Dear Prof. Pretzsch,
Following your letter regarding the manuscript A Deterministic Harvest Scheduler Using Perfect
Bin-Packing Theorem submitted to European Journal of Forest Research for publication, we are
sending the rebuttal letter explaining the changes performed on the manuscript. The changes
incorporate the suggestions of the reviewers, regardless the first or second submission. We found
the comments very helpful and constructive. We have addressed all the changes recommended by
the reviewers and we are confident that the new version of the manuscript is easier to understand
and has a more fluent scientific discourse. The revisions, starting with the last submission, are
addressed below.
Second submission
GUEST EDITOR COMMENTS: Please adjust the layout of the manuscript to the Journal style
and consider the suggestions of the reviewer carefully.
We changed four out of the initial six figures, and we have added a new figure (Figure 3-present
submission) showing the current status of the forest, to clarify the comparison between the
proposed algorithm and simulated annealing and linear programming.
Reviewer#1:
Revisions
This paper was difficult to review a second time. The responses to the first
reviews were absent, and there was no way (other than a direct comparison to
the first submission) to locate where changes were made to the paper.
The comments of the reviewers to the first submission were completely addressed and are
presented in the first submission section. The significant changes that were made on the first
version made indeed the comparison between versions difficult, without an additional letter
identifying the changes. However, the second version of the manuscript was submitted as a new
article; therefore, no explanations on the changes performed on the first version of the manuscript.
Methodologically, the authors seem intent on proving that the adjusted FFD
is better than simulated annealing, and rather than emphasize that simulated
annealing has been proven to be a very good heuristic (as noted in a number
of forest planning papers, when compared to near-optimal or optimal
solutions), they emphasize those instances where simulated annealing showed
poor results. At least in one case, when comparing simulated annealing and
the adjusted FFD to LP (the relaxed optimal solution), it seems that
simulated annealing results are better (lines 538-540). Further, on lines
495-503 a number of instances are noted where simulated annealing produced
better results than the adjusted FFD. As a result, lines 647-650 seem biased
(suggesting that the adjusted FFD produced the best results in all cases).
In sum, one might ask: why attack simulated annealing? A better course of
action for this research would be to simply describe the results and let the
chips fall where they may.
It was never in our intent to prove that simulated annealing is performing poorly in forest planning.
In contrary, as we stated on lines 356-368 (present submission), the proposed algorithm (i.e., the
combination of perfect bin –packing theorem with adjusted first-fit decreasing algorithm) was
compared with simulated annealing exactly because simulated annealing was proven to supply
good solutions to forest planning problems. To enforce the recognition of the good simulated
annealing performances, on lines 359-360 (present submission) we mentioned that “simulated
annealing has led to its frequent use as a test algorithm in forest planning”.
However, being a heuristic algorithm it could be expected that there are situations when simulated
annealing can be significantly outperformed by other algorithms. One of such algorithms is first fit
decreasing algorithm applied to forest estates that have a structure fulfilling the perfect binpacking theorem. In respect to instances when simulated annealing outperformed adjusted first-fit
decreasing algorithm (lines 538-540), we changed the first sentence of the paragraph (lines 540542 in the present submission) by adding “at most once during the planning period”, which clarify
in what conditions linear programming and simulated annealing (and for that matter, any heuristic
algorithm) could provide better results than adjusted first-fit decreasing algorithm (i.e., the
violation of the perfect bin-packing theorem). In fact there are documented instances when first fid
decreasing algorithm performs worse than other heuristic techniques, with the comment that in all
those instances the conditions of the perfect bin-packing theorem were violated. In the context of
line 546 (present submission) “a LP solution smaller than MVHA was expected as MVHA…” (nota
bene: consequently the aspatial first-fit decreasing algorithm-conclusion drawn from lines 288-290
of the present submission). To clarify the necessity to fulfill the PBPT conditions we have added
the sentence from line 288-290 “The FFD algorithm is a perfect scheduler for forests for which the
THLB fulfills the PBPT conditions”.
Similarly with the comments for line 538-540 were the comments for lines 495-503. We agree
with the reviewer that the paragraph as it was written could lead to the impression that simulated
annealing produces better results than adjusted FFD. To address this possible misunderstanding,
we identified the cases when adjusted FFD could performs worse than simulated annealing, and
enhanced the explanation with the details from lines 508-509 (present submission): “However,
when the corollary of the PBPT was not met, ….”.
The inclusion of the sentence from lines 288-290 (present submission) and the additions from lines
507-508 v, together with the explanations of the adjusted FFD from the lines 658-659 (present
submission) clarify the misunderstandings that can arise from lines 647-650 that were also
mentioned by the reviewer.
Lines 161-167: As noted in the previous review, these statements are only
true when the forest is "normal" (when there are equal hectares of forest in
each age class). When a forest is not normal, maximizing even-flow will
require scheduling stands for harvest when stand-level optimality is not
attained.
The reviewer rises a valid point, that it seems that first-fit decreasing algorithm would work only
for normal forest, as defined by Clutter et al (1983). However, the balanced age-classes is not a
fundamental condition for the idea of normal forest, as it was defined by Hundeshagen (1826) and
enhanced by Heyer (1841) (i.e., a normal forest is a forest having equal perennial annual harvested
volume). In the context of Hundeshagen (1826) and Heyer (1841) the definition of the normal
forest of Clutter et al (1983) is just a particular case, and it is natural to ask whether or not more
general settings (not as restrictive as the balanced age-class distribution) can ensure the even-flow
of the harvested volumes. Clutter et al (1983) have a very good discussion regarding the factuality
of the normal forest (understood as balanced age-classes), which they call it a “mental construct”
rather than an existing forest. From this perspective the perfect bin-packing theorem and its
corollary plays a crucial role by proving the necessary conditions to have a constant annual
harvested volume, namely the normal forest as defined by Hundeshagen (1826) and Heyer (1841).
To address the comments of the reviewer we have enhanced the paragraph describing the pivotal
role played by the perfect bin-packing theorem by adding several sentences (lines 164 -173-present
submission) that we think clarify the relationship between the normal forest and perfect binpacking theorem. Furthermore, we have included a new figure (Figure 3-present submission)
showing the age class distribution for the three study areas, which revealed a non-normal forest as
defined by Clutter et al (1983). Nevertheless, the results clearly show the possibility to reach the
global optimality (maximum harvested volume annual) as the solution supplied by the adjusted
first-fit decreasing algorithm is within 5% from the global optimum, while considering spatial
constraints. We added the sentences form lines 474-479 (present submission) to provide a more
powerful explanation of the importance of the perfect bin-packing theorem in the achievement of
the global optimality.
The comparison of MVHA to any of the other methods (particularly simulated
annealing) is either not valid, or needs to be clarified. From what this
reviewer can tell by reading the paper, MVHA seems to allow multiple
clearcut entries into a stand over the time horizon, while the others (LP,
SA) do not (see lines 534-535). Therefore, is the comparison noted on lines
575-578 valid?
As the reviewer noted, one of the strength of the MVHA lay in the allowance of multiple harvests
during the planning period. However, MVHA performances also depend on the capacity to actual
scheduling the multiple harvests (not only allowing that) during the planning period. To clarify the
reader that comparisons from lines 575-578 are valid we started by adjusting the sentence
describing the linear programming (lines 529-530), namely by explicitly stating that when harvests
are scheduled using linear programming a stand cannot be harvested more than once during the
planning period (lines 540-542 - present submission). While multiple harvests during the planning
period offer an advantage to adjusted first-fit decreasing algorithm and simulated annealing
compared to linear programming, the case when both adjusted first-fit decreasing algorithm and
simulated annealing were constrained to harvest a stand at most once during the planning period
(i.e., the preset harvest age constrain) provided a valid comparison of the three planning techniques.
In these conditions, the linear programming supplied the largest solution (line 529 in the second
submission and line 540 in the present submission). However, the statement from lines 575-580
compare all the results supplied by simulated annealing, including the ones that allowed multiple
harvests during the planning period, to MVHA; therefore the comparison between MVHA and
simulated annealing is valid. The reviewer was right to notice that among the results used for
comparisons with MVHA were included also the ones that did not allowed multiple harvests
during the planning period. However, the results supplied by simulated annealing that allowed
multiple harvests during the planning period were significantly smaller than MVHA (the optimal
solution), not only the ones that forced at most one harvest during the planning period.
The Figures are poor - font sizes are too large and the layout of the
figures is messy.
We redraw all the figures, except figures 1 and 2, which showed the study areas (Figure 1) and
described the adjusted first-fit decreasing algorithm (Figure 2). Additionally we included a new
figure that shows the initial age-class distribution of the timber harvesting land-base.
The references are a mess. Some (lines 673-678) do not list the place of
publication. Others (the Canadian Journal of Forest Research papers) do not
need to show the French version of the journal name. There are also a number
of situations in the presentation of references where they are not
consistent with this journal's format. Further, "Mcdill" (line 758) is
incorrect, as is "Spectrum" (line 765), and the names and initials of
several authors are incorrect. I would suggest a thorough checking of each
citation against the original document.
We acknowledge the mistakes noted by the reviewer in the references. We checked all the
references and we hoped that we have identified and corrected all the mistakes. Furthermore, we
changed the reference style to conform to the journal requirements.
First submission
Reviewer #1
Major revisions
1. Inadequate literature review
We consider the recommendation of the reviewer and changed and enhanced the introduction by
modifying some of the original sentences and including new sentences to provide an adequate
literature review. Therefore, the introduction of the current submission is almost 30% larger than
the introduction of the first submission (i.e. 654 words compared to 455 words). One of the points
raised by the reviewer was the need to justify the emphasis placed by our approach on MAI (i.e.,
“The author should discuss why other forest-level models have not placed such emphasis on
maximizing MAI at the stand level.”). To address the reviewer comments we expanded the second
section from the Methods (i.e., Optimal harvesting age and mean annual increment) and explained
why we have used MAI as the main attribute in testing the new forest planning technique.
Therefore, we have included and explained the equations that can be used in eventuality that a
larger array of attributes is considered (lines 110-141 - present submission). However, as the goal
of our paper was to present the method not a management strategy, we reduced the number of
possible attributes to one, the volume. The reduction of the number of attributes did not altered the
findings of our paper, but reduced the complexity of the discourse and maintained the focus of the
article on the method rather than on the details (lines 136-139).
2. Poorly written
We significantly changed the article, as entire sections of the papers were completely rewritten;
one example being the Methods section. The changes in the methods section, especially the
inclusion of the linear programming, lead to changes in the Results and Discussion section too.
3. Should compare to optimal solution
The reviewer suggests comparing the proposed algorithm to known optimal solutions, by either
choosing a smaller data set or by using linear programming. As we already used three data sets to
prove the performances of the algorithm it would have confused the reader to include an additional
dataset just for comparison purposes. Consequently, we decided to include in the analysis the
solution supplied by a linear programming representation of the planning problem (lines 422-432 present submission).
Minor revisions
P. 1 , line 20—it is not self-evident, to this reader, why thinning or shelterwood treatments ought
never be constrained spatially.
Changed the sentence to clearly express the reason for using clearcuts: introduction of the green
up/adjacency delay (lines 59-63 in the present submission)
3. P. 2, lines 27-29—I thought you might be building up to the requirement for binary decision
variables, and the combinatorial explosion in computing time needed to solve models with such
variables. Green-up is but one of many spatial constraints that require planners to use binary
decision variables.
We agree with the reviewer, but the objective of the paper is to present the method and its
performances by using some of the most commonly constraints, not to detail some of the
technicalities related with the constraints. Therefore, we did not elaborate on the complexity of the
algorithms that use binary decision variables.
4. P. 2, line 46—not hypothetical data. Perhaps artificial, or computer-generated.
Changed hypothetical data to computer generated data (line 85 –present submission)
5. P. 3, line 49—not sure what mil stands for.
Changed mil to millions (line 91 – present submission)
6. P. 3, line 52—management plans have authors; they are therefore not cited as Anonymous.
Included the authors of the Land and Resource Management Plans (lines 97-98– present
submission)
7. P. 3, line 47—not sure what approach you are referring to. Please describe.
Changed the sentence by eliminating “the approach of” as it was not needed (line 86- present
submission)
8. Table 1—Dog is spelled incorrectly? (Doig?)
Changed the spelling to Doig.
9. P. 4, line 75—they do not determine harvesting age; they support decisions on harvesting age.
The sentence was eliminated completely as the entire section was rewritten.
10. P. 4, line 77—determined by solving models of the harvest-scheduling problem—not simply
applying algorithms.
The sentence was eliminated completely as the entire section was rewritten.
11. P. 4, line 80—this can be disputed. What about the economic rotation age arising from the
Faustmann formula?
The sentence was eliminated completely as the entire section was rewritten. However, we provided
a complete set of equations that incorporate not only the economic rotation but also other attributes.
12. Lines 91-102—this discussion belongs on the literature review, not methods.
The sentence was eliminated completely as significant portions of the section were rewritten.
13. Line 104—do you mean "harvest-scheduling model"?
Changed harvest scheduler to harvest-scheduling model as suggested by reviewer (line 157-present
submission).
14. Line 112—after citation, start a new paragraph.
Started a new paragraph (line 181-present submission)
15. Line 124—perhaps a brief mention or discussion of the concept of "regulated forest" is
appropriate here.
We mentioned and discussed the concept of “normal forest” as suggest by the second reviewer
rather than “regulated forest” (lines 196 and 164-173 - present submission)
16. Line 139—uniformily (adverb).
Changed to uniformly (line 229- present submission)
17. Line 150—it is not clear what you mean by "harvesting moment"; also, there is no y
Adjust the set of equation (3) to reflect properly the symbols (lines 243-249- present submission)
18. Line 147—all equations in a manuscript must have a unique id-number assigned.
We consider the mixed integer problem as an entity, and we did not associate an individual number
to each equation used to formalize the planning problem as we taught that it would clutter the
discourse, and no latter reference to an individual equation was made.
19. Why do you have-- /Age --- in the objective function? Not clear
Adjust the equations to reflect the new symbols
20. Immediately following the formulation, it is standard practice to describe, in words, each
equation, by number.
We described the equations used by the mixed integer programming problems immediately after
formulation, as suggested by the reviewer (lines 253-267- present submission)
21. Line 152--Upon what do you base these limits to problem size? Experience? If so, describe.
Changed the paragraph entirely and the sentence was replaced with a series of sentences describing
the computation time issue associated with the forest planning problems (lines 277-286 – present
submission)
22. Line 160—the following is not clear=="the real time computations requirement"
The paragraph changed significantly and the “real time” group was eliminated completely from the
manuscript.
23. Line 163—what is "real time"?
The “real time” in computing quantifies the elapsed time between the event and the response of a
system. However, the term “real time” was eliminated from the manuscript.
24. Line 220—tabu, not taboo.
Changed to “tabu” (line 361- present submission)
25. Line 226—run time depends on problem size (#binary decision variables). Therefore, 40
minutes might be reasonable if the problem sizes are similar.
We changed the simulated annealing section significantly and the sentence referring to 40 min was
deleted and replaced by a more detailed explanation of the selection of the run time (lines 401-407
– present submission)
26. Line 229—I recall that the run-time needed for simulated annealing to reach, with certainty,
an optimal solution has been worked out by someone (please cite); and that, incidentally, this runtime was greater than the run-time needed for complete enumeration and evaluation of all possible
solutions; i.e., guaranteed optimality is pointless with this algorithm.
The authors who proves the statement are Geman S and Geman D (1984).
27. Line 242—every source I've read on determining the parameters for the simulated annealing
algorithm recommends that these be selected experimentally, for each model and problem instance
involved. I would, therefore, question the usefulness of your selected parameters since you
determined them, apparently, through a priori reasoning.
An entire paragraph inside the Simulated annealing section explained how the parameters were
selected. New additional runs were performed to ensure the appropriateness of the starting
parameters (lines 368-401-present submission).
28. Line 280—possible since—not possible as.
Changed to “possible since” (line 493 – present submission)
29. Stopped review of manuscript, since major revisions are required beyond this point.
The rest of the manuscript suffered significant changes imposed by the inclusion of the linear
programming results.
Reviewer #2
Revisions
1. How was adjacency handled in the "adjusted FFD"? The paper seems to indicate that it was not
explicitly addressed (see lines 402-410), which leads one to conclude that adjacency violations
were not assessed when using FFD even though the authors assert that the "algorithm has the
property of self-organization" (not sure what that means when applied to adjacency restrictions...).
The adjacency constraint was imposed using the unit restriction model, as defined by Murray
(1999). The FFD (as a bin-packing heuristic algorithm) has the property to self organize such that
would resemble the perfect bin-packing theorem conditions, therefore, tend to converge to
solutions close to optimal solution (Csirik et al 1999). We changed this paragraph to better reflect
the implementation of adjacency constraint (lines 304-328- present submission).
2. How was adjacency handled in SA? Was the area restriction model or the unit restriction model
used?
It was the unit restriction model.
3. Given that adjacency was not modeled in FFD, and seems to have been incorporated into SA,
the comparison of timber harvest volume results between the two is invalid. In addition, a
comparison of the computational times is invalid, as checking adjacency violations requires a
significant amount of time in some problems.
This point was made clear in the answer to the first comment of the reviewer.
4. Figure 1 contains too much information - the biogeoclimatic zones could be removed, since only
one covers most of the three study areas. In addition, one study area is only partially shown.
The figure was adjusted to reflect the reviewer suggestions. The area that the reviewer probably
think that is only partially shown (a straight line oriented north-south) is just a results of the fact
that in that region a straight line is the provincial boundary between Alberta and British Columbia.
5. g(A) (line 68) is not the same as g(t) (in the equation on line 69).
The entire paragraph of harvesting age and mean annual increment was re-written and the
functions g(A) and g(t) were eliminated.
6. The optimal harvest age at the stand level (lines 79-80) is when MAI is maximized only when
volume production is the goal, not when economics or other concerns are the goal.
We have completely rewritten the optimal harvesting age section of the manuscript, and have
provided the equations that could be used to incorporate more attributes in the forest planning
process, not only volume (lines 110-145– present submission). The volume, and consequently
MAI, was used only to present the new algorithm.
7. A perfect scheduler (lines 105-107) would harvest stands at the age of maximum MAI to achieve
an even-flow wood volume over time only when the initial age class distribution represents a
normal forest (it is evenly distributed, in terms of land area, among the age classes).
As we proved in the manuscript, the requirement to achieve global optimality (i.e., simultaneously
optimality at the stand and forest level) is not necessarily constrained to evenly distributed age
classes, but to the fulfillment of the perfect bin-packing theorem. In fact, all three study areas
exhibited an unbalanced age-class distribution, a non-normal forest according to Clutter et al
(1983) (Figure 3-present submission) but the AAC was within 5% from the global optimality
(Figure 5 a, b and c – present submission).
8. Lines 116-118, and lines 135-137: For a constant MVHA, the stands all have to be the same size
for this to work.
The reviewer statement identifies a particular solution among the possible solutions. A situation in
which the stands have not the same size but the MVHA is reached is the case of a forest with 12
stands: 3 of size 1, 3 of size 2, 3 of size 3 and 3 of size 4 (whatever the units are). If all the stands
have the same optimal harvesting age and the rotation is 3 then MVHA can be reached and equals
10 = 1+2+3+4 (the sum of stands with unequal size). However, to address the comments of the
reviewer for the general case (not as simple as the one mentioned above), we have included a
complete description of the situation when the initial distribution of the stands is not uniform (lines
193-221-present submission). Furthermore, the initial statements from lines 116-118 and lines 135137 were adjusted to provide a more complete description of the relationship between bin-packing
theorem and MVHA (lines 184-189 and 225-227).
9. Lines 233-235: in the equations, the indices i and f, for Ti and Tf, need to be sub-scripted.
The formulas used to determine the run time were eliminated, as significant portions of the
simulated annealing section were re-written.
10. Lines 271-272: This sentence does not make sense.
The sentence was rewritten (lines 479-481 – present submission), as well as significant portions of
the results.
11. Lines 331-332: In some of the previous work, the authors assumed that the rotation age for
clearcutting was flexible (any age above some minimum age), and that the stands could only be
harvested once during the Time Horizon (not once during a planning period - a sub-set of the time
horizon). Perhaps the rotation age could be less than the length of the planning horizon, but in
these cases the authors took care to make sure that the time horizon was shorter than the potential
rotation ages.
We changed the sentence mentioned by the reviewer and replace it with two new sentences explain
the connection between the rotation age and length of the planning period.
12. Line 347: Not sure why using LP analyses would be invalid - one can design a problem to
schedule multiple harvests in stands within a pre-defined time horizon.
The sentence was eliminated as solutions supplied by linear programming were used in the
discussion. Significant parts of the Discussion section were changed to address the comments of
the reviewer, such as the usage of linear programming.
13. Line 361: Although 100 runs of heuristics were used in Bettinger et al. (2002), there were not
"required." This amount of runs was used to develop a large sample of solutions from which
statistical analysis was performed. As a result, 660 minutes (line 365) was not required for the
computing time, and any other comparisons along these lines are not really appropriate (e.g., line
373).
As suggested by the reviewer the comparisons between the numbers of runs were eliminated.
14. The reference to Wah and Wang (1999) illustrating how SA does not perform well is not a fair
assessment of SA. There are other references on the use of SA in forestry that show SA does
perform well (see references below).
We covered a broader spectrum of references to provide the reader with examples where simulated
annealing does not performs as well as it is expected. Nevertheless, the authors acknowledged the
excellent performance of simulated annealing when applied to forest planning problems (lines 356358).
15. Lines 386-389: The authors suggest that additional management prescriptions are needed
when one uses SA to show improvements in harvest volumes. This shouldn't be the case.
The sentence was changed to reflect our ideas on the usage of simulated annealing in conjunction
with additional management prescription (lines 628-630 – present submission).
16. The parameters used within SA may not have been appropriate. Other work illustrates that the
initial temperature might actually need to be much higher than what was used here to allow SA to
freely move to a good place in the solution space. Otherwise, SA gets stuck in a bad place in the
solution space, and cannot free itself.
An entire paragraph inside the Simulated annealing section explained how the parameters were
selected. New additional runs were performed to ensure the appropriateness of the starting
parameters (lines 368-405-present submission).
16. Table 1: change "surface" to "land area"
We changed the word “surface” to ‘land area” throughout the manuscript.
17. Figure 2, middle of the figure: There is a reference to "eliminate the stand and the adjacent." If
so, does this algorithm actually model the same problem as SA?
The figure 2 was redone to improve the understanding of the algorithm.
18. Figure 3: font sizes are too large and are inconsistent.
Change the figure completely (Figure 4 – present submission).
19. Figure 4. This should be broken down into three separate figures.
We broke down the figure in three separate figures (Figure 5 a, b and c – present submission).
References
Clutter JL, Forston JC, Pienaar LV, Brister GH, Bailey RL (1983). Timber management: a
quantitative approach. John Wiley &Sons, New York
Csirik J, Johnson DS, Kenyon C, Shor PW, Weber RR (1999) A self organizing bin packing
heuristic. In Goodrich MT, McGeoch CC (eds): Algorithm Engineering and Experimentation.
Lecture Notes in Computer Science 1619, Springer-Verlag, Berlin, pp 246-265
Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration
of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6: 721-741
Heyer CJ (1841) Die Waldertragsregelung. Verlag B.C. Ferber, Giessen
Hundeshagen JC (1826) Die Forstabschätzung aufneuen wissenschaftlichen Grundlagen . H.
Laupp, Tübingen