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

该项目将继续研究动态、格型、d-Schur凸成本和凹成本规划，并将其应用于库存控制、调度、网络和多人决策。格子规划和网络流中的替代、互补和波纹理论将继续发展，使人们能够预测由于参数变化而导致的最优和均衡决策的变化方向，而不需要计算。这项工作将在多个重要方向继续和扩展，包括随机网络流、Leontief替换系统和高效算法的开发。存在规模经济的决策问题会导致最小成本的数学规划。将继续研究这些问题，以确定可以在多项式时间内解决的大类问题。不确定条件下序贯决策的重要问题可归结为马尔可夫分枝决策过程。这一领域将研究各种问题，包括受控种群、几何种群增长、计算复杂性和广义半马尔可夫决策过程。将特别关注为大规模系统开发具有保证的高效率和快速运行时间的近似方法。这项工作将应用于产量管理、不确定情况下的单产品/多产品/梯队/设施库存模型等领域。

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.