Chaojun Xu

A new heuristic for plant-wide schedule coordination problems: The intersection coordination heuristic

Abstract This work addresses the coordination heuristics of two large-scale flexible multi-stage batch (flow shop) scheduling problems, which are currently solved independently by tailored algorithms that consist of mixed-integer linear optimization and heuristics. The approach is motivated by an industrial-scale steel making process that consists of a melt shop as the first production section and a hot rolling mill as the second production section. The first section produces intermediate products, i.e. slabs, which are stored in an intermediate storage area and which are consumed by the second section. The coordination objective is to reduce the storage time of the slabs or, more generally, the storage time between two sections taking into account the objectives of the two distributed scheduling solutions. A generic model formulation for multi-stage batch schedule coordination problems is presented. Three different schedule coordination heuristics are discussed and compared for simplified case studies: the heuristic based on Lagrangean decomposition (LD), a derivative-free optimization algorithm – Multilevel Coordinate Search (MCS), the new intersection coordination heuristic (IC) and monolithic MILP model solved by CPLEX (MONO). The proposed bi-level intersection coordination heuristic uses the knowledge on the bottlenecks of the two processes to build a simplified model for the upper-level coordinator which coordinates the lower-level distributed MILP schedulers via coordination variables iteratively. The numerical comparisons show the advantage of the IC among these three coordination approaches in terms of solution quality and computational effort. The limitations of LD, MCS, MONO and IC for the plant-wide schedule coordination problem are discussed in view of the requirements of large-scale industrial schedule coordination problems.

Coordination of Distributed Production Planning and Scheduling Systems

Abstract In this paper, the requirements of industrial solutions to plant-wide planning and scheduling problems are discussed. The state-of-the-art algorithms for the coordination of local schedulers are reviewed and a new heuristic method is presented that utilizes the existing distributed scheduling algorithms by considering the coupled due dates and release dates in the distributed schedulers and by penalizing the slacks between the individual optimized schedules and the linking variables iteratively. The performance of the proposed coordination algorithm is evaluated for a prototypical distributed production scheduling problem which consists of two MILP scheduling models. The numerical results show that the proposed coordination scheme is superior compared to fully decentralized and to centralized scheduling algorithms and to other cooperative scheduling methods with respect to solution quality and computational effort.

An innovative scheduling coordination method for improved productivity and energy efficiency of a large-scale integrated steel plant

Abstract Energy efficiency will play an important role in improving the heavy industrys environmental and economic performance. In this work, an innovative scheduling coordination method to coordinate two consecutive production sections in an integrated steel plant - melt shop and hot rolling mill - is discussed. Between the two sections a slab yard acts as a buffer for intermediate products – slabs. Planning and scheduling of the two sections are currently solved independently by two industrial optimization solutions, observing complex production rules and different objectives. The proposed coordination method reuses the existing optimization modules and minimizes the storage time in the slab yard. Furthermore, the coordinated schedule enables some slabs from the melt shop to be charged directly into the reheating furnace of the hot rolling mill without losing considerable thermal energy (hot charging). The challenges and the approaches to coordinate two industrial schedulers incorporating several optimization steps, for instance mixed integer linear programming (MILP) and heuristics are presented. The coordination approach is validated by testing it with real production data from a real life steel plant and the potential to save energy and reduce production time is demonstrated.

A new Coordination Heuristic for Plant-wide Planning and Scheduling

Abstract The work is motivated by a large-scale steel making process that consists of a meltshop as the first production section and a hot rolling mill as the second production section. The first section produces intermediate products (steel slabs in different quality) which can be stored in an intermediate storage (a slab yard) and which are consumed by the second section. Production planning for each of the sections constitutes a difficult multi-stage scheduling problem, these are currently solved independently. In this paper approaches to the coordination of the formerly uncoordinated schedulers are discussed. The objective is to reduce the lead time of stored intermediates. Shortening the lead time can significantly reduce the energy consumption since the hot slabs produced by the melt shop cool down over time and need to be reheated for the hot rolling mill, consuming large amounts of natural gas. A generic model formulation for batch schedule coordination problems is presented. The model is based on due date / release date constraints for each set of slabs. Three different algorithms to optimize the due / release dates such that the storage times of intermediates are minimized are discussed and compared: an algorithm based on Lagrangean decomposition, the black box algorithm MCS and a new coordination heuristic. The comparison shows the advantage of the proposed heuristic in terms of solution quality and computational effort. At the end the problems encountered when applying Lagrangean decomposition techniques to the scheduling coordination problem when the objective function is piecewise linear are discussed.