Guido Sand

Scope for industrial applications of production scheduling models and solution methods

Abstract This paper gives a review on existing scheduling methodologies developed for process industries. Above all, the aim of the paper is to focus on the industrial aspects of scheduling and discuss the main characteristics, including strengths and weaknesses of the presented approaches. It is claimed that optimization tools of today can effectively support the plant level production. However there is still clear potential for improvements, especially in transferring academic results into industry. For instance, usability, interfacing and integration are some aspects discussed in the paper. After the introduction and problem classification, the paper discusses some lessons learned from industry, provides an overview of models and methods and concludes with general guidelines and examples on the modeling and solution of industrial problems.

Modeling and solving real-time scheduling problems by stochastic integer programming

This contribution deals with scheduling problems of flexible chemical batch processes with a special emphasis on their real-time character. This implies not only the need for sufficiently short response times, but in particular the burden of in-complete knowledge about the future. To solve such problems, the application of two-stage stochastic integer programming techniques on moving horizons is proposed. They reflect the need for immediately applicable decisions and the potential of later recourse actions to cope with realized uncertainties. In addition to the classical expected value objective, simple measures of risk can be included. Motivated by an example process, some essential modeling prerequisites are discussed. As an important first step, the master scheduling problem is studied and a number of master scheduling models are presented. Large mixed-integer linear problems arise, which are well-suited for a dual decomposition approach. Numerical experiments with a problem-specific solution algorithm demonstrate the applicability of the method to real-world problems.

Scheduling and energy - Industrial challenges and opportunities

Abstract Recent developments in energy markets, such as the increasing share of inherently volatile renewable power in the energy supply mix and the need of reducing carbon emissions while improving the production efficiency, make the operating environment of process industries more dynamic and complex. At the same time, continued advances in the mathematical programming and IT technologies open up new opportunities to tackle the related operational scheduling problems in a more integrated way at an ever larger scale. This paper discusses the industrial challenges arising from the deregulation of the electricity markets and stronger presence of unpredictable renewable energy sources. It gives a brief overview of methods currently available followed by set of real industrial case studies. The paper concludes with a discussion of the main challenges and opportunities relevant to the presented examples.

A hybrid evolutionary algorithm for solving two-stage stochastic integer programs in chemical batch scheduling

Abstract This contribution deals with the solution of two-stage stochastic integer programs with discrete scenarios (2-SIPs) that arise in chemical batch scheduling under uncertainty. Since the number of integer variables in the second-stage increases linearly with the number of scenarios considered, the real world applications usually give rise to large scale deterministic equivalent mixed-integer linear programs (MILPs) which cannot be solved easily without incorporating decomposition methods or problem specific knowledge. In this paper a new hybrid algorithm is proposed to solve 2-SIPs based on stage decomposition: an evolutionary algorithm performs the search on the first-stage variables while the second-stage subproblems are solved by mixed-integer programming. The algorithm is tested for a real-world scheduling problem with uncertainties in the demands and in the production capacity. Numerical experiments have shown, that the new algorithm is robust and superior to state-of-the-art solvers if good solutions are needed in short CPU-times.

Optimization of steel production scheduling with complex time-sensitive electricity cost

Abstract Energy-intensive industries can take advantage of process flexibility to reduce operating costs by optimal scheduling of production tasks. In this study, we develop an MILP formulation to extend a continuous-time model with energy-awareness to optimize the daily production schedules and the electricity purchase including the load commitment problem. The sources of electricity that are considered are purchase on volatile markets, time-of-use and base load contracts, as well as onsite generation. The possibility to sell electricity back to the grid is also included. The model is applied to the melt shop section of a stainless steel plant. Due to the large-scale nature of the combinatorial problem, we propose a bi-level heuristic algorithm to tackle instances of industrial size. Case studies show that the potential impact of high prices in the day-ahead markets of electricity can be mitigated by jointly optimizing the production schedule and the associated net electricity consumption cost.

Approximation of an ideal online scheduler for a multiproduct batch plant

Abstract In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant, which includes an explicit representation of uncertainties. An ideal online scheduler is approximated by a hierarchical approach with two-levels, on which optimisation problems are formulated as mathematical programs and solved by non-standard algorithms. The focus is on the hierarchical framework and the upper level planning problem where uncertainties are modelled explicitly. The key features of the planning model and of the solution algorithm are explained and numerical results are presented.

Optimization-based design of reactive distillation columns using a memetic algorithm

The design optimization of reactive distillation columns (RDC) is characterized by complex nonlinear constraints, nonlinear cost functions, and the presence of many local optima. The standard approach is to use MINLP solvers that work on a superstructure formulation where structural decisions are represented by discrete variables and lead to an exponential increase in the computational effort. The mathematical programming (MP) methods which solve the continuous sub-problems provide only one local optimum which depends strongly on the initialization. In this contribution a memetic algorithm (MA) is introduced and applied to the global optimization of four different formulations of a computational demanding real-world design problem. An evolution strategy addresses the global optimization of the design decisions, while continuous sub-problems are efficiently solved by a robust MP solver. The MA is compared to MINLP techniques. It is the only algorithm that finds the global solution in reasonable times for all model formulations.

Online Scheduling of Multiproduct Batch Plants under Uncertainty

In this contribution, we propose a telescopic decomposition approach for solving scheduling problems from the chemical processing industries online. The general concept is realized for a real-world benchmark process by a two-level algorithm, which comprises a planning step with explicit consideration of uncertainties and a scheduling step where nonlinearities are include in the model. Both steps constitute optimization problems, which are modeled and solved by mathematical programming techniques. Besides conceptual considerations concerning online scheduling, we present the two mathematical models and their problem specific solution algorithms with some numerical results.

Flexible and configurable MILP-models for meltshop scheduling optimization

Abstract This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapted to different plant structures. Moreover, the flexibility allows for modeling individual characteristics of parallel equipment, particular processing and changeover times, scarce resources and maintenance requests. A small example illustrates the size and solution time of a typical model instance.

Engineered versus standard evolutionary algorithms: A case study in batch scheduling with recourse

An engineered evolutionary algorithm for a realistic chemical batch scheduling problem with uncertain data is developed systematically. The problem is formulated as a two stage stochastic integer program with discrete scenarios. The model is solved by a stage decomposition-based hybrid algorithm using an evolutionary algorithm combined with mixed-integer programming. Earlier experiments with a standard evolutionary algorithm led to the hypothesis that the constrained search space is not covered well such that in some cases the population converges to a subset of the solution space which does not include the best known solution. An efficient engineered evolutionary algorithm is developed which is shown to cover the feasible set significantly better such that a high quality feasible schedule can be generated comparatively fast. As the hierarchical structure of the case study is typical for many batch scheduling problems, some general principles may be postulated from the experience gained here.