We resolve an open question raised by Feige & Scheideler by showing that the best known approximation algorithm for flow shops is essentially tight with respect to the used lower bound on the optimal makespan. We also obtain a nearly tight hardness result for the general version of flow shops, where jobs are not required to be processed on each machine. Similar results hold true when the object...

We consider the NP-hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson’s rule. For m = 2, we present a 32 -approximation algorithm, and for m = 3, we present a 12 7 -approximation algori...

This paper addresses the problem of minimizing the makespan on a two-stage parallel flow shops with proportional processing times. The problem of scheduling n independent jobs on m proportional parallel flow shops to minimize makespan is known to be NP-hard and hence too difficult to solve in polynomial time. A multiphase heuristic algorithm to minimize the makespan on two proportional parallel...

conventional passive distribution networks are changing to modern active distribution networks which are not radial. conventional load flow methods should be modified for new distribution networks analysis. in modern distribution networks distributed generation (dg) units are embedded with conventional and/or renewable resources. dg units are generally modeled as pv or pq nodes which inject ...

In the past, we demonstrated how fuzzy concepts can easily be used in the Johnson algorithm for managing uncertain scheduling on two-machine flow shops. This paper extends these concepts to fuzzy flow shops with more than two machines. A new fuzzy heuristic flow-shop scheduling algorithm (the fuzzy Gupta algorithm) is then designed since optimal solutions seem unnecessary for uncertain environm...

Flexible flow shops are becoming increasingly common in industry practice because of higher workloads imposed by jobs on one or more stages, thus requiring two or more units of the same machine type. We present a methodology for solving this important problem, namely group scheduling, within the context of cellular manufacturing systems in order to minimize the total completion time of all grou...