The lessons of flowshop scheduling research
Operations Research
Flowshop scheduling with dominant machines
Computers and Operations Research
Two-stage flowshop scheduling with a common second-stage machine
Computers and Operations Research
The strong NP-hardness of two-stage flowshop scheduling with a common second-stage machine
Computers and Operations Research
Hybrid flow shop scheduling: a survey
Computers and Industrial Engineering
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information Processing Letters
A heuristic method for two-stage hybrid flow shop with dedicated machines
Computers and Operations Research
The optimal number of used machines in a two-stage flexible flowshop scheduling problem
Journal of Scheduling
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This paper considers the problem of scheduling a two-stage flowshop that consists of a common critical machine in stage one and two independent dedicated machines in stage two. All the jobs require processing first on the common critical machine. Each job after completing its critical operation in stage one will proceed to the dedicated machine of its type for further processing in stage two. The objective is to minimize the weighted sum of stage-two machine completion times. We show that the problem is strongly NP-hard, and develop an O(n^3) polynomial time algorithm to solve the special case where the sequences of both types of jobs are given. We also design an approximation algorithm with a tight performance ratio of 43 for the general case.