Closed-loop data-driven robust optimization framework for planning supply chain networks

Because of the impact the realizations of uncertainties have on planned systems, much of research works and efforts have been focused on incorporating uncertainties into optimization modelling. A common approach to optimize under uncertainty is the robust optimization paradigm because it only requires minimal amount of information on the underlying distribution of the uncertainty parameters and resolves into counterpart problems that are computationally tractable. However, a main weakness of the robust optimization approach is its tendency to produce overly conservative solutions. The target oriented robust optimization (TORO) is an approach that has been previously developed to address this issue. Unlike the classical robust optimization technique, the TORO approach converts the original objectives to system performance targets and seeks to instead maximize an uncertainty budget referred to as the robustness index while ensuring that system targets are satisfied. Another approach to address the pessimism of robust optimization solutions is the use of data-driven machine learning modelling techniques to tighten the uncertainty sets of the uncertain parameters. However, these existing approaches operate only on a one-way sequential flow, where the data-driven estimation module and the optimization module implement their respective tasks independently from each other. This overlooks the potential of capturing a feedback channel within the solution framework to update forecasts and decisions based on the most recent realizations of the uncertainty and system outcomes. Thus, this research proposed a closed-loop data-driven robust optimization framework and its application to multi-stage production and logistics planning problems experiencing endogenous uncertainties. Two illustrative case studies were explored and presented to illustrate the capabilities of the proposed closed-loop data-driven target-oriented robust optimization approach. The proposed framework is applied to an ATM cash replenishment and routing problem, which combines two common problem classes in supply chain management, namely (1) inventory planning and (2) vehicle routing problem. The objective is to determine the optimal schedule and amounts of cash replenishments made to each ATM and the routes taken each period that minimizes costs incurred from holding costs, transportation costs, replenishment costs, and stockout penalties while facing uncertainties in daily deposit and withdrawal transactions. A hypothetical case study with synthetically generated historical data on individualized ATM deposit and withdrawal transactions per day is solved to demonstrate the framework. Furthermore, three levels of the case study are shown, particularly using (1) the classical robust optimization approach, (2) the TORO approach, and (3) the TORO approach incorporating the consideration of stockout-dependent demand forecasts. Similarly, the proposed framework is demonstrated on a retail supply chain distribution problem. The primary aim of the problem is to determine the optimal distribution flow and inventory schedule in each facility within each echelon of the supply chain, which are composed of suppliers, warehouses, and stores such that profits are maximized while under demand uncertainties. The closed-loop data-driven TORO solutions were obtained using data from Turkish retail company. Computational experiments through solving each problem and implementing Monte Carlo simulation on the solutions obtained show that the robust optimization solutions, both those obtained from the classical robust approach and TORO methodology, are relatively immune to uncertainty realizations compared to the deterministic solution. However, it is apparent that the classical robust solution is too conservative. The performance of the TORO solutions is competitive or better than the robust and deterministic solutions in terms of solution stability and system performance. Additionally, comparing solutions obtained through the proposed closed-loop framework against solutions generated using the traditional open-loop approach illustrated that the conventional methods result in conservative and less robust solutions. Finally, instead of planning using inaccurate forecasts and pessimistic scenarios, the closed-loop framework enables newly available information to be leveraged to update forecasts and optimal decisions dynamically leading to improved outcomes. Overlooking dynamic relationships of endogenous uncertainties led to planned systems that are unable to satisfy system objectives. Lastly, the closed-loop data-driven TORO framework allows decision-makers to select among an array of solutions depending on their risk appetites and allows for faster turnaround to decision making as the optimization problems retain their computational tractability