A GAPN Approach for the Flexible Job-Shop Scheduling Problem with Indirect Energy and Time-of-Use Electricity Pricing

Round 1

Reviewer 1 Report

This is a very interesting study presenting a novel approach based on genetic algorithms and Petri nets to minimize the total FJSP-IT production cost. The research question is important, and the research presents a strong potential to contribute to both academia and the industry. The study also employs local data (Guangdong, China) as a case study, which provides solid support to the proposed GAPN approach. The manuscript seems highly readable with clear figures as well as detailed explanations. The authors are highly suggested to provide cut down some irrelevant background information and highlight the problem the novel approach can resolve in their introduction with updated references Overall, it is believed that the manuscript is merit in its quality and has the potential to be published with a minor revise.

Author Response

Point 1: The authors are highly suggested to provide cut down some irrelevant background information and highlight the problem the novel approach can resolve in their introduction with updated references.

Response 1: Some text are cut and the main contributions are listed in the Section 1.

Reviewer 2 Report

The authors have described a Genetic Algorithm Petri Net based approach for solving a flexible job shop scheduling problem with indirect energy cost considerations and compare different operation time policies. 

Comments:
  1) Please explain the full form of FJSP-IT where it is first mentioned in the manuscript
  2) A clear explanation of why a MILP or MINLP formulation is not preferred/suitable over Petri nets optimized by Genetic algorithms is not described
  3) The authors have not explained clearly the rationale behind why the indirect energy costs increases the complexity of modeling 
  4) Please correct the grammar errors and typos in the manuscript carefully
  5) Can the authors explain the rationale behind why the problem is decomposed into resource allocation and operating time determinations instead of a one-shot problem?
  6) The authors can add solution time to Table 6. The definitions and context around minimal and mean iterations needs to be elaborated upon
  7) A clear description of the novelty of the techniques applied for FJSP compared to other works needs to be specified

Author Response

Point 1:  Please explain the full form of FJSP-IT where it is first mentioned in the manuscript

Response 1: The sentence “, in which indirect energy is considerable and ToU pricing is adopted, and hence operation time policies should be suggested.” has beed added to explain the full form of FJSP-IT.

Please see the paragraph 1 on page 3.

Point 2:  A clear explanation of why a MILP or MINLP formulation is not preferred/suitable over Petri nets optimized by Genetic algorithms is not described

Response 2: We found that a few literatures has given explanation of the problem above, and the explanation has been newly cited in the paragraph 4 on page 3.

The cited text are the following:

It is concluded in [39,49] that the GAPN is an approach that provides good performance in reasonable computer times and at the same time, can be adapted to real settings where many constraints such as multiplicity of resources, recirculation, and assembly operations are not traditionally handled by classical algorithms such as linear and mixed integer programming, branch and bound, dynamic programming.

Point 3:  The authors have not explained clearly the rationale behind why the indirect energy costs increases the complexity of modeling

Response 3: The clause has beed revised to explain why the indirect energy costs increases the complexity of modeling.

The original sentence: indirect energy enhances the complexity of modelling the problem since a generic FJSP has complex sequence and shared resource constraints.

The revised sentence: indirect energy enhances the complexity of modelling the problem since a new type of cost should be introduced in the objective and decision.

Please see the paragraph 5 on page 3.

Point 4:  Please correct the grammar errors and typos in the manuscript carefully

Response 4: Yes, we have checked the manuscript carefully and corrected some grammar errors and typos. We are sorry for our carelessness.

Point 5:  Can the authors explain the rationale behind why the problem is decomposed into resource allocation and operating time determinations instead of a one-shot problem?

Response 5: Yes, the decomposition is mostly for reducing the complexity of solving FJSP-IT. As mentioned in problem definition, the decision of FJSP-IT involves determining allocate(o) and start(o), and start(o) will significantly expand the solution space. If the FJSP-IT is considered as an one-shot problem, the optimal solution will be hard to search. Additionally, operation time policy will be hard to evaluate with undetermined allocate(o).

The explaining sentences are added in the the paragraph 1 in Section 4.1.

Point 6: The authors can add solution time to Table 6. The definitions and context around minimal and mean iterations needs to be elaborated upon

Response 6:

First, we don’t think the solution time should be added to Table 6 since the time complexity of the algorithm are analysised in the Section 4.2.1. Generally, the time performance of algoritm is not evaluated by actual running time but time complexity analysis.

Second, the following definitions for minimal and mean iterations are added at the start of the Section 5.2.1:

For each experiment, the minimal iteration means the minimal number of iterating generation to reach the optimal solution. For each configuration, the minimal iteration means the minimal one of the minimal iterations of replicated configuration experiments, and the mean iteration means the mean value of the minimal iterations of replicated configuration experiments.

Point 7:  A clear description of the novelty of the techniques applied for FJSP compared to other works needs to be specified

Response 7: We think the novelty has been specified in the penultimate paragraph in the Section 1. There we have clearly pointed out the contributions of the approach presented in this paper.