(471f) Real-Time Supply Chain Optimization Using Deep Learning-Based Model Predictive Control

A supply chain is composed of entities such as suppliers, manufacturers, distributors, and retailers. It performs key functions of purchasing raw materials, manufacturing products, and distributing products to satisfy customers’ demand (Mastragostino et al., 2014). These entities are typically involved in the upstream and downstream flows of materials, products, information, and finances. The smooth and efficient operation of a supply chain system is critical to an enterprise in achieving satisfactory economic performance and maintaining competitiveness in a global market.

For a large-scale supply chain system, the constrained optimization models are often large and complex, and solving them in a reasonable time is challenging in many applications (Schildbach and Morari, 2016). The computational burden increases when integer decision variables and nonlinearity are involved (Schulz et al, 2005). Moreover, when uncertainty associated with the parameters of the optimization problems is considered, the problem formulation becomes more complex. A popular method for operational supply chain optimization under uncertainty is stochastic programming. In two-stage stochastic programming, uncertain parameters are typically represented by a set of scenarios in accordance with a probability distribution. The expectation of the objective function over the set of scenarios is optimized subject to common first-stage decisions. For adequate characterization of the uncertainty, the number of scenarios could be very large. Therefore, stochastic programs are often difficult to solve due to their high dimension and complexity that increase with the number of scenarios. Finding the optimal solution of stochastic linear programming or mixed-integer linear programming problems can be time-consuming (Mastragostino et al., 2014; Torres et al., 2022). This indicates that real-time supply chain optimization is challenging in many cases.

Traditional supply chains are experiencing an evolution into digital supply chains and entering the era of Supply Chain 4.0 (Frederico et al., 2020). To meet the real-time property required by Supply Chain 4.0, a real-time supply chain control technique is needed. To this end, this work investigates a deep learning-based model predictive control (DLMPC) technique for supply chain operations. MPC is a multivariable control method that utilizes a system model to predict future system states and determine optimal control inputs (Qin and Badgwell, 2003). This technique has been widely applied to industrial processes and then introduced to supply chain systems. An MPC problem in the form of a linear program (LP) or quadratic program (QP) can be formulated as a multi-parametric LP or QP by considering the current system state as parameters. Its optimal solution is a piecewise affine function that depends only on the current state, which can be precomputed offline and stored for online use. However, as the planning horizon and the number of constraints increase, the required storage increases exponentially, which makes it difficult to obtain and apply the explicit MPC law. This has motivated the development of the deep learning-based explicit MPC technique, in which an artificial neural network is used to approximate the explicit MPC laws (Karg and Lucia, 2020; Kumar et al., 2021). DLMPC can still be applied when the problem is a nonlinear or mixed-integer MPC. Considering the computational burden of optimal control of large-scale supply chains, this technique would seem to have potential in aiding real-time supply chain control.

This work presents a DLMPC method for operational supply chain optimization in real time. The method follows an offline-online procedure. In the offline phase, the state-space model of a supply chain system is developed and the MPC problem for supply chain operation is formulated. Then, the MPC problem is solved for a set of initial states to obtain the corresponding optimal inputs. A deep neural network (DNN) is built and trained by using the optimal state-input pairs as training data to approximate the optimal MPC law. In this work, the supply chain MPC problem is formulated as a mixed-integer linear program. The proposed method considers past inputs at each decision period and accommodates time delays in the system. In the online phase, the DNN controller is employed to provide real-time decisions. A heuristic method is developed for feasibility recovery with the binary decision variables taken into account. Furthermore, a data generation method that utilizes both random samples and closed-loop simulation samples is presented, which can avoid overfitting and improve overall accuracy.

The proposed supply chain control method is validated on two case studies through closed-loop simulation. The first one involves a linear MPC problem, and the second one involves a more complicated mixed-integer linear MPC problem. Results show that DLMPC can achieve high accuracy in approximation of MPC decisions and a significant reduction in the online computation time. The average loss in closed-loop performance in the two cases is 0.43% and 1.8%, respectively. This technique represents a shift toward removing the cap on the complexity of the online optimization problem, and thus more sophisticated formulations can be adopted for real-time decision-making. Another advantage is that it avoids the need for an optimization solver in real-time execution.

References

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Karg, B., Lucia, S., 2020. Efficient representation and approximation of model predictive control laws via deep learning. IEEE Transactions on Cybernetics 50, 3866-3878.

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Mastragostino, R., Patel, S., Swartz, C.L.E., 2014. Robust decision making for hybrid process supply chain systems via model predictive control. Computers & Chemical Engineering 62, 37-55.

Qin, S.J., Badgwell, T.A., 2003. A survey of industrial model predictive control technology. Control Engineering Practice 11, 733-764.

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Torres, J.J., Li, C., Apap, R.M., Grossmann, I.E., 2022. A review on the performance of linear and mixed integer two-stage stochastic programming software. Algorithms 15.