Dynamic, Concave-cost, and Lattice Programming with Application to Inventory Control and Scheduling

这个项目将继续工作动态，晶格，d-舒尔- 凸费用和凹费用规划及其应用 库存控制、调度、网络和多人决策。 格规划和替代、补充理论 网络流量的涟漪将继续发展， 使人们能够预测最佳的变化方向， 由参数变化产生的均衡决策， 计算 这项工作将继续下去，并以各种形式加以推广。 包括随机网络流的重要方向， Leontief代换系统与有效 算法 决策问题中存在的经济- 规模导致最小凹成本的数学规划。 这些 将继续研究各种问题， 可以在多项式时间内解决的各种问题。 不确定性下序贯决策的重要问题 可以看作是马尔可夫分支决策过程。 各种 将研究这方面的问题，包括控制 种群，几何种群增长，计算复杂性 广义半马尔可夫决策过程 将特别注意发展近似 保证高效和快速运行的方法 对于大型系统。 这项工作将应用于产量 管理，单一和多产品/梯队/设施库存 不确定性下的模型，以及其他领域。

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.