Method for determining slab length and slab charging position within walking-beam heating furnace

A method of determining a slab length and a charging position of a slab in a walking-beam heating furnace, the method comprising:

• in determining a length of a slab to be charged into at least one walking-beam heating furnace and a charging position of the slab using mixed integer programming,
• using, as constraint conditions,
• a constraint equation defining an overhang amount,
• a constraint equation defining a scab defect occurrence probability corresponding to the overhang amount from a predetermined model that defines a relationship between the overhang amount and a probability of occurrence of a scab defect occurring at a skid portion, and
• a constraint equation defining upper and lower limits of slab length,
• further using an evaluation function that uses a constraint equation defining the scab defect occurrence probability, and
• determining the length of the slab and the charging position of the slab to minimize the evaluation function under the constraint conditions, wherein
• as the overhang amount,
• a lead end overhang amount, defined as a distance between a lead end coordinate of the slab in the heating furnace and a second skid coordinate counted from a lead end in a tail end direction, and
• a tail end overhang amount, defined as a distance between a tail end coordinate of the slab in the heating furnace and a second skid coordinate counted from a tail end in a lead end direction, are used.