILP model based on a time-indexed formulation. Besides the framework of the SSDOP approach and consistent net present value calculations, this model includes two additional special and original features: a detailed nonlinear price structure for the raw material purchase model, and a detailed discussion of transport times with respect to the time discretization scheme involving a probability concept. In a maximizing net profit scenario the client reports cost saving of several millions US

Modeling Languages in Mathematical Optimization

.The strategic feature present in the model is analyzed in a consistent framework based on the operational planning model, and vice versa. The demand driven operational planning part links consistently to and influences the strategic. Since the results (strategic desicions or designs) have consequences for many years, and depend on demand forecast, raw material availability, and expected costs or sales prices, resp., a careful sensitivity analysis is necessary showing how stable the decisions might be wit h respect to these input data.

Solving Planning and Design Problems in the Process Industry Using Mixed Integer and Global Optimization

This volume presents a unique combination of modeling and solving real world optimization problems. It is the only book which treats systematically the major modeling languages and systems used to solve mathematical optimization problems, and it also provides a useful overview and orientation of todays modeling languages in mathematical optimization. It demonstrates the strengths and characteristic features of such languages and provides a bridge for researchers, practitioners and students into a new world: solving real optimization problems with the most advances modeling systems.

Production scheduling of a large-scale industrial continuous plant : Short-term and medium-term scheduling

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 industry. 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 problems. 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.

RECENT IMPROVEMENTS TO A VERSION OF THE WILSON-DEVINNEY PROGRAM

In this work, we describe a framework for short-term and medium-term scheduling of a large-scale industrial continuous plant. For medium-term scheduling, two sub-problems are solved using a rolling-horizon based decomposition scheme. An upper-level model is used to find the optimal number of products, and the length of the time horizon to be considered for solving the lower level short-term scheduling problem. At the lower level, we proposed an improved model for short-term scheduling of continuous processes using unit-specific event-based continuous-time representation. The proposed formulation is demonstrated on a large-scale industrial case study comprising up to 100 units with 1/3 processing and 2/3 storage units operating in a continuous-mode for producing more than 100 different products over a one month time horizon.