On the relations between optimal solutions for different types of min-sum balanced just in time optimisation problems

The relations between optimal solutions for different types of min-sum balanced JIT optimisation problems are examined. It is shown that the so-called min-sum-absolute and min-sum-squared problems, subject to the so-called oneness condition, have the same set of optimal solutions and that this property cannot be extended to other types of min-sum problems. It is also shown that any optimal solution for the min-sum-absolute problem with oneness property if any exists is optimal for the min-sum-squared.