(477c) Optimal Operation of Semiconductor Manufacturing Supply Chains under Uncertainty Using Simulation-Based Optimization

Optimally managing production and inventory in supply/demand networks is necessary for the profitable operation of manufacturing enterprises. The supply chain problems typically encountered in the semiconductor industry are characterized by significant nonlinearity, stochasticity, and constraints. Historically, the management of these networks has been performed by the use of Economic Order Quantity (EOQ) approaches, heuristic business rules, and deterministic linear programming [1]. The relative ease-of-use and entrenchment of these policies makes them desirable from a supply chain manager's perspective, but under conditions of uncertainty, problems may arise leading to excess inventories, the need for large safety stocks to avoid backorders, and uneven production that is undesirable to factory management. These problems, together with the highly dynamic nature of the supply/demand networks, provide motivation for the development of a control-oriented approach.

The use of Model Predictive Control (MPC) as a tactical decision policy in supply/demand networks has been the subject of increasing interest in the past few years [2,3,4]. These novel inventory management policies have been shown to exhibit desirable performance and robustness properties, and can be tuned to provide acceptable levels of performance under conditions of supply and demand stochasticity, erroneous demand forecasts, and limited production/inventory/shipping capacity [4]. Although much progress has been made in the use of MPC for the management of inventory in supply/demand networks, the systematic tuning and parameterization of these policies has not been addressed. The focus of this paper is the use of a stochastic simulation-based optimization algorithm, Simultaneous Perturbation Stochastic Approximation (SPSA), as a strategic planning layer that serves to assist the MPC-based policy to meet long-term financial goals. SPSA is an optimization technique that has several advantages over traditional finite-difference stochastic approximation methods. The basis of the method is an efficient and intuitive "simultaneous perturbation" estimate of the gradient. Only two measurements of the objective function are required per iteration, regardless over the number of search dimensions. Therefore, the time required to capture numerical estimates of the gradient is only a function of the time required to run two simulations, and not dependent on the number of search dimensions [5].

SPSA represents a versatile, flexible approach that can be used to address diverse problems associated with the optimal operation of supply chains. One such problem is the systematic tuning of the MPC decision policy (the choice of weights and move suppressions) with respect to a financial objective function. Another meaningful problem is the optimal selection of safety stock levels and factory starts targets over a strategic planning horizon. Yet another interesting problem that can be solved with the SPSA approach is optimal model specification (i.e., selection of nominal throughput time and yields) in the controller decision policy. As a simulation-based optimization framework, the SPSA approach is capable of addressing these issues simultaneously under conditions of uncertainty, and with respect to a meaningful user-defined objective function (which will most likely be financial in nature).

This approach is presented in a case study involving a representative manufacturing supply chain in the semiconductor industry consisting of a network of fabrication/sort , assembly/test, and finishing/test facilities. In contrast to previous work that relied on simplified abstractions of the manufacturing nodes in the network, the fabrication facility in this case study is represented by a stochastic, nonlinear discrete event simulation. The model incorporates production bottlenecks, machine break-down time, and re-entrancy, thus accurately capturing the dynamics of a real semiconductor manufacturing process. The use of discrete event simulation allows the proposed control methodology to be tested with an industrially-meaningful benchmark problem and validates the use of the proposed control-oriented approach on a real manufacturing system.

The results show that the optimal values for inventory targets and move suppression are a function of the degree of stochasticity inherent in the manufacturing process and the accuracy of available demand forecasts. Typical optimal solutions are characterized by the necessity of having larger safety stocks in the inventory stages closest to the customer and reducing excess inventories at the start of the manufacturing process. As the degree of demand uncertainty increases, further financial benefit is gained by increasing safety stock levels at all echelons of the supply chain. For the semiconductor manufacturing problem, it is shown that the performance of the decision policy (measured on a financial basis) is a strong function of the inventory targets supplied by the strategic planning layer and is less insensitive to changes in controller tuning and nominal controller model parameters. This provides the supply chain manager important insights into the tuning and modeling process, as financial benefits can be reaped without a significant decrease in system robustness. The results of this study confirm our belief that SPSA is a powerful, flexible approach that can serve as a valuable tool to supply chain operations.

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[4] Seferlis, P., Giannelos, N. F., 2004. A two-layered optimisation-based control strategy for multi-echelon supply chain networks. Computers and Chemical Engineering 28, 799-809.

[5] Braun. M. W., Rivera, D. E., Flores, M. E., Carlyle, W. M., Kempf, K. G., 2003. A Model Predictive Control framework for robust management of multi-product, multi-echelon demand networks. Annual Reviews in Control 27, 229-245.

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