Hybrid Flow Shop with Parallel Machines at the First Stage and Dedicated Machines at the Second Stage

Abstract

In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NPhard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

An Effective Optimization Approach to Minimize Waste in a Complex Industrial System

“…( [27], [30]) and Yang. [4]. For the other parameters, the datasets depend on the family instances, as presented below.…”

“…Following the α|β|γ notation of Graham et al [3], this problem can be noted as HF2(PD2,Pm)|ST g,sd ,lag+ i |Nbr_IT+, where ST g,sd designates the constraint sequence-dependent group setup, lag+ i designates the maximum machine time lag for j i , and Nbr_IT+ is a notation introduced by us to designate the number of IT grater than perishability time limit (θ). In the previous notation; proposed by Yang et al [4], the dedicated machines appear in the term as PD2, while the identical parallel machines at S2 are represented by Pm. This problem could also be noted HF2 (R2,Pm)|Mj,ST g,sd , lag+ i |Nbr_IT+; following Ribas et al [5] notations.…”