Mark Trumbo

The Slab-Design Problem in the Steel Industry

Planners in the steel industry design a set of steel slabs to satisfy the order book subject to constraints on (1) achieving a total designed weight for each order using multiples of an order-specific production size range, (2) minimum and maximum sizes for each slab, and (3) feasible assignments of multiple orders to the same slab. We developed a heuristic solution based on matchings and bin packing that a large steel plant uses daily in mill operations.

Finishing line scheduling in the steel industry

A new solution for large-scale scheduling in the steelmaking industry, called Finishing Line Scheduling (FLS), is described. FLS in a major steel mill is a task to create production campaigns (specific production runs) for steel coils on four continuous processes for a one-month horizon. Two process flows are involved in FLS, and the balancing of the two process flows requires resolving conflicts of due dates. There ate also various constraints along the timeline for each process with respect to sequences of campaigns and coils. The two types of constraints--along process flows and timelines--make the FLS problem very complex. We have developed a high-performance solution for this problem as follows: Input coils are clustered by two clustering algorithms to reduce the complexity and size of the problem. Campaigns are created for each process from downstream to upstream processes, while propagating upward the process timings of the clusters. Timing inconsistencies along the process flows are then repaired by scheduling downward. Finally, coils are sequenced within each campaign. The FLS system enabled a steel mill to expand its scheduling horizon from a few days to one month, and to improve decision frequency from monthly to daily.

Variable resolution Markov modelling of signal data for image compression

Traditionally, Markov models have not been successfully used for compression of signal data other than binary image data. Due to the fact that exact substring matches in non-binary signal data are rare, using full resolution conditioning information generally tends to make Markov models learn slowly, yielding poor compression. However, as is shown in this paper, such models can be successfully applied to non-binary signal data compression by continually adjusting the resolution and order to minimize the code-length of the past samples in the hope that this choice will best compress the future samples as well, a technique inspired by Rissanens minimum description length (MDL) principle. Performance of this method meets or exceeds current approaches.

Variable decay rate histogram modelling for image compression

Several methods exist for adaptation to non-stationary statistics in histogram modelling. Among the techniques that perform local adaptation by decaying histogram counts, we show that fixed decay rate schemes are sub-optimal. We use an order-0 model and an arithmetic coder to demonstrate that improved performance can be obtained by using a variable decay rate scheme that uses the derivative of the per-symbol codelength sequence to control the rate of decay.