Coil batching to improve productivity and energy utilization in steel production

This paper investigates a practical batching decision problem that arises in the batch annealing operations in the cold rolling stage of steel production faced by most large iron and steel companies in the world. The problem is to select steel coils from a set of waiting coils to form batches to be annealed in available batch annealing furnaces and choose a median coil for each furnace. The objective is to maximize the total reward of the selected coils less the total coil'coil and coil'furnace mismatching cost. For a special case of the problem that arises frequently in practical settings where the coils are all similar and there is only one type of furnace available, we develop a polynomial-time dynamic programming algorithm to obtain an optimal solution. For the general case of the problem, which is strongly NP-hard, an exact branch-and-price-and-cut solution algorithm is developed using a column and row generation framework. A variable reduction strategy is also proposed to accelerate the algorithm. The algorithm is capable of solving medium-size instances to optimality within a reasonable computation time. In addition, a tabu search heuristic is proposed for solving larger instances. Three simple search neighborhoods, as well as a sophisticated variable-depth neighborhood, are developed. This heuristic can generate near-optimal solutions for large instances within a short computation time. Using both randomly generated and real-world production data sets, we show that our algorithms are superior to the typical rule-based planning approach used by many steel plants. A decision support system that embeds our algorithms was developed and implemented at Baosteel to replace their rule-based planning method. The use of the system brings significant benefits to Baosteel, including an annual net profit increase of at least 1.76 million U.S. dollars and a large reduction of standard coal consumption and carbon dioxide emissions

The situation of lymphadenopathy at different histological stages.

<p>Note: percentage = cases of patients / total number of patients with the corresponding histopathology.</p><p>The situation of lymphadenopathy at different histological stages.</p

Liver signal grade at different histological stages.

<p>Liver signal grade at different histological stages.</p

Clinical characteristics of the 45 PBC patients.

<p>Clinical characteristics of the 45 PBC patients.</p

male, 61 years, axial T2-weighted image shows periportal halo signs as hypointense areas around the portal veins (<i>arrows</i>).

<p>male, 61 years, axial T2-weighted image shows periportal halo signs as hypointense areas around the portal veins (<i>arrows</i>).</p

Specific distribution of enlarged lymph nodes.

<p>Specific distribution of enlarged lymph nodes.</p

female, 50 years, stage II with signal grade 2 and halo sign grade 2.

<p>female, 50 years, stage II with signal grade 2 and halo sign grade 2.</p

Halo sign grade at different histological stages.

<p>Halo sign grade at different histological stages.</p

male, 37 years, stage I with signal grade 1 and halo sign grade 1.

<p>male, 37 years, stage I with signal grade 1 and halo sign grade 1.</p

male, 54 years, stage IV with signal grade 3 and halo sign grade 3.

<p>male, 54 years, stage IV with signal grade 3 and halo sign grade 3.</p