In mathematics transportation theory is the framework used for “determining the optimal transportation and allocation of resources.” If you need to plan how many seats to overbook on an airline, or how to distribute a certain number of teachers across a state, backhoes across construction projects, or fertilizer across the world, there’s a whole branch of mathematics dealing with the complexities involved in coming up with an optimal assignment schema where you get the biggest bang for your buck.  

Missionary assignments are, in a way, a big matching and allocation problem. Off the top of my head I can think of several variables that help produce a weighted function for determining the optimal fit for each missionary candidate. There would be a demand side and a supply-wide of the equation, with missionary fit feeding into mission-specific demands. 

On the missionary side:

• Prior foreign language experience, both for the actual language, and perhaps as a signal that they are capable of learning Hungarian, Japanese, or some of the more difficult languages. 
• Whether they are native to that country: Natives are probably more culturally and linguistically effective.
• Health issues: Presumably these would constrain how poor their assigned field of labor is.

On the mission field side:

• Effectiveness per missionary in that area: they may decide to allocate more missionaries to higher baptizing countries while still keeping at least a certain minimum operating force in every country according to some threshold.  
• Needs in those specific missions as missionaries ebb and flow. While much of this is stochastic, even some of the unknowns might be predictable. For example if 20% of missionaries assigned to Japan return home early, but only 10% of missionaries to the US do, then they need to systematically call more to Japan than they otherwise would. However, this would also include a stochastic term for unpredictables. Presumably this “error term” would be random across missions, but who knows. 
• Visa and geopolitical problems provide another big, unpredictable variable. If visas all the sudden become available after a dearth then a lot of missionaries need to be ready to go at the drop of a hat. Conversely, if visas become restricted or geopolitical situations shut down certain areas (often for reasons that were probabilistic but somewhat predictable), then those missionaries need to be reassigned, ideally to areas that are fits for their language skills (I had a sister missionary in my ward that never made it to Taiwan for geopolitical reasons and ended up in California, and in my visa-waiting mission in Spanish-speaking Las Vegas we had a lot of called-to-Venezuela missionaries, it happens.) Supply chain capacity buffer concepts could be useful here. It’s worth noting that with these and, for example, unknown health issues, the fit score may undergo an updating process after the initial inputs are processed. 

Like your credit or life insurance premiums, this could be something rather automated like everything else is becoming in life, with a mission-by-mission specific “fit” score calculated for each prospective missionary, and then an algorithm that maximizes the best fit between mission and missionary variables. 

Missionary companionship assignments are another case that could be treated as a math problem. In this case with a little bit of graph theory thrown in. Two nodes (or three for a trio) are optimally matched given basic parameters like seniority, need for supervision, nativity, language skills, etc.

Of course, this process is utterly uninspiring and insipid on its own. We believe in the role of the spirit for decisions like this. Case in point: BYU professor Van Gessel is one of the most prominent Japanese-to-English translators in the world. He was the translator for Endo Shusaku, consulted on the Martin Scorsese movie version of Silence, and received a prize from the Emperor of Japan for his translations. And he was called as a mission president–to Oregon. The people involved in his calling were clearly open minded enough to see him as more than a generically righteous Japanese speaker. Some times His ways are not our ways. But I wonder if there is or will ever be some kind of formal quantification and recommendation system to help general authorities to “study it out in [their, or the AI’s] mind” before going to the Lord in prayer about it, since there’s a whole mathematical subfield dedicated to this problem. (Not saying there should be, I’m just having fun thinking through the possibilities).