A dynamic game model for distribution problems with non-stochastic uncertainty

A discrete-time dynamic production/distribution problem for a commodity is considered, comprising several delivery points. At each time, only the global amount of the demand is known, whereas the demand at each delivery point is only bounded above. The system has both production and transportation capacity constraints. Capacities and demand bounds can vary with time. The problem is that of finding initial conditions from which control (i.e. production/transportation) strategies exist that can fulfill any demand using the available system capacities. A two-person dynamic game model on a network is formulated for this problem. It is shown that the required sets of initial conditions are O-base polyhedra; a procedure to derive them is provided, and an upper bound on the number of required steps is derived.