I have heard some people advocate that minimum wage should be automatically adjusted for inflation, reindexed on a yearly basis. For instance, if the minimum wage is $10/hr and inflation is at 5% that year, then next year the minimum wage should automatically be increased to $10.50/hr.

What would be the advantages and disadvantages of tying minimum wage to inflation?

Note that other answers on this site indicate that there is debate over whether an increase in minimum wage causes inflation, so answers should not assume one outcome or the other.