Due-date assignment and single machine scheduling with compressible processing times

In this paper we consider a due-date assignment and single-machine scheduling problem in which the jobs have compressible processing times. Two models are defined according to the due-date assignment methods used. The first model applies the common (constant) due-date assignment method to assign the due-dates, while in the second model the due-dates are assigned using the slack due-date assignment method. The objective is to determine the optimal sequence, the optimal due-dates and the optimal processing time compressions to minimize a total penalty function based on earliness, tardiness, due-dates and compressions. We solve the problem by formulating it as an assignment problem which is polynomially solvable. For the case that all the jobs have a common upper bound for compressions and an equal unit compression penalty, we present an O(n log n) algorithm to obtain the optimal solution.