Studies in Stochastic Production Systems

这笔赠款为开发基于计算机的有限能力生产系统数学模型提供资金，包括具有随机需求的单项模型、共享关键能力限制资源的多项模型以及具有有限生产能力和随机需求的供应链。对于单项模型，目标是首先确定最优策略具有简单形式的有限容量随机生产系统的类别。下一个目标是确定一大类模型，它们的成本函数可以用一种已经成功地用于研究订货而不是制造的库存问题的形式来编写。这种特殊形式的成本函数通过灵敏度和最坏情况分析，保证了基于确定性需求系统的解所得到的启发式算法的稳健性，以及无分布的成本上限。然后，这些启发式算法将扩展到共享关键能力资源的多个项目，以及具有有限生产能力和随机需求的多项目、多阶段系统。研究的目的是获得对各种生产和需求环境的结构和敏感性分析结果，并利用这些结果开发有效的算法和接近最优的启发式算法。如果成功，这项研究的结果将导致对面临随机需求的制造系统的更好的理解和更好的管理生产和库存的能力。对这类系统的更好理解将来自对成本函数的敏感性分析，以及揭示在最坏情况下随机性对成本影响的封闭形式的成本上界。更好地管理这类系统的能力将来自基于计算机的高效算法和健壮启发式的开发。

This grant provides funding for the development of computer-based mathematical models for finite-capacity production systems, including single-item models with random demand, multi-item models that share a critical capacitated resource, and supply chains with finite production capacity and random demands. For single item models the aim is to first determine the class of finite-capacity stochastic production systems for which the optimal policy has a simple form. The next goal is to determine a broad class of models whose cost function can be written in a form that has been successfully used in the study of inventory problems where items are ordered rather than manufactured. This special form of cost function guarantees, via sensitivity and worst case analyses, the robustness of heuristics obtained based on the solution of systems with deterministic demands, as well as distribution-free cost upper bounds. These heuristics will then be extended to multiple items sharing a critical capacitated resource and to multi-item, multi-stage systems with finite production capacity and random demands. The objective is to obtain structural and sensitivity analysis results for a wide variety of production and demand environments, and to use these results to develop efficient algorithms and near-optimal heuristics.If successful, the results of this research will lead to an improved understanding, and better ability to manage production and inventories in manufacturing systems facing random demands. Improved understanding of such systems will come from the sensitivity analysis of cost functions and from closed form cost upper bounds that reveal the cost impact of randomness in the worst case. Better ability to manage such systems will come from the development of computer based efficient algorithms and robust heuristics.