Jay D. Schwartz

Simulation-based optimization of process control policies for inventory management in supply chains

A simulation-based optimization framework involving simultaneous perturbation stochastic approximation (SPSA) is presented as a means for optimally specifying parameters of internal model control (IMC) and model predictive control (MPC)-based decision policies for inventory management in supply chains under conditions involving supply and demand uncertainty. The effective use of the SPSA technique serves to enhance the performance and functionality of this class of decision algorithms and is illustrated with case studies involving the simultaneous optimization of controller tuning parameters and safety stock levels for supply chain networks inspired from semiconductor manufacturing. The results of the case studies demonstrate that safety stock levels can be significantly reduced and financial benefits achieved while maintaining satisfactory operating performance in the supply chain.

Control-Relevant Demand Forecasting for Tactical Decision-Making in Semiconductor Manufacturing Supply Chain Management

Forecasting highly uncertain demand signals is an important component for successfully managing inventory in semiconductor supply chains. We present a control-relevant approach to the problem that tailors a forecasting model to its end-use purpose, which is to provide forecast signals for a tactical inventory management policy based on model predictive control (MPC). The success of the method hinges on a control-relevant prefiltering operation applied to demand estimation data that emphasizes a goodness-of-fit in regions of time and frequency most important for achieving desired levels of closed-loop performance. A multiobjective formulation is presented that allows the supply-chain planner to generate demand forecasts that minimize inventory deviation, starts change variance, or their weighted combination when incorporated in an MPC decision policy. The benefits obtained from this procedure are demonstrated on a case study drawn from the final stage of a semiconductor manufacturing supply chain.

Simulation-based optimal tuning of model predictive control policies for supply chain management using simultaneous perturbation stochastic approximation

Efficient management of inventory in supply chains is critical to the profitable operation of modern enterprises. The supply/demand networks characteristic of discrete-parts industries such as semiconductor manufacturing represent highly stochastic, nonlinear, and constrained dynamical systems whose study merits a control-oriented approach. Model predictive control (MPC) is presented in this paper as the basis for a novel inventory management policy for supply chains whose dynamic behavior can be adequately represented by fluid analogies. A simultaneous perturbation stochastic approximation (SPSA) optimization algorithm is presented as a means to obtain optimal tuning parameters for the proposed policies. The SPSA technique is capable of optimizing important system parameters, such as safety stock targets and/or controller tuning parameters. Two case studies are presented. The results of the optimization on a single-echelon system show that it is advantageous to act cautiously to forecasted information and gradually become more aggressive (with respect to factory starts) as more accurate demand information becomes available. For a three-echelon problem, the results of the optimization demonstrate that safety stock levels can be significantly reduced and financial benefit gained while maintaining robust operation in the supply chain

Control-relevant demand modeling for supply chain management

Abstract The development of control-oriented decision policies for inventory management in supply chains has received considerable interest in recent years, and demand modeling to supply forecasts for these policies is an important component of an effective solution to this problem. Drawing from the problem of control-relevant identification, we present an approach for demand modeling based on data that relies on a control-relevant prefilter to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecast signals to a tactical inventory management policy based on Model Predictive Control. Integrating the demand modeling and inventory control problems offers the opportunity to obtain reduced-order models that exhibit superior performance, with potentially lower user effort relative to traditional “open-loop„ methods. A systematic approach to generating these prefilters is presented and the benefits resulting from their use are demonstrated on a representative production/inventory system case study.

Towards control-relevant forecasting in supply chain management

The focus of this paper is understanding the effects of demand forecast error on a tactical decision policy for a single node of a manufacturing supply chain. The demand forecast is treated as an external measured disturbance in a multi-degree-of-freedom feedback-feedforward internal model control (IMC) based inventory control system. Because forecast error will be multifrequency in nature, the effect of error in different frequency regimes is examined. A mathematical framework for evaluating the effect of forecast revisions in an IMC controller is developed. A simultaneous perturbation stochastic approximation (SPSA) optimization algorithm is implemented to develop an optimal tuning strategy under these conditions. For the IMC-based inventory controller presented it is concluded that the most desirable performance may be obtained by acting cautiously (e.g. implementing small changes to factory starts) to initial forecasts and gradually becoming more aggressive on starts until the actual demand change is realized.

A Control Theoretic Evaluation of Schedule Nervousness Suppression Techniques for Master Production Scheduling

In manufacturing operations, a Master Production Schedule (MPS) can be used to make mid-range planning decisions that not only influence the production decisions for a manufacturing facility, but serve as input into other decision systems to determine materials ordering, staffing, and other business requirements. With the advance of computing and data acquisition technologies, an MPS can be recomputed on a more frequent basis to make the production schedule more agile in meeting customer needs. However, uncertainty in the demand forecast or production model may also increase the possibility and/or severity of “schedule nervousness”. The mitigation techniques of frozen horizon, move suppression, and schedule change suppression are evaluated to determine the robust stability margins of each approach at their performance-optimal tunings. Since an MPS is typically computed using Linear Programming these techniques are formulated in this manner, and therefore an empirical Nyquist stability analysis using Empirical Transfer Function Estimates (ETFE) is employed. The technique of move suppression is shown to provide better robust stability margins in the small-scale problem. Further evaluation is needed on scheduling problems of industrial size.

Control-relevant estimation of demand models for closed-loop control of a production-inventory system

The development of control-oriented decision policies for inventory management in supply chains has received considerable interest in recent years, and demand modeling to supply forecasts for these policies is an important component of an effective solution to this problem. Drawing from the problem of control-relevant parameter estimation, this paper presents an approach for demand modeling in a production-inventory system that relies on a control-relevant weight to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecast signals tactical inventory management policies based on Internal Model Control. The formulation is multi-objective in nature, allowing the user to emphasize inventory variation, starts change variation, or a weighted combination. By integrating the demand modeling and inventory control problems, it is possible to obtain reduced-order demand models that exhibit superior performance. A systematic approach for generating these weights is presented and the benefits resulting from their use demonstrated on a representative production-inventory system case study.

A system identification approach to PDE modeling of a semiconductor manufacturing process

Abstract Efficient supply chain management is a crucial imperative for modern, global enterprises. Tactical decision policies based on process control principles have been developed in the literature for managing production-inventory systems and supply chain networks. To be effective these decision policies depend on accurate nominal models. With a discrete-event simulation acting as a “truth model”, we employ system identification techniques to parameterize a nonlinear Partial Differential Equation (PDE) model of the semiconductor manufacturing process. A case study shows that the identified PDE model can accurately predict the output of the discrete-event simulation, but without the high computational burden.

Control-relevant demand forecasting for management of a production-inventory system

Forecasting highly uncertain demand signals is an important component for successfully managing inventory. We present a control-relevant approach to the problem that tailors a forecasting model to its end-use purpose, which is to provide forecast signals to a tactical inventory management policy based on Model Predictive Control (MPC). The success of the method hinges on a control-relevant prefiltering operation that emphasizes goodness-of-flt in the frequency band most important for achieving desired levels of closed-loop performance. A multi-objective formulation is presented that allows the supply chain planner to generate demand forecasts that minimize inventory deviation, starts change variance, or their weighted combination when incorporated in an MPC decision policy. The benefits obtained from this procedure are demonstrated on a case study where the estimated demand model is based on a AutoRegressive (AR) process.

A control-relevant approach to demand modeling for supply chain management

Abstract The development of control-oriented decision policies for inventory management in supply chains has drawn considerable interest in recent years. Modeling demand to supply forecasts is an important component of an effective solution to this problem. Drawing from the problem of control-relevant parameter estimation, this paper presents an approach for demand modeling in a production-inventory system that relies on a specialized weight to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecasts to inventory management policies based on internal model control or model predictive control. A systematic approach to generate this weight function (implemented using data prefilters in the time domain) is presented and the benefits demonstrated on a series of representative case studies. The multi-objective formulation developed in this work allows the user to emphasize minimizing inventory variance, minimizing starts variance, or their combination, as dictated by operational and enterprise goals.