Robust Counterpart Research Articles

Enhancing supply chain resilience facing partial and complete disruptions: The application in the cooking oil industry

Nowadays, food supply chains are more vulnerable to disruptions due to competition, uncertain environments, and global catastrophes such as the recent pandemic. Due to the importance of addressing disruption risks, this study develops a hybrid mechanism to enhance resilience in a multi-product supply chain. The proposed mechanism improves supplier resilience in a Cooking Oil Supply Chain (COSC) network design. First, we identify elements that affect supplier resilience and present a mechanism based on the Analytical Network Process (ANP) to evaluate resilience. In addition, several strategies are determined to enhance network resilience. Moreover, a stochastic mathematical formulation is proposed to utilize suppliers’ scores and a combination of identified strategies to strengthen supply chain resilience. The developed stochastic model encompasses three objectives and considers possible partial and complete disruptions of the supply chain network. Furthermore, we develop a robust counterpart formulation to handle the disruption uncertainty of the COSC and utilize the Normalized Normal Constraint (NNC) method to generate Pareto optimal solutions. Lastly, we put the implemented mechanism into practice in a real-world case to demonstrate its effectiveness in enhancing supply chain resilience. Likewise, we unveil that the implementation of suitable resilience strategies within the supply chain can lead to substantial improvements in performance metrics. For example, the results obtained illustrate that by embracing resilience strategies, the proposed mechanism has the potential to reduce the overall cost of the supply chain by as much as 56%.

Frailty in inflammatory bowel disease: analysis of the National Inpatient Sample 2015-2019.

Preoperative frailty has been associated with adverse postoperative outcomes in various populations, but of its use in patients with inflammatory bowel disease (IBD) remains sparse. The present study aimed to characterize the impact of frailty, as measured by the modified frailty index (mFI), on postoperative clinical and resource utilization outcomes in patients with IBD. This retrospective population-based cohort study assessed patients from the National Inpatient Sample database from 1 September 2015 to 31 December 2019. Corresponding International Classification of Diseases 10th Revision Clinical Modification codes were used to identify adult patients (>18 years of age) with IBD, undergoing either small bowel resection, colectomy or proctectomy. Patient demographics and institutional data were collected for each patient to calculate the 11-point mFI. Patients were categorized as either frail or robust using a cut-off of 0.27. Primary outcomes were postoperative in-hospital morbidity and mortality, whilst secondary outcomes included system-specific morbidity, length of stay, in-hospital healthcare costs and discharge disposition. Logistic and linear regression models were used for primary and secondary outcomes. Overall, 7144 patients with IBD undergoing small bowel resection, colectomy or proctectomy were identified, 337 of whom were classified as frail (i.e., mFI < 0.27). Frail patients were more likely to be women, older, have lower income and a greater number of comorbidities. After adjusting for relevant covariates, frail patients were at greater odds of in-hospital mortality (adjusted odds ratio [aOR] 5.42, 95% CI 2.31-12.77, P < 0.001), overall morbidity (aOR 1.72, 95% CI 1.30-2.28, P < 0.001), increased length of stay (adjusted mean difference 1.3 days, 95% CI 0.09-2.50, P = 0.035) and less likely to be discharged to home (aOR 0.59, 95% CI 0.45-0.77, P < 0.001) compared to their robust counterparts. Frail IBD patients are at greater risk of postoperative mortality and morbidity, and reduced likelihood of discharge to home, following surgery. This has implications for clinicians designing care pathways for IBD patients following surgery.

Robust Optimization of Vaccine Distribution Problem with Demand Uncertainty

This study proposes a multi objective optimization model for vaccine distribution problems using the Maximum Covering Location Problem (MCLP) model. The objective function of the MCLP model in this study is to maximize the fulfillment of vaccine demand for each priority group at each demand point. In practice, the MCLP model requires data on the amount of demand at each demand point, which in reality can be influenced by many factors so that the value is uncertain. This problem makes the optimization model to be uncertain linear problem (ULP). The robust optimization approach converts ULP into a single deterministic problem called Robust Counterpart (RC) by assuming the demand quantity parameter in the constraint function is in the set of uncertainty boxes, so that a robust counterpart to the model is obtained. Numerical simulations are carried out using available data. It is found that the optimal value in the robust counterpart model is not better than the deterministic model but is more resistant to changes in parameter values. This causes the robust counterpart model to be more reliable in overcoming uncertain vaccine distribution problems in real life. This research is limited to solving the problem of vaccine distribution at a certain time and only assumes that the uncertainty of the number of requests is within a specified range so that it can be developed by assuming that the number of demand is dynamic.

Robust two-stage optimization consensus models with uncertain costs

In the consensus-reaching process (CRP), decision-makers (DMs) frequently encounter the dilemma of too much uncertain information, which can lead the actual decision to deviate from the optimal solution obtained by the currently used consensus models. To do this, we construct two robust two-stage optimization consensus models with uncertain costs and obtain their robust two-stage counterparts. We then apply a Benders decomposition algorithm to solve the resulting models. Finally, the experimental results show that the new models are better suited for uncertain contexts and could help DMs produce more reliable choices.

En-route charge scheduling for an electric bus network: Stochasticity and real-world practice

Bus electrification, with its high energy conversion efficiency and zero tailpipe emissions, has a significant impact on addressing the petroleum crisis and lowering carbon emissions in urban transportation. However, long charging times and uncertain operational risks hinder their wider adoption. This paper explores the robust en-route charge scheduling problem for electric buses to overcome uncertain energy consumption while ensuring charging accessibility. The problem is first described as a deterministic mixed-integer linear programming model that employs a time-of-use electricity price to balance the charging demand. Additionally, a robust counterpart model is formulated to account for stochastic energy. Numerical studies are designed to evaluate the proposed model in a real network, followed by a sensitivity analysis to investigate the impact of battery type, fleet composition, and depth of discharge on the charging schedule. The results show that the robust optimization model provides system feasibility against uncertainty with a comparable price and emissions.

A sample robust optimal bidding model for a virtual power plant

In many energy markets, the trade amount of electricity must be committed to before the actual supply. This study explores one consecutive operational challenge for a virtual power plant—the optimal bidding for highly uncertain distributed energy resources in a day-ahead electricity market. The optimal bidding problem is formulated as a scenario-based multi-stage stochastic optimization model. However, the scenario-tree approach raises two consequent issues—scenario overfitting and massive computation cost. This study addresses the issues by deploying a sample robust optimization approach with linear decision rules. A tractable robust counterpart is derived from the model where the uncertainty appears in a nonlinear objective and constraints. By applying the decision rules to the balancing policy, the original model can be reduced to a two-stage stochastic mixed-integer programming model and then efficiently solved by adopting a dual decomposition method combined with heuristics. Based on real-world business data, a numerical experiment is conducted with several benchmark models. The results verify the superior performance of our proposed approach based on increased out-of-sample profits and decreased overestimation of in-sample profits.

Robust Short-Term Operation of AC Power Network With Injection Uncertainties

With uncertain injections from Renewable Energy Sources (RESs) and loads, deterministic AC Optimal Power Flow (OPF) often fails to provide optimal setpoints of conventional generators. A computationally time-efficient, economical, and robust solution is essential for ACOPF with short-term injection uncertainties. Usually, applying Robust Optimization (RO) for conventional non-linear ACOPF results in computationally intractable Robust Counterpart (RC), which is undesirable as ACOPF is an operational problem. Hence, this paper proposes a single-stage non-integer non-recursive RC of ACOPF, using a dual transformation, for short-term injection uncertainties. The proposed RC is convex, tractable, and provides base-point active power generations and terminal voltage magnitudes (setpoints) of conventional generators that satisfy all constraints for all realizations of defined injection uncertainties. The non-linear impact of uncertainties on other variables is inherently modeled without using any affine policy. The proposed approach also includes the budget of uncertainty constraints for low conservatism of the obtained setpoints. Monte-Carlo Simulation (MCS) based participation factored AC power flows validate the robustness of the obtained setpoints on NESTA and case9241pegase systems for different injection uncertainties. Comparison with previous approaches indicates the efficacy of the proposed approach in terms of low operational cost and computation time.

Integrated Forward and Reverse Cross-Docking with Vehicle Routing and Scheduling Under the Uncertainty of Inspection Results: A Genetic-Mathematic Algorithm

Despite the recognized advantages of cross-docking in forward logistics, very few studies have investigated reverse cross-docking, and these studies do not consider the operational uncertainties of returned products in the reverse flow, which is required in practice. This paper introduces a vehicle routing and scheduling problem for the integration of forward and reverse logistics, in which the cross-docking facility is employed as (i) the distribution center in forward flow and (ii) the collection and dispatching center of returned products in reverse flow. We present two modes based on the inspection point: (i) retailer site or (ii) cross-dock. A deterministic mixed integer linear programming model is presented for the retailer-site inspection mode to minimize the total operational costs. For the second mode, a robust optimization counterpart of the modified deterministic model is formulated to account for the uncertainties arising from the inspection results revealed at the cross-dock. A genetic-mathematic algorithm is proposed to solve the large-sized instances. Through numerical studies, we evaluated the performance of the algorithm and demonstrated cost reductions and truck utilization improvements as benefits of integration. Moreover, in sensitivity analyses using a quasi-real case of a personal electronic device supply chain, and employing simulation, the price of robustness of the second model was evaluated by considering various budget sets, which justified the full robustness and application of the cross-dock as the inspection point in the closed-loop supply chain.

The Association Between Multidimensional Frailty and Poor Venous Accesses in a Geriatric Population: A Retrospective Study.

Since the association between frailty and difficulty in finding venous access (VA) is largely unexplored and unclear in geriatrics, the aim of this study is to demonstrate how multidimensional frailty is associated with bad VA in a population of older hospitalized people. Multidimensional Prognostic Index (MPI), based on eight different domains usually assessed in comprehensive geriatric assessment, was used for identifying multidimensional frailty; VA heritage was investigated using a questionnaire prepared by a trained nurse, based on clinical experience. Overall, 145 patients were included (mean age 78.6 ± 7.6; males 51.0%). Frailer people, identified as an MPI >0.66 (MPI 3), had a significantly higher presence of bad VA (49.0% vs. 27.3% in MPI 3 and MPI 1 groups, p = 0.045), no success at first attempt (49.0% vs. 22.7% in MPI 3 and MPI 1 groups, p = 0.03), reported more frequently pain during VA attempts (63.3% in MPI 3 vs. 27.3 in MPI 1, p = 0.002), and significantly higher scores in the Numeric Rating Scale compared to their robust counterparts. Taking robust participants in MPI 1 as reference, after adjusting for potential confounders, frailer people (MPI 3) were at increased odds of bad VA (odds ratio [OR] = 2.72; 95% confidence interval [CI]: 1.16-6.41; p = 0.02), not success at first attempt (OR = 3.67; 95% CI: 1.09-12.57; p = 0.04), and presence of pain during VA attempt (OR = 4.26; 95% CI: 1.30-13.92; p = 0.02). In conclusion, our study demonstrated an association between multidimensional frailty and bad VA in a population of older hospitalized people.

Robust GEPSVM Classifier: An Efficient Iterative Optimization Framework

The proximal support vector machine via generalized eigenvalues (GEPSVM) is a well-known pattern classification method. GEPSVM, however, is prone to outliers due to its use of the squared L2-norm distance criterion. A robust GEPSVM version is proposed to tackle this problem using L1-norm distance optimization technique (GEPSVML1). As optimizing a GEPSVML1 with L1-norm terms can be challenging, we have developed an iterative algorithm to address the L1-norm ratio problem associated with GEPSVML1. Furthermore, an efficient iterative optimization framework has been developed to conveniently address related optimization problems. The research contribution of this paper lies in providing a theoretical analysis of the algorithm’s convergence. Besides, we find that the L1-norm distance-based methods in real-world applications, especially for handling samples with outliers, sometimes provides an unsatisfactory recognition result. Thus, a generalized version of GEPSVML1 is proposed. The L1-norm distance is replaced with a Lp-norm distance in GEPSVML1 (GEPSVMLp). It is the robust counterpart of GEPSVML1 and GEPSVM. It is worth noting that we fine-tune GEPSVMLp’s parameters to strike a balance between training time and classification accuracy, an especially crucial step for larger datasets. Our experiments indicate that the proposed GEPSVMLp is more efficient and robust than the competitors in numerous experimental settings. Overall, our work demonstrates the importance of developing robust pattern classification methods in the presence of outliers and provides a practical solution for handling such cases in real-world applications.

Exploring the metabolomics profile of frailty- a systematic review.

Frailty is a multifaceted geriatric syndrome characterized by an increased vulnerability to stressful events. metabolomics studies are valuable tool for better understanding the underlying mechanisms of pathologic conditions. This review aimed to elucidate the metabolomics profile of frailty. This systematic review was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-analysis (PRISMA) 2020 statement. A comprehensive search was conducted across multiple databases. Initially, 5027 results were retrieved, and after removing duplicates, 1838 unique studies were subjected to screening. Subsequently, 248 studies underwent full-text screening, with 21 studies ultimately included in the analysis. Data extraction was performed meticulously by two authors, and the quality of the selected studies was assessed using the Critical Appraisal Skills Program (CASP) checklist. The findings revealed that certain Branched-chain amino acids (BCAAs) levels were lower in frail subjects compared to robust subjects, while levels of glutamate and glutamine were higher in frail individuals. Moreover, sphingomyelins and phosphatidylcholines (PC) displayed a decreasing trend as frailty advanced. Additionally, other metabolic derivatives, such as carnitine, exhibited significant associations with frailty. These metabolites were primarily interconnected through biochemical pathways related to the tricarboxylic acid and urea cycles. Notably, frailty was associated with a decrease in metabolic derivatives, including carnitine. This study underscores the intricate relationship between essential metabolites, including amino acids and lipids, and their varying levels in frail individuals compared to their robust counterparts. It provides a comprehensive panel of metabolites, shedding light on their potential associations with frailty and expanding our understanding of this complex syndrome.

Approximate Kernel Learning Uncertainty Set for Robust Combinatorial Optimization

Support vector clustering (SVC) has been proposed in the literature as a data-driven approach to build uncertainty sets in robust optimization. Unfortunately, the resulting SVC-based uncertainty sets induces a large number of additional variables and constraints in the robust counterpart of mathematical formulations. We propose a two-phase method to approximate the resulting uncertainty sets and overcome these tractability issues. This method is controlled by a parameter defining a trade-off between the quality of the approximation and the complexity of the robust models formulated. We evaluate the approximation method on three distinct, well-known optimization problems. Experimental results show that the approximated uncertainty set leads to solutions that are comparable to those obtained with the classic SVC-based uncertainty set with a significant reduction of the computation time. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by the German-French Academy for the Industry of the Future [Data-driven collaboration in Industrial Supply Chains project].

A robust optimization approach to a repair shop network planning

Robust optimization model is a paradigm for decision-making under uncertainty, where parameters are given in the form of uncertainty sets. In this paper, we develop a robust optimization model for a repair shop network planning problem. The linear optimization model involves product of uncertain parameters in the constraints. We formulate its robust counterpart with the help of min-max regret and Lagrangian dual approach, considering the partial information of uncertain parameters is given in the form of ellipsoidal and polyhedral uncertainty sets. We also consider ellipsoidal+polyhedral uncertainty set, which is the intersection of ellipsoidal and polyhedral uncertainty sets. We apply the robust optimization model to a bi-objective multi-plant repair shop network planning problem where multiple pieces of equipment are repaired and overhauled using several resources over a multi-period planning horizon. We consider uncertainty in resource and demand parameters. Numerical examples are presented for illustrating the theoretical results.

Robust optimization method of emergency resource allocation for risk management in inland waterways

This study proposes a robust optimization method for waterborne emergency resource allocation in inland waterways that addresses the uncertainties and mismatches between supply and demand. To accomplish this, we integrate the risk evaluation of maritime with a robust optimization model and employ the Entropy Weighted Method (EWM)-Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)-Analytic Hierarchy Process (AHP) method to evaluate the risk of various areas. The approach enables exploration of the relationship between maritime risk and emergency resource allocation strategy. The robust optimization method is used to deal with uncertainty and derive the robust counterpart of the proposed model. We establish an emergency resource allocation model that considers both the economy and timeliness of emergency resource allocation. We construct an optimization model and transform it into an easily solvable robust counterpart model. The results demonstrate that the proposed method can adapt to real-world scenarios, and effectively optimize the configuration effect while improving rescue efficiency under reasonable resource allocation. Specifically, the proportion of rescue time saved ranges from 28.52% to 92.60%, and the proportion of total cost saved is 95.82%. Our approach has significant potential to provide a valuable reference for decision-making related to emergency resource allocation in maritime management.

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines the piecewise-linear approximations and iteratively solves convex approximation problems. The convergence analysis provides a bound on the optimality gap as a function of approximation errors. Based on this bound, we prove that the proposed B&B algorithm terminates in a finite number of iterations and the worst-case bound to obtain an ϵ-optimal solution reciprocally depends on the square root of ϵ. Numerical experiments on Cobb–Douglas production efficiency and equitable resource allocation problems support that the algorithm efficiently finds a highly accurate solution while significantly outperforming the benchmark algorithms for all the small size problem instances solved. A modified branching strategy that takes the advantage of non-linearity in convex functions further improves the performance. Results are also discussed when solving a dual reformulation and using a cutting surface algorithm to solve distributionally robust counterpart of the Cobb–Douglas example models.

Designing robust green sustainable supply chain network by bi-objective optimization method

Designing a green supply chain is becoming popular in the context of sustainable development. To address this academic concern, this paper designs a multi-product, multi-echelon green supply chain network (GSCN) from economic and environmental aspects. During the modeling process, the main challenge is to access the accurate probability distributions of uncertain parameters from limited historical data. To overcome this difficulty, this paper develops a distributionally robust design framework for bi-objective GSCN, where the distribution information of uncertain parameter is partially available and characterized by ambiguity sets. For the tractability, this paper discusses robust counterpart reformulation under Wasserstein-distance-based ambiguity sets. Finally, the obtained mixed integer programming model is resolved via commercial optimization software. To validate the proposed optimization framework, we design a meat supply chain network for a Chinese realistic food enterprise. The computational results demonstrate that the proposed distributionally robust model can provide reliable solutions compared with stochastic optimization method.

Robust condition‐based production and maintenance planning for degradation management

We study the robust production and maintenance control for a production system subject to degradation. A periodic maintenance scheme is considered, and the system production rate can be dynamically adjusted before maintenance, serving as a proactive way of degradation management. Optimal control of the degradation rate aims to strike a balance between the risk of failure and the production profit. We first consider the scenario in which the degradation rate increases linearly with the production rate. Different from the existing literature that posits a parametric stochastic degradation process, we suppose that the degradation increment during a period lies in an uncertainty set, and our objective is to minimize the maintenance cost in the worst case. The resulting model is a robust mixed‐integer linear program. We derive its robust counterpart and establish structural properties of the optimal production plan. These properties are then used for real‐time condition‐based control of the production rate through reoptimization. The model is further generalized to the nonlinear production–degradation relation. Based on a real production–degradation dataset from an extruder system, we conduct comprehensive numerical experiments to illustrate the application of the model. Numerical results show that our model significantly outperforms existing methods in terms of the mean and variance of cost rate when degradation model misspecification is presented.

Robust Laguerre‐based model predictive control for trajectory tracking of a mobile robot using an linear matrix inequality (LMI)‐based approach

AbstractThis paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies.

Existence of solutions to $$\Gamma $$-robust counterparts of gap function formulations of uncertain LCPs with ellipsoidal uncertainty sets

Existence of solutions to $$\Gamma $$-robust counterparts of gap function formulations of uncertain LCPs with ellipsoidal uncertainty sets

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.