Minimizing tardiness scheduling measures with generalized due-dates and a maintenance activity

We study single machine scheduling problems with the following features: (i) Generalized due-dates are considered, i.e., the j-th due-date is assigned to the j-th completed job; (ii) A fixed maintenance activity during which no production is feasible is assumed; (iii) The objective functions are minimizing various tardiness measures. Specifically, four objective functions are considered: total tardiness, maximum tardiness, the number of tardy jobs and total late work. We introduce pseudo-polynomial solution algorithms for these NP-hard problems. Our numerical tests indicate that instances of medium size of all four problems are solved in very reasonable running times.