Proportionate Flow Shop Scheduling with Two Competing Agents to Minimize Weighted Late Work and Weighted Number of Late Jobs

2020 ◽  
pp. 2050046
Author(s):  
Ren-Xia Chen ◽  
Shi-Sheng Li
Keyword(s):  
Flow Shop ◽  
Optimal Schedule ◽  
Flow Shop Scheduling ◽  
Pareto Optimal ◽  
Optimal Point ◽  
Late Work ◽  
Proportionate Flow Shop ◽  
Weighted Number ◽  
Number Of Late Jobs ◽  
Late Jobs

We investigate a competitive two-agent scheduling problem in the setting of proportionate flow shop, where the job processing times are machine-independent. The scheduling criterion of one agent is to minimize its total weighted late work, and the scheduling criterion of the other agent is to minimize its total weighted number of late jobs. The goal is to find the Pareto-optimal curve (i.e., the set of all Pareto-optimal points) and identify a corresponding Pareto-optimal schedule for each Pareto-optimal point. An exact pseudo-polynomial-time algorithm and an [Formula: see text]-approximate Pareto-optimal curve are designed to solve the problem, respectively.

scholarly journals Scheduling a proportionate flow shop of batching machines

2020 ◽  
Vol 23 (5) ◽  
pp. 575-593
Author(s):  
Christoph Hertrich ◽  
Christian Weiß ◽  
Heiner Ackermann ◽  
Sandy Heydrich ◽  
Sven O. Krumke
Keyword(s):  
Polynomial Time ◽  
Flow Shop ◽  
Fixed Number ◽  
Release Dates ◽  
Proportionate Flow Shop ◽  
Weighted Number ◽  
Late Jobs ◽  
Two Machines ◽  
Completion Times ◽  
Sum Of Completion Times

Abstract In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number $$m \ge 2$$ m ≥ 2 of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are 0. Previously, polynomial time algorithms have only been known for two machines.

scholarly journals Multimodal Optimization of Permutation Flow-Shop Scheduling Problems Using A Clustering-Genetic-Algorithm-Based Approach

2021 ◽  
Vol 11 (8) ◽  
pp. 3388
Author(s):  
Pan Zou ◽  
Manik Rajora ◽  
Steven Y. Liang
Keyword(s):  
Genetic Algorithm ◽  
Clustering Algorithm ◽  
Flow Shop ◽  
Optimal Schedule ◽  
Flow Shop Scheduling ◽  
Multimodal Optimization ◽  
Shop Scheduling ◽  
Permutation Flow Shop Scheduling ◽  
Permutation Flow Shop ◽  
Global Optima

Though many techniques were proposed for the optimization of Permutation Flow-Shop Scheduling Problem (PFSSP), current techniques only provide a single optimal schedule. Therefore, a new algorithm is proposed, by combining the k-means clustering algorithm and Genetic Algorithm (GA), for the multimodal optimization of PFSSP. In the proposed algorithm, the k-means clustering algorithm is first utilized to cluster the individuals of every generation into different clusters, based on some machine-sequence-related features. Next, the operators of GA are applied to the individuals belonging to the same cluster to find multiple global optima. Unlike standard GA, where all individuals belong to the same cluster, in the proposed approach, these are split into multiple clusters and the crossover operator is restricted to the individuals belonging to the same cluster. Doing so, enabled the proposed algorithm to potentially find multiple global optima in each cluster. The performance of the proposed algorithm was evaluated by its application to the multimodal optimization of benchmark PFSSP. The results obtained were also compared to the results obtained when other niching techniques such as clearing method, sharing fitness, and a hybrid of the proposed approach and sharing fitness were used. The results of the case studies showed that the proposed algorithm was able to consistently converge to better optimal solutions than the other three algorithms.

Two-machine flow-shop scheduling to minimize total late work: revisited

2018 ◽  
Vol 51 (7) ◽  
pp. 1268-1278 ◽  
Author(s):  
Xin Chen ◽  
Zhongyu Wang ◽  
Erwin Pesch ◽  
Malgorzata Sterna ◽  
Jacek Błażewicz
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Late Work ◽  
Shop Scheduling

Clarification of lower bounds of two-machine flow-shop scheduling to minimize total late work

2018 ◽  
Vol 51 (7) ◽  
pp. 1279-1280
Author(s):  
Jacek Błażewicz ◽  
Xin Chen ◽  
Richard C. T. Lee ◽  
Bertrand M. T. Lin ◽  
Feng-Cheng Lin ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Late Work ◽  
Shop Scheduling

Review of the ordered and proportionate flow shop scheduling research

2013 ◽  
Vol 60 (1) ◽  
pp. 46-55 ◽  
Author(s):  
S.S. Panwalkar ◽  
Milton L. Smith ◽  
Christos Koulamas
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Proportionate Flow Shop

scholarly journals ON THE DISTRIBUTION OF PARETO OPTIMAL SOLUTIONS IN ALTERNATIVE SPACE – THE INVESTIGATION OF MULTI OBJECTIVE PERMUTATION FLOW SHOP SCHEDULING PROBLEMS

2006 ◽  
Vol 12 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Martin Josef Geiger
Keyword(s):  
Flow Shop ◽  
Search Space ◽  
Flow Shop Scheduling ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Multi Objective ◽  
Permutation Flow Shop Scheduling

The paper presents a study of the search space topology in the context of global optimization under multiple objectives. While in mono criterion problems a single global optimum has to be identified, multi objective problems require the identification of a whole set of equal. Pareto optimal alternatives. It is unclear up to now, however, whether Pareto optimal solutions appear relatively concentrated in search space, or whether their relative positions are rather distant. This open issue is addressed to the multi objective permutation flow shop scheduling problems. Distance metrics is introduced to asses numerical evaluation of the concentration of Pareto sets. It can be seen that independent from the chosen optimality criteria, Pareto optimal alternatives appear relatively concentrated in alternative space. The result holds for an extensive range of generated problem instances for which the exact global optima are known as well as for benchmark instances taken from literature. The importance of the results can be seen in the context of metaheuristic local search approaches for which meaningful implications derive.

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