An efficient optimal solution to the coil sequencing problem in electro-galvanizing line Lixin Tang a,Ã , Yang Yang a , Jiyin Liu a,b a Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, Shenyang, China b Business School, Loughborough University, Leicestershire LE11 3TU, UK article info Available online 29 January 2010 Keywords: Steel production Electro-galvanizing line Sequencing Modelling Dynamic programming abstract This paper studies a coil sequencing problem that arises from electro-galvanizing line in steel industry. The problem is to find a processing sequence of steel coils such that the switching costs between consecutive coils are minimized while satisfying technical restrictions. The problem can be decomposed into several independent sub-problems, each corresponding to a turn which is a sequence of continuously processed coils with the same post-processing requirement. The coils in each turn can be further divided into several families each consisting of the coils with the same width. Based on analysis of the problem properties, a two-phase polynomial algorithm is developed to obtain an optimal turn. The sequence of coils in a family with given boundary coils (first and last coils) is determined in the first phase using a polynomial dynamic programming algorithm. In the second phase, the optimal turn is formed by another polynomial dynamic programming algorithm which takes the boundary coils for each family as state variables. The efficiency of the proposed algorithm is demonstrated through computational experiments. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Electro-galvanizing is performed on a continuous plating line for steel coils released from the annealing process. It is part of the finishing processes after cold rolling in iron and steel works. The cold rolling and finishing processes in iron and steel production consist of five major stages: acidwashing, cold rolling, annealing, electro-galvanizing and color coating, as it is shown in Fig. 1. There are two ways for annealing: batch annealing and continuous annealing. Both of them can supply material coils to the electro-galvanizing line. In practice, electro-galvanizing produces a thin layer of even coating of zinc on the substrate metal for corrosion resistance. The coating does not peel, flake or crack even if the electro-galvanized materials are rolled, formed, bent and curved. This property makes the coated metal desirable materials for many applications such as household application, display cases, automobiles and building materials. Hence electro- galvanizing can yield a high added value to the metal. To remain competitive it is critical for steel companies to guarantee product quality and control production costs of their electro-galvanizing lines. As it is shown in Fig. 2, the coils to be processed in the electro-galvanizing line need to pass through three main sections of the line: pre-processing, plating cell and post-processing. The coils to be processed are first opened up as a strip on the pay-off reels (POR 1 and POR 2). Because there are two pay-off reels in an electro-galvanizing line, the opening up operation can continuously provide steel strips. Then the end of the strip from each coil is welded to the start of the following one on the welder (WLD). The resulting long continuous steel strip from the coils is then processed in the main sections of the electro-galvanizing line. The operation (PRE-P) in the pre- processing section aims at getting rid of pickling oil and surface dirt, which consists of a rinse, a pickling treatment and a second rinse prior to the plating section. Plating of zinc takes place in the plating cell section where the final thickness of zinc layer gradually builds up on the surface of the steel strip as it moves along the section, according to specified requirement. After plating, the strip runs through the post-processing (POST-P) section. In order to improve the surface quality, the coils should pass through their corresponding post-processing liquid according to their requirements. For the line studied in this paper, there are three post-processing liquids concerned: phosphating liquid, passivating liquid and special post- processing liquid for coated steel coil with anti-finger printed property. Some products do not require post-processing. Therefore, there are four post-processing requirements concerned in this paper. After all the processing, the continuous strip is cut by shears (SHR) into required lengths and rolled up on tension reel (TR) as final product coils. The entry looper (ENL) and ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/caor Computers & Operations Research 0305-0548/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2010.01.009 Ã Corresponding author. Tel./fax: + 86 24 83680169. E-mail addresses: qhjytlx@mail.neu.edu.cn (L. Tang), yangyang@ise.neu.edu.cn (Y. Yang), j.y.liu@lboro.ac.uk (J. Liu). Computers & Operations Research 37 (2010) 1780–1796