There are two lines of argument that were advanced against central planning in the calculation debate that began the 1930s: one from Mises and another from Hayek.
Mises argued that without private property in the means of production there can be no prices for the factors of production and without prices for the factors of production the efficient technique of production in a given line of production cannot be determined. Different technically possible methods of production which use different machines, natural resources, and labor skills cannot be compared in the units of the inputs themselves to determine which technique uses the least inputs. An automobile, for example, can be built with a more capital-intensive or an more labor-intensive process, it can be powered by an internal-combustion or electric engine each of which requires a different configuration of inputs to produce, etc. The number of machines cannot be added to the number of labor hours to determine minimum input use. Linear programming does nothing to solve this problem. And, as Mises pointed out, this is a fundamental conceptual problem that exists regardless of the complexity of production across the entire economy.
The other fundamental problem that Mises raised with central planning, which also exists regardless of the complexity of production throughout the economy, is the uncertainty of the future. Efficient use of resources cannot rely solely on existing knowledge. Production aims at the realization of ends in the future. Efficiency, therefore, requires accurate entrepreneurial anticipation of how given courses of action will play out into the future. This is why central planners cannot rely on the existing prices of capitalism on the day of the revolution to guide their production decisions. Linear programming, obviously, does not solve, or even address, this problem.
On the calculation argument, take a look at Joe Salerno’s epilogue to Mises’s original 1920 article:
Hayek introduced a second line of argument, namely, the problem of obtaining the information sufficient for the central planners to make efficient production decisions. His main point was that such information is, at least partially, tacit. It consists of production know how that is contingent on person, place, and time. There is no process, Hayek argued, except market prices that can compile and transmit this information to production decision- makers. Linear programming does not address this problem.
Hayek also stressed that the knowledge necessary for central planners to make efficient production decisions is complex and constantly changing. There is no known method to compile such information into useful form except the pricing process of the market. The advocates of central planning took this last point, on which they thought faster, bigger computers could provide a solution, and asserting a theoretical solution declared victory over Mises and Hayek.
Lucas Engelhardt has called into question the veracity of such a procedure on its own grounds: