(723c) Robust Decision Making for Hybrid Process Supply Chain Systems Via Model Predictive Control

A supply chain (SC) is a network of facilities that performs the functions of raw material procurement, raw material transformation into intermediate and finished products, and distribution of products to customers. In a chemical process supply chain (PSC), such as in the petrochemical or pharmaceutical industry, manufacturing is a major component. Supply chain management (SCM) and supply chain optimization (SCO) are concerned with the coordinated optimization of business processes, including strategic network design, purchasing, production, transportation and distribution in order to bring greater net value to the customer, at minimum overall cost. Poor SCM can contribute to undesirable performance such as the bullwhip effect, defined as the amplification in demand variability observed when moving up the supply chain from retailers to suppliers. Applications for SCM that integrate classical control technology have been motivated by the need for effective quantitative approaches to mitigate inefficiencies in the supply chain. These applications generally apply feedback laws for maintaining inventory positions and satisfying demand [Sarimveis et al., 2008]. However, the limitations associated with classical control technology, such as the inability to explicitly consider interactions or delays in the supply chain, can be averted by applying an advanced control method like model predictive control (MPC). As a result, MPC has been successfully applied for SCM in the literature [e.g., Wang and Rivera, 2008].

The supply chain model is a vital component of an MPC-based strategy, which must describe adequately the dynamic behavior of the system. The simplest model captures inventory dynamics based on the quantity of material entering and leaving the echelon at each time period; however a more sophisticated model addresses the hybrid continuous-discrete nature of the supply chain.  In a supply chain the discrete nature arises from disjunctive logical conditions governing decision-making (e.g. production scheduling), generally giving rise to a mixed-integer-programming model. This has motivated MPC-based formulations for SCM of hybrid supply chain systems [e.g., Perea-Lopez et al., 2003; Mestan et al., 2006]. Uncertainty is a relevant issue in SCO, and if not addressed, can contribute to poor decision making. An approach to capture uncertainty explicitly at each execution of the model predictive controller is provided through robust MPC. With robust MPC, the model used for control, and unmeasured disturbances are considered uncertain; therefore, the future closed loop behavior is uncertain because the control action depends on the uncertainty propagation. An “open loop” approach to robust MPC, which neglects the partial compensation for uncertainty by feedback may lead to overly conservative control action. Previous work on robust MPC has attempted to approximate the future closed loop behavior of the system [e.g., Kothare et al., 1996; Li and Marlin, 2009].

In this paper we present an optimization-based decision making tool for the control of a hybrid supply chain system, via a robust MPC strategy. The proposed formulation captures uncertainty in model parameters and demand by stochastic programming, accommodates hybrid process systems with production decisions governed by logical conditions, and addresses multiple supply chain performance metrics, within an integrated optimization framework. In this work, a scenario-based approach is used to capture uncertainty through a finite number of discrete realizations of uncertain parameters. Furthermore, a nuance in this work is the application of a stochastic forecasting model to generate demand scenarios. Multi-objective optimization is useful  for addressing  simultaneously conflicting supply chain performance metrics such as customer service and economics. A Pareto frontier is generated to illustrate the trade-off existing between these metrics. Furthermore, this paper proposes an approach to reduce the conservativeness of “open loop” decision making under uncertainty, by approximating the closed loop prediction of uncertainty propagation with two-stage stochastic programming. The formulation is applied to the SCM of a multi-product supply chain. Through simulation, the robust framework is shown to provide a substantial reduction in the occurrence of back orders when compared with a nominal MPC implementation.  Additionally, the “closed loop” approach provides an equivalent level of customer service at a reduced operating cost, when compared with the “open-loop” approach to robust MPC.

This paper will present the following: (i) a mathematical formulation of the dynamic supply chain model describing the hybrid system, (ii) details of the “open loop” and approximated “closed loop” approach to robust MPC applied to SCM, and (iii) results of a case study where the formulation is applied to the control of a multi-product supply chain. Additionally, key challenges and future avenues for research are identified.

References

Kothare, M., Balakrishnan, V., and Morari, M. (1996). Robust constrained model predictive control using linear matrix inequalities. Automatica, 32, 1361–1379.

Li, X. and Marlin, T. (2009). Robust supply chain performance via model predictive control. Comput. Chem. Eng., 33, 2134–2143.

Mestan, E., Turkay, M., and Arkun, Y. (2006). Optimization of operations in supply chain systems using hybrid systems approach and model predictive control. Ind. Eng. Chem. Res., 45, 6493–6503.

Perea-Lopez, E., Ydstie, B., and Grossmann, I. (2003). A model predictive control strategy for supply chain optimization. Comput. Chem. Eng., 27, 1201–1218.

Sarimveis, H., Patrinos, P., Tarantilis, C., and Kiranoudis, C. (2008). Dynamic modeling and control of supply chain systems: A review. Comput. Oper. Res., 35, 3530–3561.

Wang, W. and Rivera, D. (2008). Model predictive control for tactical decision-making in semiconductor manufacturing supply chain management. IEEE Transactions on Control Systems Technology, 16(5), 841 –855.