Studies in Stochastic Production Systems

该赠款为有限容量生产系统的计算机数学模型的开发提供资金，包括具有随机需求的单项目模型，共享关键能力资源的多项目模型，以及具有有限生产能力和随机需求的供应链。对于单项目模型，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，这些模型的成本函数可以写成一种已经成功地用于研究库存问题的形式，其中物品是订购的而不是制造的。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解的启发式算法的鲁棒性，以及无分布的成本上界。然后，这些启发式方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。目标是获得各种生产和需求环境的结构和灵敏度分析结果，并使用这些结果开发有效的算法和接近最优的启发式。如果成功，本研究的结果将导致一个更好的理解，并更好地管理生产和库存的制造系统面对随机需求的能力。对这类系统的更好理解将来自成本函数的敏感性分析和封闭形式的成本上限，后者揭示了随机性在最坏情况下的成本影响。更好的管理这些系统的能力将来自于基于计算机的高效算法和强大的启发式的发展。

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.