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

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. © 2002 Elsevier Science B.V.