(614b) Raw Material Procurement Planning Under Uncertainty with MPC Implementation

The operation of a supply chain typically involves numerous units with many degrees of freedom by which to optimally manipulate the performance of a large network. Optimization at any period in time must therefore consider several important factors such as purchasing of raw materials and the managing of inventory levels. While local optimization of process units may lead to improved performance for the individual units, it fails to address the overall operation of the chain from which the units belong. Essentially, a lack of communication between nodes will result in suboptimal performance. By seeking to optimize the entire chain, greater economic benefits can be obtained.

When considering optimization of a process from the raw material procurement to final product, it is important to note the uncertainty inherent in all industrial environments. Uncertainties can reside in such aspects as raw material quality and customer demand. Often, overestimation of uncertainty is used along with hard constraints to solve these special optimization problems. This leads to very conservative planning decisions and thus diminishes chain profitability. This problem can be circumvented in the model through the use of chance constraints as studied by both Li et al. (2008) and Zhang et al. (2002). Rather than operate in a conservative manner with respect to uncertainty, a more aggressive technique is used, where constraints are softened to allow for violations. Certain constraints are therefore violated based on a user specified confidence level, which translates to an increase in the profit objective function value.

Careful planning must be completed in order to for the chain to operate efficiently under these uncertainties. In order to manage this network, logical decisions must be made in conjunction with the settings for continuous decision variables. A mixed integer approach is well suited to appropriately model a process with both continuous variables and logical decisions. This has been recently studied by both Perea-Lopez et al. (2003) and Mestan et al. (2006) in which Model Predictive Control was used to optimize planning decisions using a rolling time horizon. At each time step, state variables, such as inventory levels, are updated and predictions are made using the initial plant conditions. A mixed-integer problem is then solved in order to make both continuous and binary planning decisions over the entire horizon. The solution for the first time period is then implemented as the set of optimal planning decisions.

An added benefit to planning with this MPC approach allows for the inclusion of feedback in the presence of production demand uncertainty. At each time step the model is corrected according to the measured demand and re-optimized accordingly.

A case study is examined based on an industrial example of steel production through the use of scrap metal. Various metals can be purchased at prices according to scrap type and quality. These scraps are charged to a batch furnace and melted into product. Depending on the grade of metal produced, the scraps must be blended in a way as to limit the amount of trace components in the final product. The uncertainty in scrap quality therefore has a large impact on the process.

The study shows how raw material purchasing, inventory management, and batch production can be planned using a mixed integer formulation with MPC implementation. The model incorporates raw material uncertainty with imbedded chance constraints and feedback using a rolling prediction horizon.

The purpose is to demonstrate the economic benefits of planning scrap purchases and steel production in a multiperiod setting. By bridging the gap between the purchasing and operation units, an intelligent planning scheme can be created that considers the economic costs of the integrated framework under uncertain market conditions.

Li, P., Arellano-Garcia, H., and Wozny, G. (2008). Chance constrained approach to process optimization under uncertainty. Computers and Chemical Engineering, 32, 25-45.

Mestan, E., Turkay, M., and Arkun, Y. (2006). Optimization of operations in supply chain systems using hybrid systems approach and model predictive control. Industrial and Engineering Chemistry Research, 45(19), 6493-6503.

Perea-Lopez, E., Ydstie, B. E., and Grossmann, I. E. (2003). A model predictive control strategy for supply chain optimization. Computers and Chemical Engineering, 27, 1201-1218.

Zhang, Y., Monder, D., and Forbes, J. F. (2002). Real-time optimization under parametric uncertainty: a probability constrained approach. Computers and Chemical Engineering, 12, 373-389.