CAREER: Large-Scale Parallel Replacement Analysis

这笔赠款为大规模并行替换问题的建模和解决方案的调查提供资金。具体地说，将对具有多个挑战者的不同资产组在需求和资本预算限制下的问题进行调查。还将探讨集团资产折旧政策造成的特征，包括购买价格的规模经济、资产可获得性限制以及税后影响。将研究各种建模和求解程序，包括：(1)具有资源定向分解求解程序的一般整数规划和从整数背包覆盖发展而来的割平面算法；(2)利用资本预算约束和规模经济下最优解的特殊结构的动态规划；以及(3)随机规划，其确定性分析扩展到情景分析、随机动态规划和追索权模型。这个职业计划也是由一个密切相关的教育组成部分来定义的。由于替换分析是工程经济学中的一个基本问题，研究将促进这一核心工程学科领域的教学改进。如果成功，这项研究的结果将导致解决工业、政府和军队普遍面临的新的规模和范围的替换问题。这些结果将与运营着大量不同资产的行业合作伙伴进行核实。这些研究还应该为解决具有特殊结构的大型数学规划及其在实际问题中的应用提供进一步的洞察。该项目的教育调查将促进工程经济学教学的完善和规范，不受工程学科的限制。

This grant provides funding for an investigation into the modeling and solution of large-scale parallel replacement problems. Specifically, investigations will be pursued into problems under demand and capital budgeting constraints for heterogeneous groups of assets with multiple challengers. Characteristics including economies of scale in purchase prices, asset availability constraints, and after-tax implications caused by group asset depreciation policies will also be explored. A variety of modeling and solution procedures are to be examined, including: (1) General integer programming with resource directive decomposition solution procedures and cutting plane algorithms developed from integer knapsack covers; (2)Dynamic programming which capitalizes on the special structure of optimal solutions under capital budgeting constraints and economies of scale; and (3) Stochastic programming, with deterministic analyses extended to scenario analysis, stochastic dynamic programming and recourse models. This career plan is also defined by a closely related educational component. As replacement analysis is a fundamental problem in engineering economics, investigations will lead to teaching improvements in this core engineering subject area.If successful, the results of this research will lead to the solution of new replacement problems, both in size and scope, commonly faced by industry, the government and the military. These results are to be verified with industrial partners that operate large fleets of diverse assets. The investigations should also provide further insight into the solution of large-scale mathematical programs with special structure and their application to real problems. The educational investigation in this project will lead to an improvement and standardization of teaching engineering economy, regardless of the engineering discipline.