Multi-Objective Parallel Machine Scheduling with Eligibility Constraints for the Kitting of Metal Structural Parts
Round 1
Reviewer 1 Report
I feel the authors are not convincing enough why the state-of-the-art multi-objective solution methods can not tackle the particular production problem of metal structural parts. The abstract and introduction should be re-written and emphasis should be placed on what real-life situations have not been incorporated in the multi-objective optimization problems that have been solved and why the current solution methods are inadequate to solve the complex problem that you tackle. I mean you have to be very specific here instead of giving a general survey.
The problem description (Lines 184-203) is the most confusing I have read. The concept of profiles makes it difficult to understand.
I wonder if some of the decision variables (Lines 228-246) are decision variables at all. For example, the processing times are given and are actually input parameters rather than decision variables that users can vary to get the tradeoffs for the objectives. So, you should separate input parameters from decision variables.
First, explain the motivation in improving the standard NSGA-II algorithm. You talk about improving insufficient chromosomes, iterative quality, you make some improvements. Are these improvements standard techniques or novel techniques that are specially designed by you to solve the problem? If they are novel, then you should probably focus more on them.
In your experimental results, you say that when the number of components exceeded 300 (when the number of parts exceeded about 1500), the material utilization rate reached 95%. By selecting the appropriate number of machines, material utilization rate reached 90%. Are these material utilizations of 95% and 90% the maximum attainable? Is 98%, 99% utilization not possible with current solution methods?
Author Response
Dear expert:
We are writing the letter to convey my thanks and my major revisions of your comments. We are honored to be reviewed by your comments. Those comments, which make up for our shortcomings of considering less, are very important for enhancing our paper. All authors have read and approved the manuscript. We have carefully taken the comments into account and responded to each of the points raised by you. Some necessary corrections have been made, and all the altered passages have been highlighted in yellow. We hope that our improvements can meet your approval.
Point 1: I feel the authors are not convincing enough why the state-of-the-art multi-objective solution methods can not tackle the particular production problem of metal structural parts. The abstract and introduction should be re-written and emphasis should be placed on what real-life situations have not been incorporated in the multi-objective optimization problems that have been solved and why the current solution methods are inadequate to solve the complex problem that you tackle. I mean you have to be very specific here instead of giving a general survey.
Response 1:
We have revised the abstract (Lines20-22) and introduction of the paper. In the introduction (Lines152-172), a more in-depth analysis of cited literature is presented, re-specifying the reason why multi-objective solutions of the existing literature do not tackle the particular production problem of metal structural parts.
Point 2: The problem description (Lines 184-203) is the most confusing I have read. The concept of profiles makes it difficult to understand.
Response 2:
Thank expert for pointing out our deficiencies.
We have reinterpreted problem description (Lines 200-203) and modified Figure 1(b). According to the modified Figure 1(b), an explanation of the profile is added. The profile is a straight bar with a certain cross-sectional shape and size in this paper.
Point 3: I wonder if some of the decision variables (Lines 228-246) are decision variables at all. For example, the processing times are given and are actually input parameters rather than decision variables that users can vary to get the tradeoffs for the objectives. So, you should separate input parameters from decision variables.
Response 3:
Thank expert for pointing out our error.
Processing times are not decision variable but input variable. Input parameters have been separated from decision variables (Lines 237-239). Processing times have been changed to the directory of input variables.
Point 4: First, explain the motivation in improving the standard NSGA-II algorithm. You talk about improving insufficient chromosomes, iterative quality, you make some improvements. Are these improvements standard techniques or novel techniques that are specially designed by you to solve the problem? If they are novel, then you should probably focus more on them.
Response 4:
Our motivation for improving the algorithm was because the current research result on multi-objective optimization algorithms applied to the production scheduling did not yet have an effective algorithm to solve the mul-ti-objective optimization problem of production scheduling in metal structural parts for kitting delivery considering both material assignment and part nesting constraints as proposed in this paper. We can obtain the subordination of materials, profiles and parts by the results of the first optimization stage. Due to eligibility constraints of this subordination, there are strong coupling relationships among the sorting of parts, the sorting of each profile and the sorting of each material. Therefore, an improved algorithm is needed to solve the scheduling problem with these coupling relationships.. The improvements to the algorithm are tailored to particular problems of metal structural parts in this paper, and are based on standard techniques.
Point 5: In your experimental results, you say that when the number of components exceeded 300 (when the number of parts exceeded about 1500), the material utilization rate reached 95%. By selecting the appropriate number of machines, material utilization rate reached 90%. Are these material utilizations of 95% and 90% the maximum attainable? Is 98%, 99% utilization not possible with current solution methods?
Response 5:
We redescribed the experimental results (Lines 659-678), also added data in Figure 14 for number above 300 components.
The machine utilization and the material utilization presented in the experimental results were the optimization results obtained under the conditions of the used example data. The material utilization rate was related to the size and the dimension of the ordered parts. If the order size increases and the part size is appropriate, the proposed solution may get a higher material utilization rate. Machine utilization is related to the order size and the number of machines. The machine utilization has reached 99.04% for 40 components with 5 machines, as shown in Figure 14,. However, the decision maker needs to consider both machine utilization and the material utilization to choose a compromise set of optimized results.
The above-mentioned major revisions are responses to your comments. Once again, thank you very much for what you have done. Please accept my sincere thanks. Wish you all the best.
Reviewer 2 Report
It is an interesting paper, that shows how to integrate smart manufacturing techniques. I would still try to understand why Gurobi was selected as an optimization solver, I think that there are free solvers available.
Description of the problem and variables used for the model are extensive, but hard to read. It is hard to verify all the formulas and their interpretation. I did not see any attempt to optimize geometrical layout of the parts in question that come from the same material, in order to reduce waste for example. Or maybe I missed it. I know it would be hard to integrate shape geometrical constraints, in addition to sizing.
It is a little dissapointing that the large examples were simulated. I mean, the bus frame examples have 3 machines, while derived simulated 20 ? and number of components 300 and number of parts 1500 only on simulated examples ?
Author Response
Dear expert:
We are writing the letter to convey my thanks and my major revisions of your comments. We are honored to be reviewed by your comments. Those comments, which make up for our shortcomings of considering less, are very important for enhancing our paper. All authors have read and approved the manuscript. We have carefully taken the comments into account and responded to each of the points raised by you. Some necessary corrections have been made, and all the altered passages have been highlighted in green. We hope that our improvements can meet your approval.
Point 1: It is an interesting paper, that shows how to integrate smart manufacturing techniques. I would still try to understand why Gurobi was selected as an optimization solver, I think that there are free solvers available.
Response 1:
Mathematical programming optimizers include both free open source and commercial ones, and although there are many of them, their performance varies, and problem types that they can solve, their breadth, and depth of application also vary. Gurobi can solve many types of problems, including the mixed-integer programming, and is the best and the fastest linear programming/quadratic programming solver in the world today because of its wide range of problem types and the high solution efficiency. Gurobi has a clear advantage over other commercial and open source solvers such as CPLEX, Xpress, SCIP, Lingo, etc., as it ranks first for performance in several problem types. Also Gurobi can be easily integrated with MATLAB, Java, Python or .Net, and is more competent for a wide and complex range of scientific research and applications, so Gurobi is chosen as the optimization solver.
The reasons for using gurobi have been added in the paper (Lines 390~395).
Point 2: Description of the problem and variables used for the model are extensive, but hard to read. It is hard to verify all the formulas and their interpretation. I did not see any attempt to optimize geometrical layout of the parts in question that come from the same material, in order to reduce waste for example. Or maybe I missed it. I know it would be hard to integrate shape geometrical constraints, in addition to sizing.
Response 2:
This study covered three problems of the material assignment, the part nesting, and the kitting delivery, which was a comprehensive and complex optimization problem, so the problem and variable description used for the model was extensive. In the modeling process, we refered to the mixed-integer programming modeling approach commonly used in current related studies, and the correctness and the validity of the formulation were verified by the Gurobi solver. In terms of material waste reduction, we used a one-dimensional scheduling approach, where only the part length was considered. This is to focus the study on a comprehensive optimization approach for scheduling structural metal parts. The layout problem of integrating shape geometrical constrained raised by experts has a positive effect on improving material utilization, which is something that we will study in the future.
We showed in the text that it is a one-dimensional parts nesting problem(Lines 315~317). At the end, we explained that the nesting problem integrating geometric constraints is the content we will study in the future(Lines 737).
Point 3: It is a little dissapointing that the large examples were simulated. I mean, the bus frame examples have 3 machines, while derived simulated 20 ? and number of components 300 and number of parts 1500 only on simulated examples ?
Response 3:
The real case data was obtained from a cell of a workshop. The aim is to verify the feasibility of the model and the algorithm, as well as to describe the solution process of the proposed approach by examples of 3 machine in this paper. In order to further validate the effectiveness of the proposed approach for solving large-scale cases, application validation of large-scale cases is required. Therefore, a large number of simulation cases in different scales are constructed and studied with reference to the characteristic of real case data. The results of the simulated cases are intended to show that the proposed method is also effective when applied to large-scale metal structural part scheduling problems.
This section was supplemented with new content to (Lines629-632 ).
The above-mentioned major revisions are responses of your comments. Once again, thank you very much for what you have done. Please accept my sincere thanks. Wish you all the best.
Round 2
Reviewer 1 Report
Thank you for addressing my comments and improving the quality of your work.
