The Multi-Depot Traveling Purchaser Problem with Shared Resources

Round 1

Reviewer 1 Report

This paper introduces a new variant of the famous Vehicle Routing Problem (VRP), which is the Multi-Depot Traveling Purchaser Problem under Shared Resources (MDTPPSR). A two phase algorithm with improvement heuristics is proposed to solve the problem and experimental results are conducted to show the merits of purchasing under shared resources, compared to independent purchases in terms of cost saving and reducing the number of used vehicles.

The paper in general is well-written and the problem, the approach, and the experimental results are thoroughly explained. However, there are some minor comments that the authors may consider to improve the paper further as follows:

1-    Page 1, line 31: “procurement problems”; I believe “problems” is the not the right word to use here; you may consider “locations” or “resources”.

2-    Page 1, line 35: can you mention some practical applications of the TPP?

3-    Page 1, line 41: “ they may incur lots of losses thanks to underutilized vehicle”; since this is a negative effect, using “thanks to” is not suitable; you may consider using “due to”.

4-    Page 2, line 49: reference needed for the mentioned project.

5-    Page 2, line 50: “focuses”--> “that focuses”

6-    Page 2, line 56: “we implement…”; are you referring to your current study or a previous one? if  it is the current study please clarify this.

7-    Page 3, Figure 2: In the legends on the right hand side of the figure, I suggest to start with the empty vehicle's symbol first not the loaded vehicle symbol because it is natural that first the vehicle will be empty then it will be loaded.

8-    Page 4, line 124: what are the two main differences? I believe you mentioned only one in the next paragraph. Please number them (first, second) for clarity.

9-    Page 4, line 127: you should define what VRP stands for, even if it is well-known for readers in this field.

10- Page 4, line 128: “and delivers the products to others”--> I suggest to rephrase it as “and then delivers the products to others”, for more clarity.

11- Page 4, line 161: Please add a reference for the fact that the TPP is NP-hard.

12- Page 5, line 183: please note the wrong section numbering.

13- Page 6, Table 1: LTL and FTL are not defined previously. You should also describe all columns of the table, for example the difference between unitary demand and non-unitary demand, the difference between objective and cost allocation, etc.

14- Page 7, line 226: “that survey” --> that surveys

15- Page 9, line 274: “only is repeated”; also I suggest to rephrase the sentence as follows: “It should be noted that the latter is only possible if the vehicle has already delivered the products of other depots.”

16- Page 9, line 277: How do you differentiate between a virtual and real depot? It is not very clear why you need to add virtual depots on top of the real ones!

17- Page 9, line 279: I cannot understand what you mean by flow! Could you please clarify more.

18- Page 9, line 299: “have shown”--> “are shown”

19- Page 12, line 370: the total number of possible collaborations between depots is an order of  O(n2^?); how was this obtained? you could possibly add a proof in the appendix.

20- Page 15: equation (39) is identical to equation (38)! No mention of theta parameters in this equation.

21- Page 15, line 480: Scenario 2: how is it possible that the supplier exists without its corresponding depot? Isn't a supplier added only if the product is needed by a specific depot?

22- Page 15, line 488: “insertion”--> “inserting”

23- Page 15, Equation (40): What is j? it is not found in the figure! is there a -ve sign before delta? I don't understand  the part of the equation after distance (i, i+1); is this multiplied by the previous part? As far as I can see, it starts with a parenthesis ( and ends with a square bracket [.

24- Page 16, equation (42): same comments as equation (40).

25- Page 16, equation (44): again the equation is not clear! Where is the right hand side? Why is there a minus sign at the beginning?  Why is there an = sign between the opening [ and the closing ]? Maybe you can divide the equation into subparts and use different symbols to combine them in the final equation for clarity as it is quite long.

26- Page 17, lines 535-536: Are the products unique with respect to both the depots and the suppliers? i.e., are the products of each depot different than other depots', and the products of each supplier different than the products of other suppliers?

27- Page 17, equation (45): the superscript of the footnote looks like a power. It may be better to use another symbol like (*) for example.

28- Page 18, Table 5: Same as previous comment. You could probably use (*) and (**), etc. to explain these symbols below the table.

29- Page 19, line 568: “in 69% of instances,”; How many exactly? You should highlight these instances in bold in the table.

30- Page 19, line 589 (important comment): Are the heuristics applied independently? In the table and the figure it seems that you apply them independently, but in the conclusion you say "Moreover, applying two types of improving heuristic algorithms …"; so this gives the impression that when you say heuristic B you actually mean both A and B. Please clarify.

31- Page 19, Figure 9: Please explain x and y axes in the figure.

32- Page 20, line 620: “For instance, it might be cases” --> “there might be cases”

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presented a decomposition-based algorithm to deal with the Multi-Depot Traveling Purchaser Problem under Shared Resources. This is a carefully done study and the findings are of considerable interest. A few minor revisions are list below.

1. There are many formatting and other mistakes. Such as the format of Table 3.

2. In addition to the analysis of contributions of the innovative components, the proposed heuristic algorithm also needs to be compared with the state-of-the-art algorithms for the Multi-depot TPP under Shared Resources.

3. In section 6.2, the sentence “The proposed heuristic algorithm for the Multi-depot TPP under Shared Resources is compared to its corresponding individual case.” is awkward and has a tense mismatch. Might read better as “The proposed heuristic algorithm for the Multi-depot TPP under Shared Resources was compared to its corresponding individual case.”.

4. The parameter settings need to be given.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The work is not complete without showing an improvement over the past models. This traveling problem has been solved by several previous researchers.

Please see my attached comments.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Table 3 is not sorted alphabetically.

Add CPLEX in the references with version number.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf