scholarly journals Comparing Mixed-Integer Programming and Constraint Programming Models for the Hybrid Flow Shop Scheduling Problem with Dedicated Machines

2021 ◽  
Vol 54 (4) ◽  
pp. 591-597
Author(s):  
Asma Ouled Bedhief
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Constraint Programming ◽  
Flow Shop ◽  
Programming Model ◽  
Flow Shop Scheduling ◽  
Mixed Integer ◽  
Hybrid Flow Shop ◽  
Dedicated Machines ◽  
Hybrid Flow Shop Scheduling

The paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines and release dates. Each job must be first processed on the single machine of stage 1, and then, the job is processed on one of the two dedicated machines of stage 2, depending on its type. Moreover, the jobs are available for processing at their respective release dates. Our goal is to obtain a schedule that minimizes the makespan. This problem is strongly NP-hard. In this paper, two mathematical models are developed for the problem: a mixed-integer programming model and a constraint programming model. The performance of these two models is compared on different problem configurations. And the results show that the constraint programming outperforms the mixed-integer programming in finding optimal solutions for large problem sizes (450 jobs) with very reasonable computing times.

scholarly journals A DE-LS Metaheuristic Algorithm for Hybrid Flow-Shop Scheduling Problem considering Multiple Requirements of Customers

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yingjia Sun ◽  
Xin Qi
Keyword(s):  
Differential Evolution ◽  
Flow Shop ◽  
Programming Model ◽  
Flow Shop Scheduling ◽  
Mixed Integer ◽  
Hybrid Flow Shop ◽  
Scheduling Problem ◽  
Metaheuristic Algorithm ◽  
Shop Scheduling ◽  
Hybrid Flow Shop Scheduling

In this paper, we address a hybrid flow-shop scheduling problem with the objective of minimizing the makespan and the cost of delay. The concerned problem considers the diversity of the customers’ requirements, which influences the procedures of the productions and increases the complexity of the problem. The features of the problem are inspired by the real-world situations, and the problem is formulated as a mixed-integer programming model in the paper. In order to tackle the concerned problem, a hybrid metaheuristic algorithm with Differential Evolution (DE) and Local Search (LS) (denoted by DE-LS) has been proposed in the paper. The differential evolution is a state-of-the-art metaheuristic algorithm which can solve complex optimization problem in an efficient way and has been applied in many fields, especially in flow-shop scheduling problem. Moreover, the study not only combines the DE and LS, but also modifies the mutation process and provides the novel initialization process and correction strategy of the approach. The proposed DE-LS has been compared with four variants of algorithms in order to justify the improvements of the proposed algorithm. Experimental results show that the superiority and robustness of the proposed algorithm have been verified.

Hybrid Flow Shop Scheduling Problems with Multiprocessor Tasks

2011 ◽  
Vol 110-116 ◽  
pp. 3914-3921 ◽  
Author(s):  
Hui Mei Wang ◽  
Fuh Der Chou ◽  
Ful Chiang Wu ◽  
Meei Yuh Ku
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Mixed Integer ◽  
Hybrid Flow Shop ◽  
Test Problems ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Mip Model ◽  
Hybrid Flow Shop Scheduling ◽  
Greedy Methods

Hybrid flow shop scheduling problems with multiprocessor tasks to minimize the makespan have been addressed and solved efficiently. Several approaches were used, including greedy methods and metaheuristics. In this paper, we proposed a mixed integer programming (MIP) model that can define explicitly and precisely the nature of a given problem. We also addressed a modified lower bound to obtain tighter bounds. Additionally, we propose different decoding methods and emphasize their importance in hybrid flow shop scheduling problems with multiprocessor tasks. By using existing test problems with n=5 in examining the proposed methods, many optimal solutions can be obtained as benchmarks for reference by the MIP model. Accordingly, the results are indicative of the influence of the decoding methods on the solutions to the hybrid flow shop problems with multiprocessor tasks.

scholarly journals Multi-stage appointment scheduling for Outpatient Chemotherapy Unit: a case study

2021 ◽  
Author(s):  
Asma BOURAS ◽  
Malek Masmoudi ◽  
Nour El Houda SAADANI ◽  
Zied BAHROUN ◽  
Mohamed Amine ABDELJAOUAD
Keyword(s):  
Lower Bound ◽  
Flow Shop ◽  
Treatment Time ◽  
Flow Shop Scheduling ◽  
Mixed Integer ◽  
Computational Time ◽  
Mixed Integer Program ◽  
Hybrid Flow Shop ◽  
Multi Stage ◽  
Hybrid Flow Shop Scheduling

This paper deals with a multi stage hybrid flow-shop problem (HFSP) that arises in a privately Chemotherapy clinic. It aims to optimize the makespan of the daily chemotherapy activity. Each patient must respect the cyclic nature of chemotherapy treatment plans made by his referent oncologist while taking into account the high variability in resource requirements (treatment time, nurse time, pharmacy time). The problem requires the assignment of chemotherapy patients to oncologists, pharmacists, chemotherapy beds or chairs and nurses over a 1-day period. We provided a Mixed Integer Program (MIP) to model this issue, which can be considered as a five-stage hybrid flow-shop scheduling problem with additional resources, dedicated machines, and no-wait constraints.  Since this problem is known to be NP-hard, we provided a lower bound expression and developed an approximated solving algorithm: a tabu search inspired metaheuristic based on a constructive heuristic that can quickly reach satisfying results. To assess the empirical performance of the proposed approach, we conducted experiments on randomly generated instances based on real-world data of a Tunisian private clinic: Clinique Ennasr. Computational experiments show the efficiency of the proposed procedures: The mathematical model provided optimal solutions in reasonable computational time only for small instances (up to 10 patients).   Meta-heuristic’s results demonstrate, also, that the proposed approach offers good results in terms of solution quality and computational times with an average relative gap to the MIP solution equal to 3.13% and to the lower bound equal to 5.37% for small instances (up to 15 patients). The same gap to the lower bound increases to 25% for medium and large size instances (20-50 patients).

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