This project will continue work on dynamic, lattice, d-Schur- convex-cost and concave-cost programming with applications to inventory control, scheduling, networks, and multiperson decisions. The theory of lattice programming and of substitutes, complements and ripples in network flows will continue to be developed to enable one to predict the direction of changes of optimal and equilibrium decisions resulting from changes in parameters without computation. This work will be continued and extended in a variety of significant directions including stochastic network flows, Leontief substitution systems and the development of efficient algorithms. Decision problems in which there are economies-of- scale lead to minimum-concave-cost mathematical programs. These problems will continue to be studied with the aim of identifying broad classes of problems that can be solved in polynomial time. Important problems of sequential decision making under uncertainty can be studied as Markov branching decision process. A variety of problems will be studied in this area including controlled populations, geometric population growth, complexity of computation and generalized semi-Markov decision processes. Special attention will be focused on developing approximation methods with guaranteed high-effectiveness and fast running times for large-scale systems. This work will be applied to yield management, single- and multi-product/echelon/facility inventory models under uncertainty, and other areas.
