Discussion on two early papers of Professor Kantorovich, from 1939 and 1949, that proved to be remarkable documents in the history of management science, of linear programming, and of economic theory in general. The 1949 paper discusses transportation models for a single commodity and for many commodities (including empty vehicles), and a single-commodity model for a capacitated network, with applications to sections of the Russian railroad network. All problems considered in the 1939 paper reprinted in this issue are what would now be called linear programming problems. The coefficient matrices of the problems labeled “A” and “B” exhibit special structures somewhat similar to that of the transportation problem matrix. Problem “C,” while appearing still to have a somewhat special structure, is in fact equivalent to the general linear programming problem.

This is a report of the results of some digital computer simulation studies of a simplified model of a job shop production process. Such factors as the average effectiveness of schedules under the impact of random variations in processing times and the effect of changing operating policies are considered. The average manufacturing times and predictability of completion times were used as measures of effectiveness.

The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form. The constraints which are then violated are added in a similar way to the constraints already imposed. It is shown that under certain general conditions this procedure leads to the required optimum in a finite number of steps. The procedure is illustrated by an example while also a directory of computations is given.