Heuristics for a two-stage hybrid flowshop scheduling problem with ready times and a product-mix ratio constraint

Abstract

This paper focuses on the scheduling problem of minimizing makespan for a given set of jobs in a two-stage hybrid flowshop subject to a product-mix ratio constraint. There are identical parallel machines at the first stage of the hybrid flowshop, while there is a single batch-processing machine at the second stage. Ready times of the jobs (at the first stage) may be different, and a given product-mix ratio of job types should be kept in each batch at the second stage. We present three types of heuristic algorithms: forward scheduling algorithms, backward scheduling algorithms, and iterative algorithms. To evaluate performance of the suggested algorithms, a series of computational experiments are performed on randomly generated test problems and results are reported.Keywords Scheduling · Heuristics · Hybrid flowshop · Product-mix ratio · MakespanWe consider a scheduling problem in a hybrid flowshop (HFS). In a typical HFS, there are K serial workstations and there are multiple parallel machines at one or more workstations. This paper focuses on a two-stage hybrid flowshop in which there are multiple identical parallel machines at the first stage and a single batch-processing machine at the second stage. In the HFS considered in this study, there are two types of jobs, and a given product-mix ratio of the two job types should be kept in each batch at the second stage. Also, jobs arrive at the first stage dynamically, that is,

The hybrid flow shop scheduling problem

“…In [205] some mathematical programming formulations and heuristics are provided for a simple two stage HFS with only one machine at the second stage. [95] have recently proposed heuristics for a similar 2-stage problem with release dates and a product mix ratio constraint. A similar problem with lot streaming and the total flowtime criterion was studied by [233] and later by [119] for the makespan criterion.…”

“…F Hm, ((P M (k) ) m k=1 ))|avail|several simulation, heuristics, SA [16] F H3, ((P M (k) ) 3 k=1 ))||Cmax agent-based approach [20] F Hm, ((P M (k) ) m k=1 ))|recrc|Ū w MPF, GA, lower bounds,checks processing [47] F Hm, ((P M (k) ) m k=1 ))||Cmax Artificial Immune Systems [91] F Hm, ((P M (k) ) m k=1 ))|blocking, skip|Cmax flow lines, MPF, TS, huristics F H2, ((1 (1) , P 2 (2) ))||Cmax B&B, GA, heuristics [41] F Hm, ((P M (k) ) m k=1 ))|recrc|T w dispatching rules, heuristics [61] F H2, ((1 (1) , P 2 (2) ))|no − wait, (p j = 1) 1 |Cmax exact method [96] F Hm, ((P M (k) ) m k=1 ))||{Cmax,C} review on exact solution methods [121] F H2, ((1 (1) , P M (2) ))|avail|Cmax B&B, heuristics, complexity [38] F H3, ((RM (k) ) 3 k=1 ))|prec, block, S nsd |Cmax MPR-TS [70] F H2, ((P M (k) ) 2 k=1 )||Cmax B&B [88] F Hm, ((P M (k) ) m k=1 ))||Cmax MPR-SA, lower bounds [107] F H2, ((P 2 (1) , 1 (2) ))|batch|Cmax TSP-based heuristics [37] F H3, ((RM (k) ) 3 k=1 ))|S sd , block, prec|Cmax MPF, lower bounds, TS [50] F Hm, ((P M (k) ) m k=1 ))|assign|ĒT TS, special problem [83] F Hm, ((P M (k) ) m k=1 ))|r j |Cost TS, SA, heuristics [85] F Hm, ((RM (k) ) m k=1 ))|lot, skip|Cost GA, SA, flow lines [100] F H3, ((P M (k) ) 3 k=1 ))||Cmax heuristics [151] (1) , P 2 (2) ))|assembly (2) |F heuristics [195] F Hm, ((P M (k) ) m k=1 ))|size jk |Cmax Particle Swarm Optimization [196] F H2, ((1 (1) , P 2 (2) ))|skip (1) |Cmax heuristics 2009 [90] F Hm, ((RM (k) ) m k=1 ))|S sd , r j |αCmax + (1 − α)Ū MPF, heuristics, dispatching rules, GA [95] F H2, ((P M (1) , 1 (2) ))||Cmax heuristics, product-mix [191] F Hm, ((P M (k) ) m k=1 ))|skip, block, reentry|Cmax GA mixed with LS [229] F Hm, ((P M (k) ) m k=1 ))|size jk |Cmax Iterated Greedy (IG) [19] F H2, ((P M (1) , P M (2) ))|batch (2) |Cmax heuris...…”

Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

“…First, some authors consider a constraint that forbids starting of a job on any machine before a designated time. Such a constraint is referred to as "ready times", "release times" or "arrival times" [26,27]. Ready times are common constraints for scheduling on parallel machines [28] and online scheduling [19].…”

A hybrid genetic-gravitational search algorithm for a multi-objective flow shop scheduling problem

“…Wang & Choi, 2014), since the idle time is used in this study to calculate the completion time in second stage onwards, while the modelling developed by Choi and Wang (2012) uses the maximum time to determine the completion time. There is a literature using job ready time to calculate the completion time in second stage (Kim et al, 2007). However, the waiting time might not be considered while the job is in queue.…”