Solving the permutation flow shop problem with blocking and setup time constraints

Abstract

In this paper, the flow shop with blocking and sequence and machine dependent setup time problem aiming to minimize the makespan is studied. Two mixed-integer programming models are proposed (TNZBS1 and TNZBS2) and two other mixed-integer programming models, originally proposed for the no setup problem, are adapted to the problem. Furthermore, an Iterated Greedy algorithm is proposed for the problem. The permutation flow shop with blocking and sequence and machine dependent setup time is an underexplored problem and the authors did not find the use of mixed-integer programming models for the problem in any other work. To compare the models, a database of 80 problems was generated, which vary in number of machines and jobs. For the small sized problems, the adapted MILP model obtained the best results. However, for bigger problems, both proposed MILP models obtained significantly better results compared to the adapted models, proving the efficiency of the new models. When comparing the Iterated Greedy algorithm with the MILP models, the former outperformed the latter.

Collaborative Flow-shop Scheduling Using Simulated Annealing and First Price Sealed Bid Auction to Minimize Total Cost and Make-span

“…Model Objectives [15] distributed flow-shop single authoritative minimize make-span [4] multiple-machine flowshop single authoritative minimize cost [16] distributed flow-shop single authoritative minimize make-span [17] distributed flow-shop single authoritative minimize make-span [18] distributed flow-shop single authoritative minimize make-span [19] single flow-shop single authoritative minimize make-span [20] hybrid flow-shop single authoritative minimize make-span minimize maximum tardiness minimize idle energy consumption [11] distributed flow-shop single authoritative minimize make-span [21] two-machine flow-shop single authoritative minimize make-span minimize total energy consumption [22] single flow-shop single authoritative minimize make-span [23] single flow-shop single authoritative minimize make-span [24] multiple-machine flowshop single authoritative minimize make-span [25] multiple-machine flowshop single authoritative minimize actual flow time [8] single machine flowshop single authoritative minimize total completion time [5] parallel flow-shop single authoritative minimize make-span [26] single flow-shop single authoritative minimize make-span [10] single flow-shop single authoritative minimize total tardiness [9] parallel flow-shop single authoritative minimize total cost minimize total time this work multiple flow-shops multiple voluntary minimize production cost minimize make-span these jobs into the lines and arrange each set of jobs in every line.…”

A Parallel Permutation Flow-Shop Scheduling Model by Using a Two-Step Evolutionary Algorithm to Minimize Intermediate Storage with Tolerable Maximum Completion Time

“…When this job has finished its current stage but the machine in the next stage has not been available yet, this job must be stored in the intermediate storage. Otherwise, this job is stuck in this current job and blocks other jobs from occupying the machine in the current stage [12].…”

“…multi-objective multi-verse optimizer (IMOMVO) [22] make-span iterated greedy algorithm [3] total weighted completion time artificial bee colony algorithm [10] make-span, a measure of service level and total energy consumption MILP [16] total completion time. cloud theory-based simulated annealing (CSA) [23] total actual flow time MILP [24] total weighted tardiness constructive heuristics and branch-and-bound algorithm (B&B) [4] total tardiness GA [5] make-span and the cost of delay differential evolution (DE) and local search (LS) [12] make-span MILP and iterated greedy algorithm [25] total completion time IEGA [9] total weighted tardiness, total operation time, and total cost of the company's reputational damage MILP, MOPSO, NSGA II [7] maximum completion time of jobs constructive heuristics the distributed permutation FSP. Naderi & Ruiz [8] compared 14 heuristic-based dispatching methods to solve problems in distributed permutation FSP.…”

“…Eq. (12) shows that the offspring will replace the solution with the highest maximum completion time. Eq.…”

“…In most FSP research, intermediate storage was considered as a limitation rather than an objective. Several studies assumed that intermediate storage is limitless, whereas others considered that it is limited [11] or nil [7], resulting in the possibility of blocking [12].…”