In this research, Lagrangian relaxation algorithms are proposed for Hybrid Flow-Shop (HFS) scheduling problems. Conventional HFS consists of a series of production stages, each of which has several identical parallel machines and no buffer spaces are considered. Jobs are processed through all stages in the same direction. In the previous researches, they are assumed that the capacity of buffer ...

We present a general time-indexed formulation that contains scheduling problems with unrelated parallel machines. We derive a class of basic valid inequalities for this formulation, and we show that a subset of these inequalities are facet-defining. We characterize all facet-defining inequalities with right-hand side 1. Further, we show how to efficiently separate these inequalities.

The paper addresses the problem of scheduling in the two-stage flowshop with parallel unrelated machines and renewable resource constraints. The objective is minimization of makespan. The problem is NP-hard. Fast heuristic algorithms using list scheduling and greedy strategies are proposed. For evaluation of the performance of the algorithms computational experiments are performed on randomly g...

We show how to approximate in NC the problem of Scheduling Unrelated Parallel Machines, for a xed number of machines. We develop a (2 + ")-approximate parallel algorithm for the problem. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. T...

The unrelated parallel machine scheduling problem (UPMSP) is a typical production with certain symmetries on machines. Additional resources and preventive maintenance (PM) extensively exist machines; however, UPMSP additional PM has been scarcely investigated. Adaptive competition also seldom implemented in the artificial bee colony algorithm for scheduling. In this study, investigated, which A...

We provide several non-approximability results for deterministic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consideration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated ma...