Two-Stage Transpotation Problem with Unknown Consumer Demands: Consistency Aspects

A mathematical model of a two-stage transportation problem with unknown consumer demands and their lower and upper bounds is studied. The necessary and sufficient conditions for consistency of the constraints system of the linear programming problem, which corresponds to this model, are formulated, and justified. The classical two-stage transportation problem is given, to which the above problem is transformed if consumer demands are known, as well as the consistency conditions for constraints system of the problem. Modification of the initial model that permits product transportation only to the fixed number of consumers, which is less than their total number, is given.