The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for neig...

We consider the semilinear problem Δu=λ+(− log u+)1{u>0}−λ−(− u−)1{u<0} in B1, where B1 is unit ball Rn and assume λ+,λ−>0. Using a monotonicity formula argument, we prove an optimal regularity result for solutions: ∇u log-Lipschitz function. This introduces two main difficulties. The first lack of invariance scaling blow-up problem. other (more serious) issue term Weiss energy which potentiall...