Finding the Pareto-optima for the total and maximum tardiness single machine problem Original Research Article

The paper deals with the single machine scheduling problem where both total and maximum tardiness must be minimized. The ε-constraint approach is adopted to search for all the Pareto-optima, leading to cope with a total tardiness problem with deadlines. This latter problem is studied, identifying several dominance properties, decomposition rules and polynomially and pseudopolynomially solvable cases. A branch and bound algorithm for finding the Pareto-optima is proposed and computational results are reported for instances up to 70 jobs in size.