Re: [OPE-L] Koopmans versus Kantorovich

[Paul Cockshott <wpc@xxxxxxxxxxxxx>]

I worked out a way of doing it over the weekend. What one does is
Create a dummy variable - degree of plan fulfilment and make the output
of each of the individual goods a linear function of this dummy
variable. One then gets the linear programming solver to optimise for
the maximisation of plan fulfilment. Using that technique I was able to
get lp_solve ( a linux linear programming tool ) to exactly reproduce
the results that Kantorovich gave in his 1939 article.

I will check out the refs though

-----Original Message-----
From: OPE-L [mailto:OPE-L@xxxxxxxxxxxxxxxx] On Behalf Of Allin Cottrell
Sent: 21 May 2007 11:24
To: OPE-L@xxxxxxxxxxxxxxxx
Subject: Re: [OPE-L] Koopmans versus Kantorovich

On Sat, 19 May 2007, Paul Cockshott wrote:

> 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.

Koopmans comments on the relationship between Kantorovich's work
and linear programming in his 1960 commentary on the reprinting of
Kantorovich's 1939 article (Management Science, vol. 6, no. 4,
July 1960).  Koopmans argues that K'vich's "Problem C", "while
appearing to have a somewhat special structure, is in fact
equivalent to the general linear programming problem."

There's a critical comment by Charnes and Cooper (Management
Science, April 1962) and a response from Koopmans.

Other sources that may be useful include Leif Johansen, "L. V.
Kantorovich's Contribution to Economics" (Scandinavian Journal of
Economics, vol. 78, no. 1, March 1976) and Roy Gardner's survey
article, "L. V. Kantorovich: The Price Implications of Optimal
Planning" (Journal of Economic Lterature, Vol. 28, no. 2, June
1990).

Allin.