A bicriterion scheduling problem involving total flowtime and total tardiness

The jobshop scheduling problems occur in industry in a variety of practical situations where more than one criterion is usually important. This paper deals with one such scheduling problem with two criteria, namely, total flowtime and total tardiness, both of which need to be minimized concurrently. Two sufficient conditions for optimality are developed. These conditions are then incorporated into a branch-and-bound procedure for developing optimal solutions. Results of computational experiments for the branch-and-bound are also presented.