Studies of Stochastic Production Systems

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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.