Round 1

Reviewer 1 Report

This paper looks so good and scientific with full consideration and significance. 

Overall, maritime container terminal has been summarized by MCT. But it could be shown as MTC by many sentences. 

Author Response

Response to Reviewer 1 Comments
Point 1: Overall, maritime container terminal has been summarized by MCT. But it could be shown as MTC by many sentences
Response 1: Throughout the article the word MTC was changed to MCT

Reviewer 2 Report

Dear Authors,

Please check on the acronym; MCT as you have incorrectly used MTC several times. Important to be consistent.

In line 342 : "The model assumes that: two quays are used, having 5 cranes each one, also a minimum of one crane is able to operate on the vessel, with a maximum of 4 cranes per vessel. Each quay has a 344 longitude of 700 m." This implies that with a maximum of 4 cranes, there is always 1 crane idle? 

I am assuming that the model for the terminal is a container terminal, or?

In viewing Figure 4, I am confused as to how such a large ship, with over 350+ meters is only assigned 2 quay cranes (this is vessel 7).

In viewing Figure 6, I see that 2 cranes are assigned to vessel 3 and 3 cranes to vessel 4, which implies that the "model assumption from line 342 " is false as only 4 cranes cranes can be employed.   

In addition, it should be pointed out that are you optimising the quay or the berth? Be advised that Berths are often dedicated due to the fact that the cargo to be loaded/discharged has been positioned close to the vessel berthing so as to perform efficient cargo handling. Having the vessel placed further away from the cargo, would significantly adverse ship service time. 

I am confused with the model assumptions in that on line 325-326, you mentioned that 10 vessel instances were used in the study. Yet, in line 396 -402, Table 5 is now calculated to upwards of 35 vessels?  ("In order to analyze the model efficiency, data from vessels 5 to 35 with 100 instances each were  used. The results are shown in Table 5"). Please try to be clear as to what is being studied.

My concern is that I feel that the authors need more understanding of the berth, cargo handling and vessel planning operations. In addition, it does matter as to type of vessel that is being served as bulk vessels would have different characteristics than container vessels, which have tightly defined constraints, such as dedicated berths or terminals due to the number of containers being stored in the stacking yards.

Finally, why is your solution better than current TOS (i.e. NAVIS, etc.) What is the gap?  Be advised that there are quite a number of articles on the subject of berth planning and many of which you have omitted. Therefore, I feel your literature review is weak and encourage you to read the work of others so that your contribution is part of the body of science.

Author Response

Point 1: Please check on the acronym; MCT as you have incorrectly used MTC several times. Important to be consistent.
Response 1: Throughout the article the word MTC was changed to MCT

Point 2: In line 342 : "The model assumes that: two quays are used, having 5 cranes each one, also a minimum of one crane is able to operate on the vessel, with a maximum of 4 cranes per vessel. Each quay has a longitude of 700 m." This implies that with a maximum of 4 cranes, there is always 1 crane idle?
Response 2: Each quay has 5 cranes at its disposal, if one of the vessel uses 4 cranes, the other crane can be assigned to another vessel that berth at the same time in another part of the quay. This was already clarified in the modeling limitations (In New line 225)

Point 3: I am assuming that the model for the terminal is a container terminal, or?
In viewing Figure 4, I am confused as to how such a large ship, with over 350+ meters is only assigned 2 quay cranes (this is vessel 7).
Response 3: New line 32, indicates that the problem is related to a container terminal.
The model optimizes the waiting time for vessels, that is, it minimizes the time they wait to berth. V3 and V4 vessels arrive before V7 vessel (See Table 1), for which they are assigned before V7 vessel for berthing. The V7 vessel has to wait for a vessel to finish being served and release the cranes, in this case the V3 vessel released 2 cranes, these are assigned to the V7 vessel. The number of cranes that are assigned to a vessel does not change during the time it remains on the quay, therefore, the cranes released from the V4 vessel are not assigned to the V7 vessel. The model does not consider that the larger the vessel more cranes to use.

Point 4: In viewing Figure 6, I see that 2 cranes are assigned to vessel 3 and 3 cranes to vessel 4, which implies that the "model assumption from line 342 " is false as only 4 cranes cranes can be employed.

Response 4: See Response 2

Point 5: In addition, it should be pointed out that are you optimising the quay or the berth? Be advised that Berths are often dedicated due to the fact that the cargo to be loaded/discharged has been positioned close to the vessel berthing so as to perform efficient cargo handling. Having the vessel placed further away from the cargo, would significantly adverse ship service time.
Response 5: The objective function minimizes the waiting and handling time for all vessels (New line 259), this means that the use of the quay is being optimized. In order that this is completely clear, in line 68 and in the abstract it has been added that it seeks to optimize the use of the quay.
The model assigns the berthing place to each vessel, that is, preference zones are not allowed for berthing a vessel. This was added in the assumptions of the model (New line 220)

Point 6: I am confused with the model assumptions in that on line 325-326, you mentioned that 10 vessel instances were used in the study. Yet, in line 396 -402, Table 5 is now calculated to upwards of 35 vessels? ("In order to analyze the model efficiency, data from vessels 5 to 35 with 100 instances each were used. The results are shown in Table 5"). Please try to be clear as to what is being studied
Response 6: There is a bug that has been corrected
Say: a case study composed by 10 vessel instances were used
Should say: an instance of 10 vessels is used as a case study (New line 365)

Point 7: My concern is that I feel that the authors need more understanding of the berth, cargo handling and vessel planning operations. In addition, it does matter as to type of vessel that is being served as bulk vessels would have different characteristics than container vessels, which have tightly defined constraints, such as dedicated berths or terminals due to the number of containers being stored in the stacking yards.
Response 7: The model is for container vessels. The model is intended to serve as the basis for what happens in a container terminal and that it works under certain assumptions and restrictions.

Point 8: Finally, why is your solution better than current TOS (i.e. NAVIS, etc.) What is the gap? Be advised that there are quite a number of articles on the subject of berth planning and many of which you have omitted. Therefore, I feel your literature review is weak and encourage you to read the work of others so that your contribution is part of the body of science.
Response 8. Terminal Operating Systems (TOS) such as NAVIS, Oscar, among others, are complete systems that provide assistance to control land and maritime operations in real time. What is intended in this article is to deal with problems that are not contemplated in these systems, such as the uncertainty in some aspects related to the BAP + QCAP and under certain assumptions and limitations.

New papers have been included that deal with the BAP + QCAP problem from other approaches (New lines 49 – 61)

Reviewer 3 Report

The topic of the article is interesting. However, some concerns in the paper make it unsuitable for publication in its current state. Therefore, I hope that the suggestions below will help the authors to prepare a much stronger version.

In Definition 2, a fuzzy singleton is defined to express a real number as a fuzzy number. Remember to also include a margin of error ε in this definition and to define a real number a as a fuzzy triangular number a ̃ = (a-ε, a, a+ε).

In Definition 6, sum and difference of fuzzy numbers are defined, it is also necessary to add multiplication of fuzzy numbers since it is used in the FFLP problem definition Eq. (5) and in Eq. (7).

In Section 2.4. Fuzzy optimization model for the BAP +QCAP with two quays, an FFLP model is proposed where many conditions are not fuzzy. The authors have to explain why they have chosen this approach and what is the added value respect to a Fuzzy LP approach.

In the notation definition paragraph ?_? and ?_? are defined as »vessel longitude« and »Longitude of quay ?« it seems that these parameters are both lengths. Also in LN 205 the parameter ?_?? is defined as the berthing time of vessel i at quay ?. The waiting time (?_?) is computed as ?_?=?_?−?_? where seems that the quay used is not important, but in LN 226 the definition is different. I strongly recommend the authors to review the definitions proposed before the model (and used in the model) to correct inconsistencies and eventually add explanations. Moreover, the authors are asked to explain the parameter M, it seems to be a sufficiently large number that is generally used in Mixed Integer Linear Programming.

In Section 2.5 Fuzzy optimization model solution the First Yager Index is used to transform the FFLP to the Mixed Integer Linear Programming problem. The authors need to explain why they decided to use the First Yager Index for ranking fuzzy numbers, since the Yager Index is a measure of the mean value. Thus, it is subject to the pitfall of non-discrimination when the modes of the fuzzy numbers are equivalent and the spreads are symmetrical. This may lead to conflicts in the process of simulations/solutions and can hinder the computation of the solutions.

The authors also need to improve the notation, as all equations and other mathematical expressions, both in the continuous text and when presented in separate lines, should be punctuated appropriately according to their function in the sentence.

Also, some typos need to be corrected in LNS: 191, 217, 281, 287, 317, 322, Fig. 7 (Targer value). LNS:331 vessel longitude?

In LNS 361-364 a blue circle is mentioned, as the conflict area between the departure and berthing of vessels V5 and V9. Can you explain this in more detail on Fig. 4.

Author Response

Point 1: In Definition 2, a fuzzy singleton is defined to express a real number as a fuzzy number. Remember to also include a margin of error ε in this definition and to define a real number a as a fuzzy triangular number a ̃ = (a-ε, a, a+ε).
Response 1: Definition 2 has been modified, the margin of error is included.
in Definition 6 a real number a is defined as a ̃ = (a-ε, a, a+ε).

Point 2: In Definition 6, sum and difference of fuzzy numbers are defined, it is also necessary to add multiplication of fuzzy numbers since it is used in the FFLP problem definition Eq. (5) and in Eq. (7).
Response 2: The fuzzy number multiplication operation has been included in Definition 7

Point 3: In Section 2.4. Fuzzy optimization model for the BAP +QCAP with two quays, an FFLP model is proposed where many conditions are not fuzzy. The authors have to explain why they have chosen this approach and what is the added value respect to a Fuzzy LP approach
Response 3: The classical fuzzy linear programming methods are used when the parameters are fuzzy; in this work some of the decision variables are fuzzy, for this case the FFLP approach is the most appropriate.
This explanation has been included in section 2.2

Point 4: In the notation definition paragraph ?? and ?? are defined as »vessel longitude« and »Longitude of quay ?« it seems that these parameters are both lengths. Also in LN 205 the parameter ??? is defined as the berthing time of vessel i at quay ?. The waiting time (??) is computed as ??=??−?? where seems that the quay used is not important, but in LN 226 the definition is different. I strongly recommend the authors to review the definitions proposed before the model (and used in the model) to correct inconsistencies and eventually add explanations. Moreover, the authors are asked to explain the parameter M, it seems to be a sufficiently large number that is generally used in Mixed Integer Linear Programming.
Response 4: Throughout the article the word “longitude” has been replaced by “length.

Errors that have been corrected
Say: (??=??−??)
Should say: (??=???−??)
Say: (??=?? +ℎ?)
Should say: (??= ???+ℎ?)
In New line 250, is added to M is a sufficiently large number

Point 5: In Section 2.5 Fuzzy optimization model solution the First Yager Index is used to transform the FFLP to the Mixed Integer Linear Programming problem. The authors need to explain why they decided to use the First Yager Index for ranking fuzzy numbers, since the Yager Index is a measure of the mean value. Thus, it is subject to the pitfall of non-discrimination when the modes of the fuzzy numbers are equivalent and the spreads are symmetrical. This may lead to conflicts in the process of simulations/solutions and can hinder the computation of the solutions.
Response 5: In this work, the objective of the fuzzy model optimization is to achieve an ordering (planning) for the berthing of vessels, therefore, any ordering method that orders fuzzy numbers could be used. Ordering methods that use intervals to order fuzzy numbers are not recommended, as they could add more imprecision to the model.
This explanation has been included in lines: 117 - 120

Point 6: The authors also need to improve the notation, as all equations and other mathematical expressions, both in the continuous text and when presented in separate lines, should be punctuated appropriately according to their function in the sentence
Response 6: The indicated corrections were made

Point 7: Also, some typos need to be corrected in LNS: 191, 217, 281, 287, 317, 322, Fig. 7 (Targer value). LNS:331 vessel longitude?
Response 7: Errors that have been corrected
Line 191
Say: veseel
New line 233 should say: vessel
Line 217
Say: denoted by denoted by
New line 254 should say: denoted by
Line 281
Say: (?1?,?2?,?3?
New line 318 should say: (?1?,?2?,?3?)

Line 287
There was a writing error in the objective function; the objective function has been modified
Say: ?í?Σ13((?1?+ℎ1?)+(?2?+ℎ2?)+(?3?+ℎ3?)?∈? New line 326 should say: ?í?Σ13((?1??−?3?+ℎ1?)+(?2??−?2?+ℎ2?)+(?3??−?1?+?∈?ℎ3?))
Line 317
Say: ∀?∈
New line 356 should say: ∀?∈?
Line 322
Say: model evaluation efficiency
New line 359 should say: model efficiency evaluation
Say: .1.80GHz
New line 361 say: 1.80 GHz
Fig. 7 fixed the bug in Figure 7
Say: Targer value
Should say: Objetive value
Line 331
vessel longitude ?
Throughout the article the word “longitude” has been replaced by “length

Point 8: In LNS 361-364 a blue circle is mentioned, as the conflict area between the departure and berthing of vessels V5 and V9. Can you explain this in more detail on Fig. 4.
Response 8: In the paper that I sent to the publisher there was the blue circle, but it seems that the editors when editing it was moved o or deleted.

In the new Fig. 4 the blue circle already appears

Round 2

Reviewer 2 Report

Thank you for the improvements and changes, as I feel satisfied with the results.