Production design and operations scheduling (PDOS) for plate products in the steel industry

The plate design solution has been deployed at a leading South Korean steel maker and has led to an improvement of about 8% in the average size of the slab while keeping waste and unplanned surplus at the caster to minimum specified levels. These savings lead to improved productivity and provided the steel maker a ROI (Return of Investment) of less than a year.

Steel is produced as coils (used for automobiles), plates (used for shipbuilding and construction) and blooms (used for beams). The focus in this project is on plate design. Orders for plates specify the size of the rectangle, a thickness (usually between 10 - 100 mm) the steel grade and quantity. The challenge in this project was to develop a system that provides an operational level production design and schedule that is cognizant of the plant level facility and capacity constraints for a rolling horizon of two days within 30 minutes.

The production of the steel process in shown in the figure 1. Molten steel from the blast furnace is refined in the blast oxygen furnace (BOF) and then cast into slabs at the caster (usually a twin-strand production process where two slabs are being cast simultaneously). The size of the slab that can be cast is (1000 - 2000mm) W x (2000 - 5000 mm) L with a set of allowable thickness (200 - 400 mm). In addition, the sequence in which slabs are cast have to satisfy geometry constraints: (i) all slabs assigned to a cast should have the same width on a strand, (ii) the length difference between the strands (the length of each strand within a cast is sum of the lengths of the slabs assigned to the strand) within a cast is restricted. In addition, refining is a batch process (around 250 tons - called a charge) and hence slabs have to be cast in batches that have the same grade. There are a large number of additional constraints for casting. In the plate design problem the slabs that are cast are subsequently rolled into "mother" plates with an appropriate thickness (decided by the orders that are assigned to the plate) with a rectangular size of upto 5m x 50m. The plate design problem that is solved by PDOS starts with an order book of plates that need to be manufactured, and consists of:

• designing a set of mother plates to cover the order book and while minimizing the waste and maximizing size (mother plate design),
• transforming the mother plate geometry into slab geometry (slab design) and
• designing a slab sequence for the caster that maximizes productivity by maximizing the number of charges per cast and minimizing the surplus slabs that are introduced tosatisfy batch constraints (cast template design).

The challenge here is to solve a hierarchical design problem (which is closely related to the classical bin packing) where one stage requires the design of cast templates using slabs which in turn have to be designed from mother plates which in turn consists of a two-dimensional packing problem. PDOS tackles this problem using a column generation approach that decomposes the mother plate design problem into:

• a master that iteratively refines the choice of candidate two-dimensional packing patterns to cover the order book, and a
• subproblem that manages the generation of these candidate patterns using a collection of heuristic algorithms for two-dimensional packing based on dual price information from the master.

As a next step the selected mother plate patterns are represented in an interval graph (this captures the flexibility in the geometry of the slab that can be used to manufacture the mother plate) which is then solved for maximal subsets to identify candidate charges. These charges are then sequenced using a beam search technique to identify a set of candidate casts from which an appropriate set of casts are chosen using a set packing formulation with capacity based side constraints. The selected casts provide a cast template for which the mother plate design is reformulated and solved (again using the column generation framework) using the geometry constraints specified by the template. The additional challenge was to generate an acceptable high quality solution that is feasible wrt all the plant specific constraints within 30 minutes. This called for some clever control of the two-dimensional mother plate pattern generation and candidate cast generation using plant specific information.



PDOS is a suite of algorithms that is customized for production design and operations scheduling in the metals industry. The development of PDOS was started in 1997 with a Japanese steel maker for the coil product which are thin and used in cars and heavy applicances. Over a period of four years, four different modules (inventory application, slab design, cast design and finish line scheduling) were designed and deployed very successfully. These modules have subsequently been extended and deployed at various Korean and Chinese steel makers.

This project has extended this portfolio of optimization based solutions to handle another important product type in the steel industry - heavy plates used for shipbuilding and construction. This project establishes PDOS as the best in class solution for operational production design and scheduling and extends it to plate design. In addition, with the successful deployment at a large South Korean steelmaker it provides an important reference for PDOS. This work is also the basis for new projects with other manufacturers of heavy plates in Japan and China.

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