Steelmaking and refining coordinated scheduling problem with waiting time and transportation consideration

This article explores the coordinated scheduling problem between production and transportation in a steelmaking shop. Two models arising from steelmaking and refining operations are considered. The first model assumes that there is a converter at the steelmaking operation and a refining furnace at the refining operation. A transporter with capacity one is available to carry out jobs from converter to a refining furnace. The objective is to minimize the maximum completion time. For this model, we provide an algorithm with worst case ratio of two and show the computational results. The second model considers more practical situation in which jobs are processed in identical parallel converters first, and then the jobs coming from same converter are transported by a dedicated trolley with capacity one to the next operations. Two objectives are considered in the second model. One is to minimize the sum of maximum completion time, idle time penalties and waiting time penalties satisfying waiting time constraints. The other is to minimize the sum of maximum completion time, idle times penalties and hot consumption penalties related to waiting times while satisfying waiting time constraints. For the model, we develop a tabu search algorithm, provide the computational results and then give the worst case analysis.