Be sure to read the rule before you leave

Hi long time lurker, first time caller. Wow this is a great question.

First a database is just data at rest; you need to do something with the data therein. Others have mentioned Linear Algebra and "Towards a New Socialism" (the Harmony Algorithm) and I want to speak to those first.

Lets start with linear algebra: good, bad, and ugly. In a (basic) linear algebra approach you'd pose problems like so:

Ax + b = y

Where A is a matrix of input-output relations: a massive matrix with each row representing a recipe for something you'd want to produce and each column being some type of input. For example perhaps 1 unit of leather takes 1 hour of labor and consumes 1 cow, you'd put a 1 in the leather column and negative 1's in both the labor and cows column. The vector b kind of represents things you'd get automatically (And we'll assume it's all zeros and toss it). And that leaves y as the goal vector (e.g. how many iphones you want to produce, how many cars, etc). Linear algebra, and the above formulation, allows you to work backwards and solve for x. This tells you how much metal you need, power, labor hours, cows, etc.

The good is it's fast, reliable and well defined if you're using it right. The bad is it's quite limited: Take energy production for example -- there are several ways to do this: wind, solar, gas, nuclear. Linear algebra isn't going to handle this well. And what happens if some outputs are both end-products but also inputs to other products? Things get messy.

But the ugly is that the linear algebra approach is literally just a system of equations that represent a mapping between two different high dimensional spaces. Every column and every row should be measuring a totally unique thing. This is not an ideal situation for planning, here outputs of one industry are inputs to another.

This limitation can be creatively addressed by subdividing the problem and combining the answers. Perhaps splitting by region, or looking at each industrial sector in isolation. Which brings us to a good time to mention the Harmony algorithm which is one approach to subdividing the problem and recombining the answers.

But before we go on from here, it's worth mentioning that there is no guarantee that solutions built from solutions to subproblems will be optimal. But they might be: it depends on the problem domain.

However there are more sophisticated models, such as the linear programming model. In this model you recast your planning problem into a description like so:

    Maximize happiness
    Where happiness is 1.5 * number of iphones, + -.5 * level of pollution + ...
      AND acres of land used < 1000
      AND number of labor hours used is < 50000
      AND number of iphones = labor hours * .01
      AND level of pollution = labor hours *.001
      AND ...

This model is much nicer: we have an objective to maximize (the happiness equation) and we can accommodate multiple production processes as constraints on the solution. We can also accommodate that making leather also produces beef, and that raising cows one way produces fertilizer but raising them another way produces pollution shit pools. So that solves the energy problem (we can also encode all of the different ways energy can be produced). We can also set hard limits on negative things (e.g. the max CO2 we want to emit).

But this model is much, much slower. I believe the largest solvers on the largest supercomputers can handle ~8 billion variables. But each production process you add could require dozens to hundreds of variables in the final model. So you're back to divide and conquer approaches.

And we've barely begun! We haven't looked at how you decide what to produce. We haven't even looked at future planning (deciding what capital goods to invest in) nor geography (Where do you build or produce these things? Where do you run rail lines? Where is the labor that needs the jobs or has the skills?).

And what about your solution quality? Do you need the best possible plan or will any reasonably good plan do (e.g. top 10% of plans)? And what about the variety of possible solutions? Maybe one good plan is based on railway lines and collective agriculture while a different really good plan achieves the same with densification and high tech industries. How do you decide what's best, but more importantly: Did your planning approach inform you that you had these very different options?

Nor have we looked at things like Cybersyn -- how do you monitor your industries and identify weird-shit-happening-now in the production process (e.g. delays in shipping, sudden bursts of productivity, rising worker unhappiness, etc) and route around it?

I don't think there is a planning "solution" but there are planning "tools". All these approaches and more should be used by a dedicated planning department that can plan and correct for many timescales and contingencies. This department would also need to communicate the plans to appropriate stake-holders.

Anyway, I hope you enjoyed reading this, I certainly enjoyed writing it :-)