Significance Comment

There are no issues with the significance of the work, in my opinion. Clearly, the human population will increase, they will need to be fed, and a smarter allocation of crops to farmlands that suit those crops is, in my mind, not simply a supplement to other solutions but an absolute necessity. By providing a simple study of how such allocation could benefit food productions, the authors have taken a major first step in an important direction. I sincerely hope that there will be more.

Quality Comment

The paper is well written and the material is presented in a clear manner. The arguments for smarter land-use strategies may not be very rigorous, but in my opinion they do not really need to be, and I think that most readers would agree with the authors’ stated motivation.

The study carried out is somewhat brute in its simplicity, but the authors themselves are aware of this and state, almost explicitly, that the main contribution of the paper is that of a thought-provoking experiment aimed at answering the basic question of “what are the potential gains of intelligently allocating which crops are grown where so as to maximize productivity?” To this end, I believe that the authors have a high-quality paper.

I have, however, two major and one minor qualms with the work, some of which will undoubtedly be biased by myself being an optimization-phile, but which I think the authors – and others working on similar problems – would be wise to consider.

First, the general problem of intelligently allocating resources is one that must have been researched to death in many different mathematical, scientific, and engineering communities, as it is a very classic problem (unfortunately, I speak mostly on gut instinct and not on concrete experience, and so cannot give pointers to any good literature). As such, the one question that kept bugging me as I read this manuscript was: “shouldn’t there already be a whole slew of theory and work on a general allocation problem that the authors’ problem is just a special case of?” If this is so, which I believe it is, then the paper could benefit significantly from referencing such work and showing how it could be applied here, thereby justifying the authors’ proposed strategy of simply filling each farmland only with the crop that grows best on that farmland, or refuting it as being inferior to other strategies that have already been proposed for similar or equivalent problems.

My other major qualm is with the authors’ chosen optimization criterion and the complete neglecting of constraints. Here, all of the crops are counted equally in the sense that a set of farmlands producing 12 tons instead of 8 is considered more optimal regardless of the diversity of the crops produced in those 12. This is, from the optimization perspective, equivalent to a multi-criterion optimization problem where the weights on the different components are all set to unity. Such a choice of weights must be justified somehow, however – for example, might it not make more sense to judge different crops by vitamin content or some cost-to-nutrition ratio? Additionally, in any real-life situation there will almost certainly be constraints that demand crop diversity and minimal amounts of each crop (e.g., would we really switch to growing rice and only rice if it were found that rice grew the best everywhere?) Any standard optimization strategy must account for such constraints in its formulation, and it is not clear how the strategy proposed here would, and whether or not the presence of such constraints would completely invalidate the strategy in the case that such constraints are too stringent.

Lastly, I think it would be nice to see the simulation files and models used to run the experiments, as they appear to be quite interesting and most likely too complex for a typical reader like me to code (but not to use). This would allow people from optimization fields to try their hand at solving this problem via alternate methods. This is a minor complaint, however.

Summary

I will leave here additional remarks that came to mind while reading the paper, as well as any points that I wasn’t able to include above:

• The country-dependent preferences (such as those discussed for Asia and Africa) are again something that could be properly handled by formally defining an optimization criterion and weighting production differently based on the kinds of crops produced.

• I don’t believe that it is correct to use the term “optimal land use” since the land-use strategy proposed is heuristic in nature and not necessarily optimal. To say that a strategy is optimal, one would need to define an optimization criterion and then show that the proposed strategy achieves an allocation plan which cannot be improved upon (i.e., no other allocation plan yields a better criterion value).

• Changing land-use policies will inevitably be a very gradual procedure, as no farmer (and probably not many governments) would suddenly accept to completely stop planting a certain crop and start planting another. In optimization terms, this would simply mean placing rate-of-change constraints in the problem formulation (e.g., no change of more than 3% of a certain crop is allowed from year to year). This also has a nice geometrical interpretation in the Figures 4 and 5 of the paper, in that one can think of all the circles starting on the diagonal line and slowly diverging from year to year (possibly converging to the solution given by the authors).

• Given all of the uncertainty present in the real world, and the fact that one can measure the productivity obtained by a certain allocation at the end of every farm year, it may be wiser to consider an iterative experimental optimization strategy that adapts the allocation from year to year based on how past adaptations have affected productivity, as such a strategy may be shown to converge to the optimal land use in theory (unlike the heuristic strategy of the authors). Some of the early work on this topic may be found in the 1950-1960 work of George Box (on “design of experiments”) and the paper of Nelder-Mead (on the “simplex method”).