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The use of linear optimization for the construction of economic plans was first introduced by Kantorovich with an algorithm similar to those later developed in the West by Danzig. In recent years linear optimization packages have become readily available on desktop computers, an example being the lp-solve system. In this paper I first show how the lp-solve package can be used to construct macroeconomic plans starting from information in IO table. I then examine the empirical computational complexity of the package in dealing with this sort of problem. This will show that the complexity is too great to allow the package to be applied to highly disaggregated IO tables. As an alternative to lp-solve I explain the Harmony algorithm and how that can be extended to the problem of multi-year plans. Performance measurements are given which indicated that the Harmony algorithm has a markedly lower computational complexity than lp-solve, making it more suitable for highly disaggregated plans.
Key words: socialist-planning; Kantorovich; complexity
The Plan Problem
Recently the entrepreneur Jack Ma (who founded Alibaba) has revived the idea of computerized economic plans (Thornhill 2017), claiming that with big data, networks and modern computing it should be possible to have detailed realtime planning of the Chinese economy. For this to be feasible in an economy as big as China, the computational complexity of the calculations has to be tractable. Research in this area goes back to Kantorovich (1965) who defined the plan problem as to find a way to combine a finite number of techniques along with a pre-given vector of resources in order to maximize the fulfillment of a plan target. The target itself was specified in terms of a vector that specifies the mix of outputs to be produced. For example, a plant producing car engine parts might have to maximize the output supplied in the fixed proportions N engine block, 4N pistons plus N crank shafts. A technique, in his terms, was a linear combination of resources that produced an output in fixed proportions. Given appropriate data about sales of consumer goods, which can be provided by electronic sales platforms like Alibaba, along with planned state purchases of public goods, the entire operation of the productive economy could be defined in these terms.