Food Production Scheduling: A Thorough Comparative Study between Optimization and Rule-Based Approaches

Round 1

Reviewer 1 Report

The manuscript presents a comparison between a mixed-integer linear programming (a MILP problem, solved using GAMS software) and a rule-based approach (using a computational tool) in the scheduling of production in two yogurt facilities in Greece. In my opinion, the manuscript is extremely well-written and presents very relevant results. A consistent review of recent works dealing with MILP applications in scheduling is presented. Considering this scenario, I suggest that the manuscript can be accepted for publication in Processes after some minor points.

Minor points and observations:

- Line 51: "an MIP model". Please define the acronym MIP (used here for the first time) and check the article.

- Line 92: In my opinion, the sentence "Except for the optimization-based approaches, other methods have been proposed to derive fast scheduling decisions, such as heuristic and metaheuristic methods, including rule-based scheduling [20] and genetic algorithms [21], [22]" can be improved. Genetic algorithms can be applied to solve MILP problems (for instance) and, thus, are optimization-based approaches.

- Line 287: "production [15]..". Please remove the extra dot.

- Lines 345-346: The authors stated that "A novel MILP model was developed to efficiently address the production lot-sizing and scheduling problem for a dairy multistage and multiproduct facility [18]". I suggest that this sentence can be rephrased, in order to clearly indicate that the MILP model was developed in a previous published work.

- Lines 541-542: The authors stated that "It is observed that SchedulePro solves the problems instantaneously and significantly faster compared to the MILP model". In my opinion, the computation times are negligible for both approaches, considering the complexity of the problem and the use of the tools. In this sense, I consider that this sentence can be altered, considering that in other situations (see lines 621-622), the computation times are very different indeed (different order of magnitude).

- Lines 621-622: In fact, for the TYRAS facility we can observe some differences between the computation times of SchedulePro and MILP/GAMS approach. As very well observed by the authors, even with higher times for the MILP approach, the computation time is perfectly compatible with a weekly production schedule.

- Lines 674-675: Again, the authors refer to the computation times ("solution speed is critical for the industrial application of a scheduling solution"). In my opinion, this statement conflicts with what was stated in lines 621-622. Please check.

In my opinion, the manuscript is extremely well-written. I suggest only a minor revision to identify some typos.

Author Response

See attached response to reviewer's comments

Author Response File: Author Response.pdf

Reviewer 2 Report

In particular, I would like to further explore the MILP model proposed in this paper. Could you please provide a detailed description of the mathematical model in the next revised version, including the decision variables and their formulations?

Furthermore, I am seeking clarification regarding the main contribution of this paper. It appears that there is a limited discussion of theoretical insights or practical applications. The authors mainly focus on the development of the MILP model and using a commercial tool, and the subsequent comparison of results. It would be valuable to highlight any unique features or novel approaches employed in the MILP model, as well as discuss potential theoretical or practical insights gained from the study.

Author Response

See attached response to reviewer's comments

Author Response File: Author Response.pdf