Pareto-optimal front generation for the bi-objective JIT scheduling problems with a piecewise linear trade-off between objectives

•This paper deals with the bi-objective optimization of total weighted earliness and tardiness (TWET) and total flowtime (TFT) in a single-machine scheduling problem with distinct job due dates and allowing inserted idle times in the schedules.•The paper proposes an optimal timing algorithm (OTA) to generate the TWET-TFT trade-off curve for a given sequence of jobs.•A Pareto-optimal front generation procedure is proposed to generate a Pareto-optimal front comprising line segments and points.•The performance of the proposed OTA and the Pareto-optimal front generation procedure was compared with a parametric simplex algorithm and an upper envelop algorithm, respectively, adopted from the literature.•Computational results reveal that the proposed methods, the OTA and the Pareto-optimal front generation procedure, outperform the respective techniques, the parametric simplex algorithm and the upper envelop algorithm, in terms of computation time.•The proposed OTA and the Pareto-optimal front generation procedure are best suited for implementation within metaheuristic algorithms compared to the methods used for comparison from the literature. This paper proposes a novel method of Pareto front generation from a set of piecewise linear trade-off curves typically encountered in bi-objective just-in-time (JIT) scheduling problems. We have considered the simultaneous minimization of total weighted earliness and tardiness (TWET) and total flowtime (TFT) objectives in a single-machine scheduling problem (SMSP) with distinct job due dates allowing inserted idle times in the schedules. An optimal timing algorithm (OTA) is presented to generate the trade-off curve between TWET and TFT for a given sequence of jobs. The proposed method of Pareto front generation generates a Pareto-optimal front constituted of both line segments and points. Further, we employ a simple local search method to generate sequences of jobs and their respective trade-off curves, which are trimmed and merged to generate the Pareto-optimal front using the proposed method. Computational results obtained using problem instances of different sizes reveal the efficiency of the proposed OTA and the Pareto front generation method over the state-of-the-art methodologies adopted from the literature.