Characterization and computation of optimal and nearly optimal multiperiod supply-chain policies with known or uncertain demands using dynamic, lattice, network, convex and concave programming. Cooperation: sharing benefits of alliances. Competition. Leontief-substitution and network-flow models. Lattice programming: comparison of optima; existence and comparison of equilibria of non-cooperative games. Stochastic comparison. Invariant properties of optimal flows: graphical optimization of supply chains. Optimality of myopic policies. Prerequisites: Math 115, optimization theory, probability.