A Robust Two-Machine Flow-Shop Scheduling Model with Scenario-Dependent Processing Times

Abstract

In many scheduling studies, researchers consider the processing times of jobs as constant numbers. This assumption sometimes is at odds with practical manufacturing process due to several sources of uncertainties arising from real-life situations. Examples are the changing working environments, machine breakdowns, tool quality variations and unavailability, and so on. In light of the phenomenon of scenario-dependent processing times existing in many applications, this paper proposes to incorporate scenario-dependent processing times into a two-machine flow-shop environment with the objective of minimizing the total completion time. The problem under consideration is never explored. To solve it, we first derive a lower bound and two optimality properties to enhance the searching efficiency of a branch-and-bound method. Then, we propose 12 simple heuristics and their corresponding counterparts improved by a pairwise interchange method. Furthermore, we set proposed 12 simple heuristics as the 12 initial seeds to design 12 variants of a cloud theory-based simulated annealing (CSA) algorithm. Finally, we conduct simulations and report the performances of the proposed branch-and-bound method, the 12 heuristics, and the 12 variants of CSA algorithm.

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

“…This model is then implemented into simulation to evaluate its performance. In this simulation, the proposed model is then compared with the existing NSGA II [9], IEGA [25], CTSA [16], and ABC [3]. In this simulation, the objectives of the NSGA II are modified so that the objectives are maximum completion time and maximum intermediate storage.…”

“…Eq. (16) shows that the highest maximum intermediate storage is the highest maximum intermediate storage among the solutions in an iteration time. Eq.…”

“…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.…”

“…To see performance of our proposed model, we are going to compare our model with the four techniques: NSGA II [9], IEGA [25], CTSA [16], and ABC [3]. These four comparing algorithms were used in several latest FSP studies as they are explained in the literature review.…”

“…Thus, this model is developed based on an evolutionary algorithm. Other metaheuristic algorithms that have been widely used in solving the FSP are genetic algorithm [3], simulated annealing [16], tabu search [17], particle swarm optimization [9], chaotic-student-psychology based optimization [18], etc.…”