Linear Programming

Linear programming describes the family of mathematical tools that are used to analyse linear programs (see definition of linear program in the glossary). The word „linear“ results from character of the objective function and the constraints and the word „programming“ results from applications in areas of planning or action scheduling.

Linear programming was first designed as planning and decision tool in setting where a central decision-maker fully in control of the various quantity variables in the system has to make consistent or optimal decision. The linear programming was developed by Kantorovich (1939) and Dantzig (1982) as a tool for optimal central decision making for primarily military purposes.

It is quite clear that the standard linear programming formulation is best suited to problems where a single decision maker optimises a central welfare function subject to technological and physical constraints. Unfortunately the standard formulation does not appear so well suited to modelling situations where many agents independently maximise their own welfare functions and jointly but inadvertently determine an outcome that can only be affected indirectly by the planner or policy maker.

References:

Dantzig, G. B. (1982). Reminiscences about the origins of linear programming, in Mathematical programming : the state of the art, Bonn, 1982 (New York, 1983), 78-86.

Kantorovich, L. V. (1939). "Mathematical Methods of Organizing and Planning Production" Management Science, Vol. 6, No. 4 (Jul., 1960), pp. 366–422.