Abstract
To solve the charge planning problem involving charges and the orders in each charge, a traveling salesman problem based charge planning model and the improved cross entropy algorithm are proposed. Firstly, the charge planning problem with unknown charge number is modeled as a traveling salesman problem. The objective of the model is to minimize the dissimilarity costs between each order and its charge center order, the open order costs, and the unselected order costs. Secondly, the improved cross entropy algorithm is proposed with the improved initial state transition probability matrix which is constructed according to the differences of steel grades and order widths between orders. Finally, an actual numerical example shows the effectiveness of the model and the algorithm.
Highlights
Primary steel making is a main stage of steel production process [1], in which oxygen furnaces or electric furnaces convert molten iron into batches of molten steel
In the charge planning model mentioned above, objective function (1) minimizes the sum of dissimilarity costs caused by each order and its charge center order, and the costs resulted from open order and the penalty costs for unselected orders
Regarding the orders as cities, the sum of dissimilarity costs caused by orders merged into charge centers, the costs resulted from open order and the penalties for unselected orders as distances, furnace capacity as the maximum distance a salesman travels, the charge planning problem can be regarded as a traveling salesman problem
Summary
Primary steel making is a main stage of steel production process [1], in which oxygen furnaces or electric furnaces convert molten iron into batches of molten steel. Xue et al [5] modeled the charge planning problem with unknown charge number and transformed the model into pseudo-traveling salesman model. In this model, the dissimilarity costs in a charge are calculated as total differences among orders in the same charge, while it is better to be calculated as differences between orders in each charge and the charge center order according to the practical steel production process. The improved cross entropy algorithm is proposed to solve the charge planning problem with unknown charge numbers and its objective is to minimize the dissimilarity costs between each order and its charge center order.
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