In this paper, the problem of two-machine flow shop scheduling to minimize total energy costs under time-of-use tariffs is investigated. As the objective function of this study is not a regular measure, allowing intentional idle-time can be advantageous. So this study considers two approaches, one for non-delay version of the problem and the other one for a situation when inserting intentional ...

Decidability results for hybrid automata often exploit subtle properties about dimensionality (number of continuous variables), and interaction between discrete transitions and continuous trajectories of variables. Thus, the decidability results often do not carry over to parallel compositions of hybrid automata, even when there is no communication other than the implicit synchronization of tim...

The cyclic permutation flow shop is one flow shop that repetitively produces product mix under permutation schedules. We propose that the cyclic permutation flow shop given the general job sequence can be modeled as a time event graph, based on which the mixed-integer programming method is applied to find the optimal schedule with maximum throughput. Two cases of cyclic permutation flow shops w...

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 APX-hardness proofs. We show that, whereas scheduling on unrelated machines with unit...

This article examines the multi-objective scheduling of a reentrant hybrid flow shop. This type of shop is composed of several stages made of several identical parallel machines. When a task has to be processed on a stage, it is assigned to the machine with the smallest workload. This problem shows a reentrant structure: each task must be processed several times at each stage. In this paper, th...

Minimum makespan scheduling of Flow Shops with Multiple Processors (FSMPs), also known as the Hybrid Flow Shop (HFS), is classified as NP complete. Thus, the FSMP largely depends on strong heuristics to develop solutions to makespan scheduling instances. An FSMP consists of m stages wherein each stage has one or more processors through which n jobs are scheduled. This paper presents a heuristic...