(61m) Perspective Reformulation of Stochastic Agrochemical Supply Chain Optimization Problem with Mean-Variance Risk Management

The global agrochemical industry presents a notably consolidated landscape wherein dominant multinational corporations hold substantial market shares. As a result, the supply chain of a single agrochemical commodity is conventionally known by an intricate network of pathways linking its origins from raw material sources to its ultimate consumers. Beyond its structural intricacy, the supply chain of agrochemicals is vulnerable to distinctive uncertainties arising from seasonal fluctuations and other impactful factors, thus necessitating the development and implementation of popular risk management tools and strategies. In this study, we model and optimize an agrochemical supply chain by developing and solving a scenario-based stochastic mixed-integer quadratic constrained program (MIQCP) using the mean-variance method to manage costs associated with demand loss or exceeded demand. We apply the perspective reformulation technique [1] to linearize the non-convex quadratic constraint (variance). This converts the problem from a non-convex MIQCP to a MILP. We solve the original MIQCP and reformulated MILP in several illustrative case studies with different sizes and compare the computational performance and results. We find that iteratively introducing perspective cuts to the reformulated MILP continuously improves the dual bound and solution time. Depending on the problem size, the reformulated MILP achieves either the global optimal solution in less computational time or a better local optimal solution within the same time compared to the original MIQCP. We conclude that perspective reformulation can be a powerful technique to solve large-scale non-convex quadratic constrained supply chain optimization problems.

References:

[1] Günlük, O., Linderoth, J. (2012). Perspective Reformulation and Applications. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY.