From: Paul Cockshott (clyder@GN.APC.ORG)
Date: Sat May 19 2007 - 08:40:13 EDT
I have just been re-reading Kantorovich's 1939 paper on mathematical methods of organising and planning production, and was struck by the way in which his formulation of linear programming is significantly different from that in standard western presentations. Kantorovich himself says: " I want to emphasize again that the greater part of the problems of which I shall speak, relating to the organization and planning of production, are con- nected specifically with the Soviet system of economy and in the majority of cases do not arise in the economy of a capitalist society. There the choice of output is determined not by the plan but by the interests and profits of indi- vidual capitalists. The owner of the enterprise chooses for production those goods which at a given moment have the highest price, can most easily be sold, and therefore give the largest profit. The raw material used is not that of which there are huge supplies in the country, but that which the entrepreneur can buy most cheaply. The question of the maximum utilization of equipment is not raised; in any case, the majority of enterprises work at half capacity." Recent Russian commentaries on his work make out that this is nothing but a token bit of marxist ideology to cloak a work that actually is quite independent of or non marxist. At first sight this would be reinforced by the fact that 10 years later linear programming or linear optimisation techniques were developed in the west as well. But the approach taken by Kantorovich seems significantly different. Western texts emphasise that the objective function being maximised is a linear combination of the outputs aX_1+ bX_2+ cX_3 this makes sense if you view a,b,c as prices at which the outputs X_i will be sold. Kantorovich on the other hand assumes that the outputs must in fixed ratios so that x_1 = a m, x_2= b m, x_3 = c m where m is the scale of production and a,b,c are multipliers In the western form the combination of outputs is a matter of indifference since they take commodity production for granted, and all they are concerned with is maximising money income. For Kantorovich the proportions of outputs are taken as given as he takes planned production for granted. Kantorovich optimises along a ray, but the western version attempts to reach a maximal hyperplane. I get the impression that there is some way of translating Kantorvich's ray formulation into the Planar formulation of Koopmans and Danzig, but I have not found a source explaining how to do it, and it looks to me as if a simplex solution would not actually meet Kantorovich's requirement. Does anyone know how one utilizes the simplex method to solve Kantorovich's problem? Paul Cockshott www.dcs.gla.ac.uk/~wpc reality.gn.apc.org ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.
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