Abstract
With the development of society, people have a higher demand for the work environment. It has aroused extensive attention of enterprises. One of the most important demands for workers is to have enough rest time to regain strength and energy during the working day. In this paper, a comprehensive mathematical model is established for the multi-objective flexible job-shop scheduling problem with flexible rest time (MOFJSP-FRT). Then a hybrid multi-objective evolutionary algorithm (MOEA) with heuristic adjustment strategies and variable neighborhood search (VNS), named HMOEAV, is proposed to solve the MOFJSP-FRT with the objectives to minimize the makespan and the machines loads balancing simultaneously. In the proposed hybrid algorithm, the machine-based encoding scheme is designed to improve search effectiveness by reducing computational complexity. Two heuristic adjustment strategies considering both the problem characteristics and the objective features are employed to initialize a high-quality population. To adequately emphasize the local exploitation ability of MOEA, VNS is incorporated into it. The non-dominated solutions got by MOEA are the initial solutions for VNS, in which three types of neighborhood structures according to problem structures are designed. The practical case in a steel structure enterprise is carried out to demonstrate the effectiveness of the proposed model and hybrid algorithm. The influences of rest time length on the MOFJSP-FRT are analyzed to give enterprises new insights to improve the scheduling efficiency while ensuring that employees have enough time to rest.
Highlights
The flexible job-shop scheduling problem (FJSP) [1] is a classic abstraction of an actual production environment, and this topic has been extensively studied for decades [2]–[5]
1) THE BOUND OF THE AVAILABLE REST TIME RANGE To determine the bound of the available rest time range, the following aspects should be considered: 1) max Tijk +τ, ensure that after the operation with the longest processing time is finished during the available rest time range, the corresponding operator still have enough time to rest; 2) consider the business hours of the enterprise restaurant
The enterprise can determine the bound of the available rest time range refer to the two aspects above and constraints (10)
Summary
The flexible job-shop scheduling problem (FJSP) [1] is a classic abstraction of an actual production environment, and this topic has been extensively studied for decades [2]–[5]. From the literatures review above, we can see that existing studies about RC-FJSP are mainly focused on the accessibility of the machines and the processing capacity of employees Those studies seldom consider the rest time even though it is a crucial factor affecting the scheduling efficiency. Reference [30] proposed a hybrid algorithm combining the use of the MOEA of a well-known Pareto-based NSGA-II technique with a novel VNS strategy to solve the political redistricting problem. The contributions of this work lie as follows: (1) a problem related to MOFJSP with FRT is developed, and the available rest time range and start-stop of FRT are studied; (2) in the proposed hybrid algorithm, the machine-based encoding scheme is proposed to improve search efficiency.
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