# Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for this reason I looked at a chance constrained model. I also want to have multiple objectives, one to minimise cost and another to maximise yield, and possibly a third to maximise coke quality. So I have thought about doing a chance constrained multiple objective model, but I am not very experienced in this area. Is there any advice or recommendations for literature to read about this problem? Thank you in advance!

• Hi danielcharters. What defines your statistical variation, that is the most important question here. Do you have data for this, or some distribution of the qualities? Or, do you know an exact uncertainty region, e.g., the quality of type $i$ will be between $[c_i -5, c_i + 5]$, etc. – independentvariable Apr 7 '20 at 18:59
• @independentvariable thank you for your response. I have analysed each coal type and fitted distributions to each of the qualities, is that what you mean? – danielcharters Apr 7 '20 at 19:10
• Yes, but why did you fit a distribution? Is there a distirbution.like frequency there? Or did you just fit a distribution to have a distribution? I am trying to figure out if you really need to use distributions or if we can use, e.g., robust optimization. – independentvariable Apr 7 '20 at 19:24
• @independentvariable yes, there is a distribution like frequency. I have modelled the blend deterministically using each quality’s average, but I don’t believe this to be an accurate representation of what is going on because there is definitely some level of randomness present in the coal’s qualities, so I would like to try incorporate that randomness in my model. – danielcharters Apr 7 '20 at 19:37