Single-machine scheduling with waiting-time-dependent due dates

We consider a single-machine scheduling problem in which due dates are linear functions of the job waiting-times and the objective is to minimize the maximum lateness. An optimal sequence is constructed by implementing an index-based priority rule for a fixed value of the due date normalizing constant k. We determine in polynomial time all the k value ranges so that the optimal sequence remains the same within each range. The optimal due dates are computed as linear functions of the global optimal value of k. The overall procedure is illustrated in a numerical example.

A modified LPT algorithm for the two uniform parallel machine makespan minimization problem

We propose a modified longest processing time (MLPT) heuristic algorithm for the two uniform machine makespan minimization problem. The MLPT algorithm schedules the three longest jobs optimally first, followed by the remaining jobs sequenced according to the LPT rule. We prove the tight worst-case ratio bound of for the MLPT algorithm which is an improvement over the tight worst-case ratio bound of 1.28 for the LPT algorithm.Scheduling Uniform parallel machines LPT Approximation algorithms

A note on the proportionate flow shop with a bottleneck machine

Choi, B.-C., Yoon, S.-H., Chung, S.-J., 2007. Minimizing maximum completion time in a proportionate flow shop with one machine of different speed. European Journal of Operational Research 176, 964-974 consider the proportionate flow shop with a slow bottleneck machine and propose the SLDR heuristic for it. Choi et al. (2007) derive a data-dependent worst-case ratio bound for the SLDR heuristic which is then bounded by two. In this note, we show that the tight worst-case ratio bound of the SLDR heuristic is 3/2.Flow shop sequencing Proportionate flow shop Makespan Approximation algorithms