A Global Solution Approach to the Energy-Efficient Ladle Dispatching Problem With Refractory Temperature Control

Abstract

The discussion of energy efficiency in the steel ladle dispatching literature is currently limited to indirectly minimizing waiting and heating times. Not explicitly considering the ladle’s thermal balance may lead to sub-optimal solutions and safety concerns regarding the condition of the refractory lining. Hence, this paper studies the energy-efficient ladle dispatching problem with refractory temperature control. A mixed integer linear problem for ladle dispatching that integrates its energy balance is presented. It enables the global solution of the problem using state-of-the-art mixed integer programming solvers. This is achieved by applying piecewise linear models with logarithmic coding to approximate the energy balance. Computational results show that the number of breakpoints employed significantly affects the approximation quality and solution time. However, we show that the error does not affect the feasibility of the problem and yields a negligible difference of 1.4% in the objective function. Hence, this viable approach enables a proper discussion on the energy efficiency of ladle dispatching decisions. For a small but representative production scenario from Tata Steel, IJmuiden, we design and execute an experiment to define a set of operational rules and discuss the potential energy savings. We conclude by presenting the existing compromise between the CO2 emissions from re-heating the ladles and the reduction in the steel temperature losses from the improved thermal management of the ladles. We show that the average steel temperature losses can be reduced up to 3 °C depending on the refractory temperature requirement. This has the potential to unlock further savings for steelmakers.

Keywords

• Energy efficiency
• ladle dispatching
• mixed integer linear programming (MILP)
• piecewise linearization
• refractory
• steelmaking