Scenario-based Robust Optimization Research Articles

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

A robust multi-objective MIP model to optimize the supply chain of steel industry taking into account the sustainability approach

The construction of a steel production plant in the countries provided that they benefit from the required raw materials, and infrastructural facilities such as roads, power plants, water, etc. are considered an economic advantage. If these prerequisites exist, the next challenge in building a steel plant is to determine the number, optimal location, and flow between the supplier and the plant and also between the plant and the consumer market. On the other hand, there is always a serious challenge for environmental issues and the impact on pastures and wildlife due to the polluting nature of this industry. In addition, considering the situation in which the amount of consumption under disruptions makes the supply chain of steel inefficient, it is necessary to design a model that is close to the real world. In this study, to obtain the optimum number and location of steel factories, material flow, and considering the sustainability approach, we design a robust three-level supply chain network for the steel industry, taking into account the sustainability approach including three objective functions. The first objective function aims to minimize logistics and production costs, the second objective function maximizes the quality score of the final selected location, and the third objective function is proposed to maximize the efficiency of product production lines. In this study, a scenario-based robust optimization model is applied to overcome the uncertainty of the proposed model. Furthermore, to incorporate the score of location into the third objective function, a decision-making method based on the sustainability approach is used. Finally, the proposed model is validated within steel industry in Iran as a case study.

Optimal energy storage system design for addressing uncertainty issues in integration of supply and demand-side management approaches

The primary goal of Sustainable Development Goal 7 (SDG 7) is to increase renewable energy use to reduce reliance on fossil fuels and mitigate climate change. Energy-intensive industries can benefit from in-house renewable power generation, reducing their reliance on fossil fuel-based grid power and making processes greener. However, integration among power generation/purchase, energy storage systems (ESS), and power consumption is crucial to overcome the intermittent nature of renewable power sources. ESS plays a vital role in increasing resilience and optimizing material production based on power availability and pricing. The efficacy of ESS needs critical evaluation considering cost, efficiency, and uncertainties related to renewable power generation and material product demand. The paper proposes two scenario-based optimization approaches to assess the impact of uncertainties on the integrated supply and demand side management (ISDM) system, focusing on lithium-ion batteries and cryogenic energy storage (CES). Compared to the conservative approach of the scenario-based robust optimization (SRO) method, the proposed stochastic simulation optimization (SSO) method provides a ‘risk-neutral’ solution, which is 6.45% less than the minimum expected cost solution. The analysis also suggests that lithium-ion batteries are more economically effective for the proposed integrated framework than CES, resulting in almost a 29% reduction in operating costs compared to no battery option. The proposed framework could contribute to sustainable and economically viable energy management practices in energy-intensive industries. Further research and implementation of such frameworks could accelerate the adoption of renewable energy and energy storage technologies in industrial processes.

Sustainable supply chain planning with the flexible provisions of inter-period emission credits borrowing and banking under a multi-period carbon trading scheme

Although the carbon emission trading regulation proves its advantage of reducing abatement costs, the timing of operating activities makes overage or shortage of allocated emission allowances quickly happen in single-year compliance, thus increasing abatement costs. The provision of inter-period emission credits banking and borrowing in a multi-period compliance phase can give emitters flexibility in emission compliance, which practices world-widely. In this study, we investigate the impact of carbon trading with inter-temporal emission credits borrowing and banking on a production–inventory–distribution system’s supply chain network decision-making and its compliance strategies by proposing a novel two-stage stochastic programming. A scenario-based robust optimization approach is presented with a post-optimization stage to obtain robustness-profit-environment balanced decision-making considering uncertain demand and stochastic carbon-trading price. The results suggests emitters should adopt specific greener techniques to reduce related emissions with priority under carbon-trading policies. The results also show the provision of carbon credits borrowing and banking has a positive influence on enhancing the efficiency in supply chain economic and ecological performance. Besides, given the flexible provisions, the manager can reallocate emission credits according to its business’s operation, and transfer more emission credits to periods of higher carbon-trading price. This findings also suggest banking in early periods instead of carelessly borrowing from future, for uncertainty in future business might make it harder or impossible to comply with emission regulation at last. To regulators, it should prevent borrowing explicitly or allow it only to a limited extent.

Validation of Fully Automated Robust Multicriterial Treatment Planning for Head and Neck Cancer IMPT

Our purpose was to compare robust intensity modulated proton therapy (IMPT) plans, automatically generated with wish-list-based multicriterial optimization as implemented in Erasmus-iCycle, with manually created robust clinical IMPT plans for patients with head and neck cancer. Thirty-three patients with head and neck cancer were retrospectively included. All patients were previously treated with a manually created IMPT plan with 7000 cGy dose prescription to the primary tumor (clinical target volume [CTV]7000) and 5425 cGy dose prescription to the bilateral elective volumes (CTV5425). Plans had a 4-beam field configuration and were generated with scenario-based robust optimization (21 scenarios, 3-mm setup error, and ±3% density uncertainty for the CTVs). Three clinical plans were used to configure the Erasmus-iCycle wish-list for automated generation of robust IMPT plans for the other 30 included patients, in line with clinical planning requirements. Automatically and manually generated IMPT plans were compared for (robust) target coverage, organ-at-risk (OAR) doses, and normal tissue complication probabilities (NTCP). No manual fine-tuning of automatically generated plans was performed. For all automatically generated plans, voxel-wise minimum D98% values for the CTVs were within clinical constraints and similar to manual plans. All investigated OAR parameters were favorable in the automatically generated plans (all P < .001). Median reductions in mean dose to OARs went up to 667 cGy for the inferior pharyngeal constrictor muscle, and median reductions in D0.03cm3 in serial OARs ranged up to 1795 cGy for the spinal cord surface. The observed lower mean dose in parallel OARs resulted in statistically significant lower NTCP for xerostomia (grade ≥2: 34.4% vs 38.0%; grade ≥3: 9.0% vs 10.2%) and dysphagia (grade ≥2: 11.8% vs 15.0%; grade ≥3: 1.8% vs 2.8%). Erasmus-iCycle was able to produce IMPT dose distributions fully automatically with similar (robust) target coverage and improved OAR doses and NTCPs compared with clinical manual planning, with negligible hands-on planning workload.

A Two-Stage Scenario-Based Robust Optimization Model and a Column-Row Generation Method for Integrated Aircraft Maintenance-Routing and Crew Rostering

A Two-Stage Scenario-Based Robust Optimization Model and a Column-Row Generation Method for Integrated Aircraft Maintenance-Routing and Crew Rostering

Scenario-Based Robust Optimization for Two-Stage Decision Making Under Binary Uncertainty

This paper addresses problems of two-stage optimization under binary uncertainty. We define a scenario-based robust optimization (ScRO) formulation that combines principles of stochastic optimization (by constructing probabilistic scenarios) and robust optimization (by protecting against adversarial perturbations within discrete uncertainty sets). To solve it, we develop a sparse row generation algorithm that iterates between a master problem (which provides a lower bound based on minimal uncertainty sets) and a history-based subproblem (which generates an upper bound and updates minimal uncertainty sets). We generate scenarios and uncertainty sets from element-wise probabilities using a deviation likelihood method or from historical samples using a sample clustering approach. Using public data sets, results suggest that (i) our ScRO formulation outperforms benchmarks based on deterministic, stochastic, and robust optimization; (ii) our deviation likelihood and sample clustering approaches outperform scenario generation baselines; and (iii) our sparse row generation algorithm outperforms off-the-shelf implementation and state-of-the-art cutting plane benchmarks. An application to a real-world ambulance dispatch case study suggests that the proposed modeling and algorithmic approach can reduce the number of late responses by more than 25%. Funding: K. Wang’s research was supported by the National Natural Science Foundation of China [Grants 72322002, 52221005, and 52220105001]

Resilient and sustainable supply chain design and planning under supply disruption risk using a multi-objective scenario-based robust optimization model

Resilient and sustainable supply chain design and planning under supply disruption risk using a multi-objective scenario-based robust optimization model

A hierarchical model for strategic and operational planning in blood transportation with drones.

Blood transportation is a critical aspect of the healthcare systems, ensuring whole blood and blood products are delivered to patients in a timely and efficient manner. However, transportation of blood and other medical supplies can be challenging, especially in urban areas with limited infrastructure and heavy traffic. Drones have become increasingly important in recent years as a means of delivering medical supplies, including blood, due to their ability to provide fast, reliable, and cost-effective transportation. This study proposes two mathematical programming models in the hierarchical structure to improve decision-making for strategic and operational planning in the blood supply chain network. The limited information available in strategic planning presents risks to the blood supply chain, making it imperative to address uncertainties. To tackle this challenge, a novel approach called Scenario-based Robust Bi-objective Optimization has been proposed. The first model employs this approach to efficiently handle demand uncertainty by simultaneously maximizing the covered demand and minimizing costs. The model is subsequently solved using the augmented ε-constraint method. The second model is a routing-scheduling operational model that aims to minimize the sum of operations time, taking into account time windows for blood collection centers and hospitals. The developed hierarchical model is implemented in a three-level supply chain of Tehran province under three crisis scenarios in different parts. The findings and analysis of this implementation suggest that it is beneficial to set up drone stations in cost-effective and central locations to avoid costly network design. Furthermore, utilizing the minimum number of feasible drones enhances operational time and results in cost savings and increased efficiency. Overall, this study highlights the potential of using drones for blood transportation in urban settings, which can have significant implications for improving the quality of healthcare delivery.

An integrated optimization model for planning supply chains' resilience and business continuity under interrelated disruptions: a case study

PurposeThe adverse interactions between disruptions can increase the supply chain's vulnerability. Accordingly, establishing supply chain resilience to deal with disruptions and employing business continuity planning to preserve risk management achievements is of considerable importance. The aforementioned idea is discussed in this study.Design/methodology/approachThis study proposes a multi-objective optimization model for employing business continuity management and organizational resilience in a supply chain for responding to multiple interrelated disruptions. The improved augmented e-constraint and the scenario-based robust optimization methods are adopted for multi-objective programming and dealing with uncertainty, respectively. A case study of the automotive battery manufacturing industry is also considered to ensure real-world conformity of the model.FindingsThe results indicate that interactions between disruptions remarkably increase the supply chain's vulnerability. Choosing a higher fortification level for the supply chain and foreign suppliers reduces disruption impacts on resources and improves the supply chain's resilience and business continuity. Facilities dispersion, fortification of facilities, lateral transshipment, order deferral policy, dynamic capacity planning and direct transportation of products to markets are the most efficient resilience strategies in the under-study industry.Originality/valueApplying resource allocation planning and portfolio selection to adopt preventive and reactive resilience strategies simultaneously to manage multiple interrelated disruptions in a real-world automotive battery manufacturing industry, maintaining the long-term achievements of supply chain resilience using business continuity management and dynamic capacity planning are the main contributions of the presented paper.

Robust sustainable canola oil-based biodiesel supply chain network design under supply and demand uncertainty.

The excessive consumption of fossil fuels has sparked debates and caused environmental damage, leading the global community to search for a suitable alternative. To achieve sustainable development goals and prevent harmful climate scenarios, the world needs to increase its use of renewable energy. Biodiesel, a clean and eco-friendly fuel with a high flash point and more lubrication than petroleum-based fuels, and without the emission of harmful environmental gases, has emerged as one of the fossil fuel alternatives. To promote the mass-level production of biodiesel, a sustainable supply chain (SC) that does not depend on laboratory production is necessary. For this purpose, this research proposes a multi-objective mixed-integer non-linear mathematical programming (MINLP) model to design a sustainable canola oil-based biodiesel supply chain network (CO-BSCND) under supply and demand uncertainty. This mathematical model aims to minimize the total cost (TC) and total carbon emission while maximizing the total number of job opportunities simultaneously. A scenario-based robust optimization (SBRO) approach is applied to deal with uncertainty. The proposed model is implemented in a real case study in Iran, and numerical experiments and sensitivity analysis are conducted to demonstrate its applicability. The results of this research demonstrate that designing a sustainable supply chain network for the production and distribution of biodiesel fuel is achievable. Moreover, this mathematical modeling makes mass-scale production of biodiesel fuel a possibility. In addition, the SBRO method adopted in this research enables managers and researchers to explore the design conditions of the supply chain network by controlling the uncertainties that affect it. This approach allows the chain's performance to be as close as possible to the actual conditions. As a result, the SBRO method enhances the efficiency of the supply chain network and boosts productivity toward achieving desired goals.

A customized multi-neighborhood search algorithm using the tabu list for a sustainable closed-loop supply chain network under uncertainty

Environmental pollution and social inequalities have prompted the agricultural industry to implement sustainable supply chain management practices. However, supply chain operations and planning in developing countries such as Iran are often not economically, environmentally, and socially sustainable. To address this challenge, this paper presents a practical optimization model for sustainable closed-loop supply chain (SCLSC) management in the agricultural industry of Iran, with a focus on the olive crop. Based on the triple bottom line concept, which considers economic, environmental, and social sustainability, the proposed model makes location, allocation, and inventory decisions under uncertainty by developing a scenario-based robust optimization model. To solve this complex network design problem, we propose a metaheuristic algorithm with a multi-neighborhood procedure that efficiently handles the complexity of the problem. Specifically, we develop a customized Simulated Annealing (SA) algorithm using a tabu list to improve the initial solution found by a constructive heuristic algorithm. Our extensive analysis and comparison of our metaheuristic algorithm against the exact solver and two other powerful metaheuristic algorithms demonstrate the applicability of our SCLSC model for the agricultural industry in Iran and the high performance of the proposed metaheuristic algorithm for solving large-scale networks.

Design of a sales plan in a hybrid contractual and non-contractual context in a setting of limited capacity: A robust approach

Many companies face capacity limitations that impair them to satisfy potential demand. In this context, sales/marketing teams have to decide which demand segments the company should prioritize. In business-to-business contexts, it is common that this selection includes customers with and without a contract. On the operations side, the production teams are interested in finding the most efficient usage for the available capacity. However, decision-making approaches to face such a challenge are scarce. In this paper, we propose a scenario-based robust optimization model to support the sales and marketing teams to define the most profitable sales plan in a setting of limited capacity, to serve multiple customers that can be either non-contractual or operate under quantity-flexibility contracts. The proposed model integrates contract design, portfolio selection, and tactical production planning decisions. By employing our model, we are able to quantify how a product’s inclusion in a contract relates not only to its own profitability but also to the profitability of the remaining products that might be offered to the customer using the same resources. Regarding the optimal flexibility level to offer to a customer, it is explained by the expected sales volume, the discount rate depending on the flexibility level, and the demand variability expectation. We expect this approach supports industrial companies in defining the mid-term sales plan and deciding on the conditions to offer to contract customers.

Optimal operation scheduling of a microgrid using a novel scenario-based robust approach

This article presents the optimal short-term scheduling of an integrated heat and power microgrid (MG) considering load uncertainty. The MG comprises combined heat and power (CHP) units, a small thermal power plant, a small boiler, an electrical energy storage system and a thermal storage tank, and can further engage in electrical energy transactions with the upstream network regarded as the day-ahead market. Given the uncertain nature of the electrical and thermal load, a novel scenario-based robust optimization framework is developed to overcome the problem uncertainties. The effectiveness of the proposed scenario-based robust scheme against conventional deterministic and stochastic scheduling methods is verified through numerical simulation on a prototype MG. The results suggest that the proposed approach can effectively forecast the uncertainties in MG load and provide the operator with more realistic results to handle the consuming load uncertainty.

Design of a robust waste recycling network integrating social and environmental pillars of sustainability

The design of an efficient Municipal Solid Waste (MSW) management network can reduce the network costs, such as investment, operational and recycling costs, and improve its sustainability, from economic to environmental and social perspectives. In this paper, a multi-objective scenario-based robust stochastic optimization model for designing a sustainable MSW management network under uncertainty is proposed. The proposed model has four objectives to seek sustainability from two quantitative and qualitative aspects. Considering the dynamicity of the factors affecting an MSW management network as well as the multiplicity of sustainability perspectives, the proposed model allows, on one hand, reaching a robust solution considering the potential scenarios, and on the other hand, integrating sustainability indicators while creating a balance between the quantitative and qualitative evaluation of such indicators. Moreover, the waste treatment technologies, as the highest added-value echelon of the MSW management network, which also distinguishes the network from a generic waste recycling network, has been investigated in the model. Finally, fuel consumption, have been particularly emphasized as critical factor, highly contributing to transportation costs and Co2 emission that are decisive criteria from both economic and environmental points of view. The proposed model and solution approach are validated through a real case study.

Robust metro train scheduling integrated with skip-stop pattern and passenger flow control strategy under uncertain passenger demands

As the passenger demands, especially commuters, in the megacities increase dramatically, the congestion problem of metro lines becomes severe and affects passengers’ travel experience. More and more metro stations have adopted passenger flow control measures to ensure operational security or implemented skip-stop patterns to ease transportation pressure. This paper investigates the collaborative optimization problem of timetable scheduling, passenger flow control, and skip-stop pattern on a metro line. A mixed integer nonlinear programming (MINLP) model is proposed to require a performance balance between service level and operation costs. The collaborative optimization model is constructed to optimize the train timetable by determining arrival and departure times with bounded dwell time and running time at intervals. Specifically, time-dependent passenger arrival rates are regarded as uncertain parameters here. The scenario-based robust optimization (SBRO) model with nonlinear constraints is further transformed into a model with linear constraints, which can be directly solved by commercial solvers. Finally, several sets of numerical experiments according to the actual data about the Beijing Changping metro line are performed to demonstrate the validity of the proposed model and method. The optimized train timetable integrated with the skip-stop pattern and passenger flow control strategy can effectively ease the congestion of stations and improve the safety and service quality of the metro system. The tradeoff between solution robustness and model robustness is obtained with critical practical insights.

Designing a reverse logistics network to manage construction and demolition wastes: A robust bi-level approach

Nowadays, due to irregular human intervention and exploitation of available resources, the environmental crisis has been one of the biggest threats in the world. These risks can sometimes come from destroying habitats and arable land. According to the importance of this issue, this study tries to design a construction and demolition wastes (C&DW) reverse logistics network. For this purpose, a bi-level mixed-integer linear programing (MILP) model is designed. The lower level determines location of C&DW recycling and disposal centers and the upper-level involves allocation of waste to the recycling and disposal centers. A scenario-based robust optimization approach is applied to cope with the uncertainty in the percentage of C&DW transported from the generation points. Eventually, the final model is solved in GAMS optimization software and its performance and efficiency are analyzed. Mazandaran province, Iran, is selected as case study because of its geographical conditions. The results show that allocation and establishment decisions are made in a way that impose the least cost to the network in different scenarios. In addition, the scenario-based robust optimization approach represents less sensitivity to solutions for considered scenarios. Also, considering the hierarchy model leads to appropriate solutions with less costs compared to the separate leader and follower models.

Central robust decision-making structure for reverse supply chain: a real pharmaceutical case

Tons of hazardous pharmaceutical waste is introduced to the environment each year, showing the significance of medicines reverse channels. Meanwhile, establishing a pharmaceutical reverse channel is complex and costly, and therefore misestimation of uncertainty in waste collection operations can lead to severe financial losses. As conventional methods for uncertainty often fail to mitigate the risk and protect the system, we propose a central robust approach, inspired by scenario-based robust optimization and supply chain coordination concepts, which can significantly reduce waste management costs in the face of uncertainty. We study the profitability in a two-layer reverse channel, where the initial number of unwanted medications is subject to discrete uncertainty. Then, we extend our problem, assuming that the customer willingness to return the items is subject to random uncertainty. A non-linear programming model, a flexible transfer price agreement, and the Nash-bargaining game model are developed to optimize and coordinate the system performance. The analytical results provide reliable insights for industry owners to manage uncertainty in the collection process. We illustrate that implementing the proposed model boosts the return quantity, leads to a remarkable improvement in the profitability of the entire chain, and improves the system adaptability with respect to changing significant market parameters or revenue fluctuations.

Multi-depot green capacitated location routing problem considering uncertainty and in-facility queuing

Nowadays, designing a framework for an environmentally-friendly waste collection network is of higher importance due to population growth. This study presents a multi-depot green capacitated location routing problem (MGCLRP) considering the time window and in-facility queuing under uncertainty. A scenario-based robust optimization is employed to deal with demand and travelling time uncertainties. Moreover, the M/M/c queuing system calculates the expected total wait time at a recycling center. As a solution method, we develop an algorithm to find the optimal number of potential locations and use this optimal number to find the main objectives of the problem. Then, two versions of NSGA-III, enhanced by greedy initializations, are proposed to solve the large-scale instances. The obtained results show the superiority of the proposed NSGA-III over the simple version of this algorithm. Finally, we investigate the applicability of the given model in a practical case study for Tehran. • Designing a Green Capacitated Location Routing Problem Considering Uncertainty and In-Facility Queuing. • Applying a scenario-based robust optimization method to manage the uncertainty. • Proposing two hybrid metaheuristic algorithms to efficiently solve the problem.