(372am) Learning Production Planners’ Unknown Objectives Via Inverse Optimization

In the chemical industry, production planning decisions are often made in a two-step process. In the first step, an optimization model is solved to obtain a base schedule. Then, in the second step, a human planner examines this base schedule and modifies it based on real-world feasibilities and business priorities to arrive at the final schedule. Ideally, the base schedule aligns with what the human planner thinks is the optimal solution such that they simply need to approve it. However, in practice, modifications are often made to this base schedule. In most cases, this is because much of the human expert knowledge is not captured in the computational optimization model. Such knowledge is often derived from many years of experience and may be associated with anticipation of future uncertainties, knowledge about reliability issues specific to the plant, and insights into the customers’ needs that may warrant prioritization of some customers over others. As a result, the objective of the human planner, which is commonly a balance between multiple objectives, may be quite different from the one implemented in the optimization model. However, the human planner’s true objective is usually not explicitly known and/or difficult to quantify.

In this work, we develop a data-driven approach to learning a human planner’s unknown objective from historical demand information and the corresponding production scheduling decisions. There are two key desirable features in the learning of a decision-making model for a human planner: (i) Interpretability, since we ultimately aim to decipher the factors that have led to different scheduling decisions. (ii) Data efficiency, since typically only a few historical schedules are available to learn the model parameters from. Given these requirements, we apply an inverse optimization approach [1, 2] where the learned predictive model retains the form of an optimization problem, which eases the incorporation of existing domain knowledge into the model in the form of constraints. We try to learn the weights for the different terms in the objective function which signify how the human planner manages the various trade-offs involved in production planning (for example, keeping inventory low vs. fulfilling all customer order on time vs. minimizing the number of changeovers).

The proposed inverse optimization problem gives rise to a bilevel optimization problem where the lower-level problems are mixed-integer linear programs. To solve the problem, we apply a cutting plane method [3] where several algorithmic modifications are made to improve computational efficiency. The proposed approach is applied to a real-world case study provided by Dow, Inc. The results highlight the efficacy of the inverse optimization method and provide insights into the main factors considered by the human planners when making scheduling decisions.

References

[1] Chan, T. C., Mahmood, R., & Zhu, I. Y. (2023). Inverse optimization: Theory and applications. Operations Research.

[2] Gupta, R. & Zhang, Q. (2023). Efficient learning of decision-making models: A penalty block coordinate descent algorithm for data-driven inverse optimization. Computers & Chemical Engineering, 170, 108123.

[3] Wang, L. (2009). Cutting plane algorithms for the inverse mixed integer linear programming problem. Operations Research Letters, 37(2), 114-116.