Data-driven Robust Optimization Research Articles

Sustainable cold supply chain design for livestock and perishable products using data-driven robust optimization

ABSTRACT Food products are a critical part of everyday life. To increase the efficiency of the food supply chain, designing a comprehensive mathematical is necessary. This study tries to optimize a protein supply chain. This supply chain is divided into livestock and perishable products. The integration of these two supply chain echelons has been applied to create an extensive model. Moreover, sustainability has been considered as a competitive advantage in the chain. Perishable products are temperature-sensitive. Hence, a cold supply chain has been considered. The model has three objective functions: maximizing the total profit, minimizing the storage cost in the cold chain, minimizing the health risk. In dealing with uncertainty, a data-driven robust optimization method has been used. Therefore, this paper used machine learning to construct the uncertainty sets from historical data. The Torabi-Hassini method has been implemented to solve the multi-objective model. Finally, to show the applicability and efficiency of the proposed approach, a real-world case study on the poultry supply chain, including abattoirs, breeding centers, slaughtering, and selling branches, has been applied. The result shows that this methodology significantly influences total profits and improves the environmental criteria in a real-world case study. Moreover, different sensitivity analyses have been prepared to help managers make a trade-off between the robustness of the model and objective function value with various weights and calculate the influence of supply chain integration on objective functions.

Data-driven robust optimization based on position-regulated support vector clustering

The changes experienced in integrating machine learning and data science into mathematical programming over the past decade remain unprecedented. They have created a novel optimization component under deep uncertainty known as “Data-Driven Robust Optimization” (DDRO). It considers a dataset's complexity, hidden information, and inherent form when creating data-driven uncertainty sets. One of the more practical machine learning algorithms for creating data-driven uncertainty sets is support vector clustering (SVC). There are no prerequisites for preliminary information to generate uncertainty sets with arbitrary geometry. Moreover, it can regularize the conservatism level and adjust a balance between the magnitude of the uncertainty set and information loss by a control parameter. Despite being superior and effective, SVC needs help selecting the best value for the trade-off parameter. This parameter impacts the robustness of the solution and the ability of SVC to handle information loss; hence, it must be accurately determined. Irrational data elimination as outliers alters the degree of conservatism, resulting in information loss and suboptimal solutions. This paper seeks to remedy this problem by suggesting position-regulated support vector clustering (PRSVC) to involve the importance of each data point in estimating the trade-off parameter. Experiments on artificial and real-world data collections indicate that, in comparison to the current SVC-based model, the proposed approach offers a more accurate decision boundary.

A data-driven robust optimization in viable supply chain network design by considering Open Innovation and Blockchain Technology

The research proposes a new method for Viable Supply Chain Network Design (VSCND) that incorporates Open Innovation (OI) and Blockchain Technology (BCT). A robust stochastic optimization and Conditional Value at Risk (CVaR) in the cost function is utilized to develop the model. This model's objective function incorporates the expected value, maximum cost, and CVaR cost. The OI and BCT platforms are suggested for an antifragile policy against disruption. In addition, CO2 emissions and energy consumption are proposed as sustainability requirements. Eventually, minimum demand satisfaction and resilience facilities by incorporating capacity based on specific scenarios are added to the model for an agile strategy. This research entails several parties, including vendors supplying the primary components and manufacturers creating products based on customer preferences. OI and BCT platforms aim to receive demand based on customer specifications and facilitate rapid transactions between components. Risk-averse decision-makers utilize a polyhedral Data-Driven Robust Optimization (DDRO) approach to manage uncertainty and flexible sets. Incorporating OI and BCT as antifragility instruments resulted in a 0.2% cost reduction for VSCNDOIBCT compared to when OI and BCT were not considered. This research suggests that integrating OI and BCT positively affects SC performance overall. The decreasing rate, DDRO coefficient, agility rate, demand variation, and problem size were subjected to a sensitivity analysis.

Decarbonizing OCP

Problem definition: We present our collaboration with the OCP Group, one of the world’s largest producers of phosphate and phosphate-based products, in support of a green initiative designed to reduce OCP’s carbon emissions significantly. We study the problem of decarbonizing OCP’s electricity supply by installing a mixture of solar panels and batteries to minimize its time-discounted investment cost, plus the cost of satisfying its remaining demand via the Moroccan national grid. OCP is currently designing its renewable investment strategy, using insights gleaned from our optimization model, and has pledged to invest 130 billion Moroccan dirham (MAD) (approximately 13 billion U.S. dollars (USD)) in a green initiative by 2027, a subset of which involves decarbonization. Methodology/results: We immunize our model against deviations between forecast and realized solar generation output via a combination of robust and distributionally robust optimization. To account for variability in daily solar generation, we propose a data-driven robust optimization approach that prevents excessive conservatism by averaging across uncertainty sets. To protect against variability in seasonal weather patterns induced by climate change, we invoke distributionally robust optimization techniques. Under a 10 billion MAD (approximately 1 billion USD) investment by OCP, the proposed methodology reduces the carbon emissions that arise from OCP’s energy needs by more than 70%, while generating a net present value (NPV) of 5 billion MAD over a 20-year planning horizon. Moreover, a 20 billion MAD investment induces a 95% reduction in carbon emissions and generates an NPV of around 2 billion MAD. Managerial implications: To fulfill the Paris climate agreement, rapidly decarbonizing the global economy in a financially sustainable fashion is imperative. Accordingly, this work develops a robust optimization methodology that enables OCP to decarbonize at a profit by purchasing solar panels and batteries. Moreover, the methodology could be applied to decarbonize other industrial consumers. Indeed, our approach suggests that decarbonization’s profitability depends on solar capacity factors, energy prices, and borrowing costs. History: This paper has been accepted as part of the 2023 Manufacturing & Service Operations Management Practice-Based Research Competition. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.0467 .

Inventory planning for self-serve pharmacy kiosks: A fill rate maximization approach

In recent years, self-serve kiosks have become increasingly popular due to their 24/7 availability and lower setup and operational costs compared to traditional brick-and-mortar stores. However, the inventory planning for pharmacy kiosks is a challenge due to its limited capacity to store thousands of drugs ordered in various quantities, each with low and sporadic drug demand. In this work, we model the pharmacy kiosk inventory planning problem as a capacitated multiproduct newsvendor problem under fill rate maximization objective. We present a data-driven robust optimization framework where product demand lies within an uncertainty set generated from product clustering. A column-and-constraint generation based solution approach is proposed to solve industry scale instances. The proposed robust framework is tested on actual pharmacy sales data and randomly generated instances with 2000 products. The robust solutions outperform scenario-based stochastic solutions with an increase in out-of-sample fill rate of 5.8%, on average, and of up to 17%. Comparative analysis with profit objective reveals that the fill rate objective results in 17% higher out-of-sample fill rate by compromising 20% in profits, on average.

Data-driven robust optimization to design an integrated sustainable forest biomass-to-electricity network under disjunctive uncertainties

The consequences of using costly, nonrenewable, and nonsustainable fossil fuels have forced countries to focus on renewable energy resources. In addition, the necessity of smooth material and information flow in the supply chain has motivated scholars to invent different mathematical approaches to designing an integrated supply chain. Such an integrated biomass-to-electricity supply chain can guarantee smooth material and information flow in the supply chain. To this end, a data-driven robust optimization approach under disjunctive uncertainties is developed for designing and optimizing an integrated sustainable biomass-to-electricity supply chain network. Instead of assuming uncertain parameters data to be less scattered or almost uniform, an uncertainty set based on data with disjunctive structures is proposed to identify the uncertainty space more accurately and flexibly. Specifically, the data on uncertain parameters are clustered using the K-means technique. Then, the primary uncertainty sets are formed for each cluster. The proposed uncertain parameter space is constructed by incorporating these primary uncertainty sets, which form using support vector clustering. We studied a case in Iran to probe the performance of the proposed approach. The computational results indicate that the proposed framework provides maximum protection against disjunctive uncertainty with minimum robustness price.

Data-driven robust optimization of dual-channel closed-loop supply chain network design considering uncertain demand and carbon cap-and-trade policy

With the popularization of Internet applications and the development of e-commerce, the number of online consumers is constantly increasing. This study aims to provide a framework for a sustainable and environmentally friendly closed-loop supply chain network with dual-channel (online channel and offline channel). The goal is to assist managers in making economically and environmentally sustainable decisions. Accordingly, a multi-period mathematical model is designed to address the challenges of the appliance industry, which faces uncertain demand. The model considers the carbon cap-and-trade policy, the regional protection policy of the retailer, and multiple transport modes in the design of the supply chain network. To handle demand uncertainty, we propose a robust model that utilizes a data-driven polyhedral uncertainty set based on principal component analysis and kernel smoothing methods and transforms the robust model into a mixed-integer linear programming problem. Additionally, we present a two-stage adaptive genetic algorithm to effectively tackle the large-scale and complex nature of the supply chain network. Extensive computations are performed to verify the algorithm's effectiveness. Finally, sensitivity analysis is conducted on key parameters to gain valuable insights. The results demonstrate that an increase in online consumers can significantly reduce stockouts, while an increase in uncertain demand leads to a substantial increase in the total cost.

Data-driven robust optimization for a multi-trip truck-drone routing problem

Using drones along with conventional vehicles, such as trucks, can potentially improve the cost-effectiveness and speed of delivery operations. This research considers a multi-trip truck-drone routing problem under uncertainty. Each truck is allowed to take multiple trips from the depot,while each drone is allowed to perform a single trip from the launch locations. Based on customer preferences, deliveries are grouped into deliveries by trucks to distribution centers and deliveries by drones from distribution centers to customers. A mixed-integer linear programming model is formulated to minimize the sum of the waiting times of all customers. To deal with uncertainty, a new two-stage clustering algorithm that uses multiple-kernel learning-based and single-kernel learning-based methods is introduced to construct uncertainty sets. In the case of column-wised uncertainty, a two-stage clustering with a dimensional separation algorithm is developedto avoid over-conservatism.A two-step solution method is provided for solving the proposed robust model to reduce the CPU time. The performance of the proposed algorithms is evaluated on several test problems. The results indicate that the developed algorithms can effectively avoid over-conservatism, reduce variables and constraints of the data-driven robust counterpart model, and reduce the CPU time required to solve the problem.

Robust active yaw control for offshore wind farms using stochastic predictive control based on online adaptive scenario generation

Subject to the inherent high uncertainty of wind, the prediction for its speed and direction may be insufficiently accurate, the resulting decision actions of active yaw control (AYC) may degrade the power gain. Therefore, this paper proposes a data-driven stochastic model predictive control (SMPC) using adaptive scenario generation (ASG) for offshore wind farm AYC. First, to build precise scenarios under the nonstationary variation of wind, an adaptive method based on Gaussian mixture model (GMM) clustering is proposed to allow online scenario identification with a compact construction. Specifically, GMM is constructed offline and two online mechanisms are developed for adaptive learning ability. To immunize the power maximization of AYC against prediction error, a data-driven robust optimization strategy is presented to realize SMPC based on generated scenarios. In order to enable real-time operation for large-scale wind farms, a novel parallel marine predator algorithm (PMPA) introduced population improvement strategy is developed to solve the robust problems with a quite lower computational burden. Finally, the simulation based on realistic wind data demonstrates the adaptive learning capacity of the proposed ASG. The result shows that the SMPC can improve the power gain by an average of 2.64% compared to the baseline predictive control.

A Novel Weighted Data-Driven Robust Optimization Approach for Creating Adjustable Uncertainty Sets

Robust optimization provides a progressive and efficient approach to dealing with uncertainty which applies to various optimization problems. However, most existing robust optimization approaches generate a unique uncertainty set for each level of conservatism, disregarding supplementary information such as predicted values. This paper proposes a new weighted data-driven robust optimization approach for creating adjustable uncertainty sets. The proposed approach enables the adjustment of the boundary reduction rate of uncertainty sets, effectively pulling uncertainty sets towards areas of higher density or towards the predicted points. Additionally, a multi-stage clustering algorithm is proposed to fully cover the areas around the predicted point. A regularization parameter search algorithm is also developed to tune the conservatism degree. The numerical results indicate that by weighting historical data, adjustable uncertainty sets with the same fraction of data coverage can be created that ensures the feasibility of the model and reduces the extra conservatism.

Data-driven robust portfolio optimization with semi mean absolute deviation via support vector clustering

Data-driven robust portfolio optimization with semi mean absolute deviation via support vector clustering

Data-driven robust optimization for contextual vehicle rebalancing in on-demand ride services under demand uncertainty

The rebalancing of idle vehicles is critical to mitigating the supply–demand imbalance in on-demand ride services. Motivated by a ride service platform, this paper investigates a short-term vehicle rebalancing problem under demand uncertainty in the presence of contextual data. We deploy a novel data-driven robust optimization approach that takes a direct path from “Data” to “Decision” instead of the predict-then-optimize paradigm and leverages the prediction problem structure to seamlessly integrate demand predictions with optimization models. We further develop a risk-based uncertainty set to evaluate how well uncertain demand is estimated from contextual data by prediction models, and discuss the classes of prediction models that are highly compatible with robust optimization models. Based on the convex analysis and duality theory, we reformulate the original models into equivalent Mixed Integer Second Order Cone Programmings (MISOCPs) that are solvable via state-of-the-art commercial solvers. To solve large-scale instances, we utilize the affine decision rule technique to derive polynomial-sized reformulations. Extensive experiments are conducted on the instances based on a real-world on-demand ride service in Chengdu. The computational experiments demonstrate the promising performance of our rebalancing strategies and solution approaches.

A data-driven robust design optimization method and its application in compressor blade

The probability-based robust optimization methods require a large amount of sample data to build probability distribution models of uncertain parameters. However, it is a common situation that only scarce sampled data are available in practice due to expensive tests. This study proposes a data-driven robust optimization framework by embedding a novel uncertainty quantification (UQ) method, which can quantify the uncertainty based on the statistical moments of scarce input data. The computational robustness and accuracy of the developed UQ methods are validated. Then, the data-driven multi-objective optimization framework is applied to improve the mean performance and aerodynamic robustness of a two-dimensional compressor blade with real stagger angle errors. Uncertainty analysis shows that there is a probability of 47.55% to deviate from the nominal total pressure loss coefficient by more than 1% for the actual performance values at high positive incidence i=7° condition. In the optimization process, the total pressure loss coefficient is selected as the objective function, while the static pressure ratio is used as a constraint. The Gaussian process regression model is trained to improve the robust optimization efficiency. The robust optimization is conducted under the most sensitive conditions. Optimized results indicate that compared with the nominal blade, the mean performance of the selected robust blades is increased by 10.9%, 8.56%, and 0.83%; the performance dispersion is decreased by 19.0%, 24.8%, and 35.3%, respectively. The optimized results can provide useful references for the robust design of compressor blades.

Multi-objective robust optimal bidding strategy for a data center operator based on bi-level optimization

This paper develops an optimal bidding strategy for a data center operator (DCO) participating in the day-ahead electricity market. The DCO is regarded as a price maker managing several data centers (DCs) located in different buses of the transmission network (TN) with local renewable power generators. Based on the Stackelberg game theory, a bi-level optimization model is established to minimize operating costs and carbon emissions while spatial and temporal dispatches of workload are performed. The bi-level optimization model is transformed into a single-level using the Karush–Kuhn–Tucker technology and linearized equivalently. The Pareto set is obtained using the epsilon constraint method. Then TOPSIS combined with Shannon entropy is used to select the optimal solution. In addition, data-driven robust optimization is employed to tackle uncertainties of renewable power generations. A DCO containing four DCs and an adapted IEEE 14-bus TN are used for the case study. The results show that dispatches of workload reduce operating costs and carbon emissions significantly. Moreover, it is better to regard the DCO as a price maker than a price taker. Finally, the results with different uncertainty budgets are analyzed. All the results and analysis demonstrate the superiority of the optimal bidding strategy proposed in this paper.

Privacy-preserving energy trading management in networked microgrids via data-driven robust optimization assisted by machine learning

Trading mechanism design, uncertainty treatment and privacy protection are the main issues in the energy management of networked microgrids (MGs). To address these issues in a comprehensive manner, this paper proposes a data-driven two-level transactive energy management framework, where the upper-level determines the optimal strategies of internal scheduling within MGs and external trading between MGs while the lower-level formulates a Nash bargaining game model for the fair allocation of trading benefits. The uncertainties of renewable energy sources are fully captured by an adjustable data-driven robust optimization approach with an uncertainty set constructed using the robust kernel density estimation (RKDE) as a machine learning technique. The resulting uncertainty set can provide robust scheduling and trading schemes even when the power generation data of wind turbines and photovoltaic systems are contaminated with anomalous samples, whereas conventional sets are not reliable in the case of contaminated data. To preserve the operational independence and information privacy of MGs, the proposed model is solved in a distributed manner by the alternating direction method of multipliers (ADMM) and the augmented Lagrange-based alternating direction inexact Newton (ALADIN) algorithms. ADMM is commonly used in previous studies, but it has low computational efficiency for handling the consensus process among a large number of MGs. This paper applies ADMM and ALADIN to enhance the applicability of the proposed model when the size and complexity of the networks increase. Numerical tests show the effectiveness of the proposed framework and solution methodology in terms of system cost, solution robustness, and convergence speed.

A new data-driven robust optimization approach to multi-item newsboy problems

<p style='text-indent:20px;'>A newsboy problem is a typical stochastic inventory management problem and has extensive applications in the fields of operational research, management sciences and marketing sciences. One of the challenges underlying such problems is to handle the uncertainty of demands. In the existing results, it is often to assume that the demand distribution is given to facilitate solution of the problems. In this paper, a novel data-driven robust optimization model for solving multi-item newsboy problems is proposed by combining the absolute robust optimization with a data-driven uncertainty set, and the latter is leveraged to address the uncertainty of demands. For the single-item situation, a closed-form solution is obtained and influences of parameters on the optimal solutions are analyzed. Owing to complexity of the multi-item situation, a uniform smoothing function is leveraged to smooth the proposed model. Then, an algorithm, called a modified Frank-Wolfe feasible direction algorithm, is developed to solve a series of smooth subproblems. Numerical simulation demonstrates that the proposed model in this paper can reduce over-conservation of robust optimization methods and is more robust than other similar well-established methods in the literature. By numerical simulation and sensitivity analysis, it is concluded that: (1) The proposed method can provide more stable optimal order policy and profits than the existing ones; (2) For a product with a higher unit purchase price, the optimal order quantities are more sensitive to its change; (3) In view of profitability, the newsboy should not to be too risk-averse.</p>

Data-Driven Robust Optimization of the Vehicle Routing Problem with Uncertain Customers

With the increasing proportion of the logistics industry in the economy, the study of the vehicle routing problem has practical significance for economic development. Based on the vehicle routing problem (VRP), the customer presence probability data are introduced as an uncertain random parameter, and the VRP model of uncertain customers is established. By optimizing the robust uncertainty model, combined with a data-driven kernel density estimation method, the distribution feature set of historical data samples can then be fitted, and finally, a distributed robust vehicle routing model for uncertain customers is established. The Q-learning algorithm in reinforcement learning is introduced into the high-level selection strategy using the hyper-heuristic algorithm, and a hyper-heuristic algorithm based on the Q-learning algorithm is designed to solve the problem. Compared with the certain method, the distributed robust model can effectively reduce the total cost and the robust conservatism while ensuring customer satisfaction. The improved algorithm also has good performance.

A bi-level model integrating planning and scheduling for the optimization of process operation and energy consumption of a PVC plant under uncertainty

PVC production by the calcium carbide method is a typical hybrid system consisting of continuous and intermittent processing, and the optimization of the whole process scheduling is of practical significance. Still, the existence of uncertain factors in the external environment and production process makes it challenging to continue to implement deterministic scheduling. This paper, therefore, proposes an integration model, the discrete-time method applied in the planning layer, and the chance-constrained programming used to deal with external uncertainties. The continuous-time modeling method based on event points is adopted in the scheduling layer, and the optimization of equipment-level operations with variable production rates is performed. Then, the data-driven robust optimization method is applied to deal with endogenous uncertainty based on the data-driven flexible uncertainty set. Finally, the results provide valuable guidance to improve the robustness and stability of the production system under uncertainty. The comparative results verify the effectiveness and superiority of the proposed model in total cost and energy consumption.

Multi-stage robust clearing model considering renewable energy output uncertainty and unit effective reserve calculation in electricity market

With the advancement of China’s carbon policy, the proportion of renewable energy, mainly wind and solar, has increased, which brings greater challenges to the reservation of power systems. Due to the complexity of China’s power systems, adopting the method of the zonal reserve to ensure stable system operation is very difficult. Among the existing clearing results for calculating reservation, the unit reservation will be restricted by the network security constraints, leading to system operation risks. To obtain the unit reservations efficiently without breaking the security constraints, this paper proposes an effective reserve calculation method for engineering implementation. A box robust optimization is further utilized for Security Constrained Unit Commitment in the method to ensure the consumption of renewable energy, and the stability and clearing efficiency of the power system. Furthermore, a data-driven robust random optimization is employed for Security Constrained Economic Dispatch optimizing the economy of power systems. This multi-stage robust optimization model, which has good extensibility, is in line with China’s clearing process. The simulation analysis based on the actual operation data of a province in China and the IEEE 300-bus system verifies the correctness and feasibility of the proposed model and theory.

A novel predict-then-optimize method for sustainable bike-sharing management: a data-driven study in China.

Sustainable operations management will appeal to the post-pandemic world. As the economy recovers, the surging demand for low-carbon bike-sharing has led to exacerbated mismatch in urban transportation. It is a serious challenge to optimize the reallocation schedule of sharing bikes among multiple positions in a network. To address the problem, we develop a novel predict-then-optimize method consisting of a data-driven robust optimization model and a branch-and-price algorithm. The optimization model derives the predicted demand surplus of each position based on historical data, enabling the optimal reallocation schedule in the network at minimum operational costs. Based on the prediction, the branch-and-price algorithm can find out the best routes of assigning bikes to specific positions that further improves transportation efficiency. Finally, we deploy the predict-then-optimize method to a realistic bike-sharing network in one major city of China. The computational results demonstrate that our method can significantly save the cost of operations and reduce the waste of resources. Therefore, the novel predict-then-optimize method has a great potential to facilitate the sustainable development of bike-sharing systems in urban transportation.