Multi-objective Stochastic Model Research Articles

Designing an Agile, flexible and resilient disaster supply chain network using a hybrid group decision-making robust optimization framework

Natural disasters are a part of human history worldwide. To mitigate after-disaster damages, it is imperative to create an effective disaster supply chain. This research proposes a stochastic multi-objective mixed-integer linear programming model for an agile, flexible disaster supply chain network. Selecting domestic first-level suppliers and foreign second-level suppliers is a complicated process. We propose a novel group decision-making (GDM) framework that utilizes k-means clustering, the Borda count method, a consensus-reaching process, and the best-worst method. This framework results in the selection of qualified suppliers at the first and second levels. The GDM process utilizes agility indicators to reduce the delivery time of commodities. A robust probabilistic programming approach is used because of the uncertainty in some critical parameters in the crisis. To solve the large-scale problems, three well-known metaheuristic algorithms are employed. Metaheuristics parameters are then set to their optimum levels using the Taguchi method. Validations of the model and the solution methodologies used are based on a case study with twelve datasets. The obtained results indicate the applicability of both our group decision-making framework and the solution methodologies employed to solve the robust optimization model.

A novel two-stage multi-objective optimization model for sustainable soybean supply chain design under uncertainty

Soybean is one of the most important agricultural products in international markets due to its high global consumption. However, there are limited studies considering sustainability issues and global economic aspects of the soybean supply chain design and optimization. Moreover, it is challenging to integrate many sustainability criteria into a single-stage optimization model for a soybean supply chain configuration. This research proposes a novel two-stage approach, integrating a multi-criteria decision-making technique and a new multi-objective optimization model to design and optimize a soybean supply chain network in Canada, considering sustainability and global factors. In Stage 1, several qualitative and quantitative sustainability criteria are considered to calculate the sustainability scores for the potential suppliers, using the Interval Type 2 Trapezoidal Best Worst Method. Then, the scores are used as input in Stage 2, where a new optimization model with four objective functions is formulated to design and optimize a soybean supply chain. The objective functions include maximization of total profit, created job opportunities, and suppliers' sustainability, and minimization of CO2 emissions. Then, the Pareto frontier is generated, using the augmented ε-constraint method which helps policymakers to make appropriate decisions. Furthermore, four cases are proposed and analyzed to assess the impacts of the objective functions on strategic and tactical decisions. The results show the importance of the presented method as an integrated approach, considering sustainability pillars in agri-food supply chains. In addition, the results indicate that the proposed stochastic multi-objective model can handle fluctuations in uncertain parameters.

Multi-Objective Optimization Model for Uncertainty Consideration of RESs & Load Demands with the Optimal Design of Hybrid CCHP by DDAO-RBFNN Strategy

This manuscript proposes a hybrid system for an integrated solar and natural gas hybrid model with photovoltaic/thermal (PV/T) collectors and gas turbines (GT). The proposed optimization method combines both Dynamic Differential Annealed Optimizations (DDAO) and Radial Basis Function Neural Network (RBFNN), so it is called the DDAO-RBFNN approach. Natural gas, solar energy, coal, and geothermal energy are the sources of the system, while electricity, cooling, and heating are the energy needs of the system. A multi-objective stochastic model incorporates load and renewable energy uncertainty to obtain more efficient, economic, and environmental decisions. By utilizing an existing data set, the proposed approach is to forecast a new set. Some characteristics, such as historical weather data, building loads, and market information are required for modelling the energy hub and unpredictable factors. The proposed RBFNN method is used to model the energy hub through data collection, analysis, and initial sampling of uncertainty factors. To provide optimal outcomes with great computational time, the accuracy of DDAO approach is used. Smart operation managements consider both the energy supply and demand sides to achieve optimal state functioning of the hybrid CCHP scheme. Finally, the proposed system is performed in MATLAB/Simulink site and the performance of the proposed method is compared with existing methods.

An inexact multi-objective mixed-integer nonlinear programming approach for water-soil-fertilizer management under uncertainty considering “footprint family-planetary boundary” assessment

Water, energy, and food (WEF) are interlinked and create a dynamic system that impacts both human well-being and ecology. Given the importance of ecology within the WEF system, water resources serve as the core issue. The allocation of water resources in irrigation districts is a challenging problem for the coordinated development of agricultural production, water resources, and the ecological environment. The integration of stochastic multi-objective programming, fuzzy credibility-constrained programming, and mixed integer programming offers a solution to this issue, with the construction of a fuzzy credibility-constrained stochastic multi-objective mixed-integer nonlinear programming model. The applicability and validity of this model were verified by applying it to the Kaikong Irrigation District (KID) of the Tarim River Basin in northwest China, with notable findings indicating that the optimized system reduces agricultural costs by 5.82%, increases irrigation water use efficiency by 1.80%, and reduces global warming potential by 6.45%. This study investigates the effects of diverse allocation strategies of water and land resources on the social, economic, and ecological subsystems and their interactions by downscaling four subprocesses PBs to the KID scale. The optimization model reveals that only the nitrogen footprint of Kuerle City surpasses the nitrogen boundary of the KID. The proposed solutions based on the model can encourage the green and ecologically-friendly development of agricultural production and can be applied to agricultural systems in arid regions with similar conditions.

Two-Stage Multi-Objective Stochastic Model on Patient Transfer and Relief Distribution in Lockdown Area of COVID-19.

The outbreak of an epidemic disease may cause a large number of infections and a slightly higher death rate. In response to epidemic disease, both patient transfer and relief distribution are significant to reduce corresponding damage. This study proposes a two-stage multi-objective stochastic model (TMS-PTRD) considering pre-pandemic preparedness measures and post-pandemic relief operations. The proposed model considers the following four objectives: the total number of untreated infected patients, the total transfer time, the overall cost, and the equity distribution of relief supplies. Before an outbreak, the locations of temporary relief distribution centers (TRDCs) and the inventory levels of established TRDCs should be determined. After an outbreak, the locations of temporary hospitals (THs), the locations of designated hospitals (DHs), the transfer plans for patients, and the relief distribution should be determined. To solve the TMS-PTRD model, we address an improved preference-inspired co-evolutionary algorithm named the PICEA-g-AKNN algorithm, which is embedded with a novel similarity distance and three different tailored evolutionary strategies. A real-world case study of Hunan of China and 18 test instances are randomly generated to evaluate the TMS-PTRD model. The finding shows that the PICEA-g-AKNN algorithm is better than some most widely used multi-objective algorithms.

A robust fuzzy stochastic multi-objective model for stone paper closed-loop supply chain design considering the flexibility of soft constraints based on Me measure

The Closed-Loop Supply Chain Network Design (CLSCND) encourages attention to the economic and environmental issues concerning returned products. CLSCND is a significant decision issue and it is accompanied by uncertainty. Hybrid uncertainties and the flexibility of soft constraints are some of the key issues in CLSCND. There is a research gap surrounding the utilization of the uncertainties of randomness, epistemic, and soft constraints simultaneously with a robust procedure. This study focuses on the Me measure and proposes a novel flexible, probabilistic, and stochastic programming based on robust optimization. In this approach, a convex mixture of the pessimistic–optimistic views based on the Me measure is implemented. The least level of satisfaction with soft constraints is determined Optimally that the need for repetitive reviews by Decision-Maker (DM) is obviated in the proposed model. Additionally, the model controls violations of soft constraints as well as stochastic deviations, probabilistic deviations, unfulfilled demand, and capacity. A case study is conducted on the development of a stone paper considering economic, environmental, and responsive objectives by minimizing total cost and carbon emissions as well as transportation and processing time. In addition, to estimate the weight of the objectives and handle the multi-objective model, the Best–Worst method (BWM) and the interactive fuzzy programming approach are employed, respectively. Robustness analysis and sensitivity analysis for the case study are then performed and the results are simulated and evaluated using the realization model. The findings revealed that the suggested model performed well.

Metaheuristic algorithms for a sustainable agri-food supply chain considering marketing practices under uncertainty

In recent decades, the rapid growth of the global population has caused a significant increase in agricultural and food product demands. Thereby, the production of various items in the agricultural food supply chain network has increased to diminish food security concerns. On the other hand, the excessive production of products has led to various issues, such as greenhouse gas emissions and increased water consumption in farmlands, followed by supply chain-related challenges affecting the intermediaries in the next network levels. In this study, an agricultural food supply chain network under marketing practices is firstly probed by developing a stochastic multi-objective programming model to effectively improve three main pillars of sustainability. A convex robust optimization approach addresses the uncertainty of the farm production capacity and the saffron demands in the supply network. The effectiveness of the proposed mathematical model is certified by a case study on saffron business using the LP-metric method. A metaheuristic-oriented methodology comprising a modified Keshtel Algorithm is adapted to deal with the NP-hardness of the problems. The performance of the proposed solution methods is evaluated by two strategies, a statistical comparison and a supportive tool developed based on multi-criteria decision-making (MCDM) methods. The results validate the capability of the applied algorithms to solve the problem in different dimensions. Moreover, the MCDM method approves that MOKASEO outclassed in small, medium, and large-sized problems compared to other algorithms.

A new vaccine supply chain network under COVID-19 conditions considering system dynamic: Artificial intelligence algorithms

With the discovery of the COVID-19 vaccine, what has always been worrying the decision-makers is related to the distribution management, the vaccination centers' location, and the inventory control of all types of vaccines. As the COVID-19 vaccine is highly demanded, planning for its fair distribution is a must. University is one of the most densely populated areas in a city, so it is critical to vaccinate university students so that the spread of this virus is curbed. As a result, in the present study, a new stochastic multi-objective, multi-period, and multi-commodity simulation-optimization model has been developed for the COVID-19 vaccine's production, distribution, location, allocation, and inventory control decisions. In this study, the proposed supply chain network includes four echelons of manufacturers, hospitals, vaccination centers, and volunteer vaccine students. Vaccine manufacturers send the vaccines to the vaccination centers and hospitals after production. The students with a history of special diseases such as heart disease, corticosteroids, blood clots, etc. are vaccinated in hospitals because of accessing more medical care, and the rest of the students are vaccinated in the vaccination centers. Then, a system dynamic structure of the prevalence of COVID -19 in universities is developed and the vaccine demand is estimated using simulation, in which the demand enters the mathematical model as a given stochastic parameter. Thus, the model pursues some goals, namely, to minimize supply chain costs, maximize student desirability for vaccination, and maximize justice in vaccine distribution. To solve the proposed model, Variable Neighborhood Search (VNS) and Whale Optimization Algorithm (WOA) algorithms are used. In terms of novelties, the most important novelties in the simulation model are considering the virtual education and exerted quarantine effect on estimating the number of the vaccines. In terms of the mathematical model, one of the remarkable contributions is paying attention to social distancing while receiving the injection and the possibility of the injection during working and non-working hours, and regarding the novelties in the solution methodology, a new heuristic method based on a meta-heuristic algorithm called Modified WOA with VNS (MVWOA) is developed. In terms of the performance metrics and the CPU time, the MOWOA is discovered with a superior performance than other given algorithms. Moreover, regarding the data, a case study related to the COVID-19 pandemic period in Tehran/Iran is provided to validate the proposed algorithm. The outcomes indicate that with the demand increase, the costs increase sharply while the vaccination desirability for students decreases with a slight slope.

Big data-driven optimization for sustainable reverse logistics network design

The reverse logistics network (RLN) design for sustainable supply chain management is a strategic decision in network configuration, and is higher influenced by uncertainty. This paper applies a bi-level stochastic multi-objective model to design an RLN for a disposable product recycling management system. The goal is to balance the overall network cost against the associated environmental risks. An LP-metric based sample average approximation is formulated to solve the optimization problem. The model is validated numerically through a disposable product firm.

A Multiobjective Stochastic Optimization Scheme for the Problem of Chemical Production for Sugarcane Companies


 
 
 
 This paper presents a multiobjective optimization stochastic scheme for production planning for sugarcane companies under uncertainty. The proposed approach considers three stages. The first stage comprises the mass and energy balances for determining process flows. The second stage considers the formulation of a Multiobjective Deterministic Model (MODM) by considering two objective functions: maximizing the gross margin and minimizing the environmental impact. The MODM is given by different production plans that respond differently to the parameters’ variability under uncertainty. Finally, the last stage considers stochastic elements (i.e., product prices, demands, and costs) within the deterministic scheme to obtain a Multiobjective Stochastic Model (MOSM). A case study’s computational results based on the Colombian sugarcane industry show the proposed scheme’s effectiveness. Results include the investment strategy for optimal production planning with an analysis of the parameters’ uncertainty on the economic performance of the planning production configurations.
 
 
 

A Stochastic Multi-Objective Model for China’s Provincial Generation-Mix Planning: Considering Variable Renewable and Transmission Capacity

The uncertain output of variable renewables adds significant challenges to the generation of affordable, reliable, and sustainable power sources in a country or region. Therefore, we propose a new stochastic nonlinear multi-objective model to optimize the power generation structure in 31 provinces of China. Considering variable renewable integration, we use Monte Carlo simulation to describe the randomness and uncertainty of renewable power output. The learning curve in the exponential expression is used to describe the nonlinear relationship between generation cost and installed capacity. The optimized results show that China can substitute fossil power with clean power. Renewable power will account for more than 42% of total power in the optimal power generation structure in 2040. In particular, the annual average growth rate of non-hydro renewable generation is expected to be 12.06%, with solar photovoltaic (PV) power growing the most by 17.95%. The share of renewable power exceeds that of thermal power in 14 provinces, and PV power represents the highest proportion at 30.21%. Reducing transmission capacity can promote the development of advantageous power in each region, such as wind power in the Northwest region and PV power in the South region, with the share increasing by 36.33% and 132.59%, respectively.

A multiobjective stochastic location-allocation model for scooter battery swapping stations

Better battery swapping station (BSS) allocation helps reduce range anxiety. But the uncertain nature of battery swapping demand (BSD) deserves attention, and few models discussed the multiobjective scooter BSS allocation. To reduce the aforesaid problem, this paper advocates the research on innovation by developing a grid-based multiobjective stochastic allocation model for scooter BSS (MSASBSS). Based on the concept of sample average approximation (SAA), Monte Carlo simulation (MCS) and traffic flow, the MSASBSS mode produced large numbers of different BSD scenarios to solve the uncertain BSD problem. Meanwhile, this mode also optimized the BSS allocation and satisfied both the various BSD scenarios and the minimal construction cost of BSSs with the average driving distance of battery swapping taken into account. In this semi-realistic study case, the MSASBSS was validated. Finally, the grid-based MSASBSS model could provide the multiobjective and visually optimized BSS allocation to decision-makers for their more flexible selection of the exact BSS locations shown in a grid. Uncertainty analyses demonstrated that the use of SAA-based algorithm could resolve the uncertain problem of BSD in relation to the scooter BSS allocation.

A Stochastic Optimization Model for Sustainable Multimodal Transportation for Bioenergy Production

While many previous studies have suggested well-defined procedures to find appropriate supply chains, a limited number of studies have been conducted with uncertain values relating to transportation costs. Most of these have included only limited detail on multimodal transportation, or have not considered economic, social, and environmental transportation cost factors together. The main purpose of this study is to suggest a multi-objective stochastic model for sustainable biomass transportation, and to identify the impact level of model selection on the transportation mode. It begins with a deterministic formulation of sustainable transportation, which is then modified to a stochastic problem with vectorization of cost parameters. Based on the model developed, we examined four uncertainty cases from a combination of annual capacity and average distance of biomass transportation. The experimental results provide more cost savings from multimodal transportation, which can be identified if we analyze transportation costs with stochastic modeling. Regarding short-distance plant cases, the study reveals that the impact of the utilization of stochastic methods is insignificant, as the costs savings from multimodal transportation is trivial. Other findings from the experiments show that multimodal transportation could provide cost savings in the economic cost factor, except in the case of low annual capacity and short average distance.

A novel multi-objective green vehicle routing and scheduling model with stochastic demand, supply, and variable travel times

We propose an optimization approach to the routing and scheduling problem for a heterogeneous transportation network that considers (i) stochastic values of demand and supply at the nodes, (ii) variable travel times between nodes conditioned by the fatigue of drivers, (iii) maximum allowed continuous driving time, and (iv) soft service time windows per customer at the nodes. The problem minimizes energy consumption and maximizes customer satisfaction. The subsequent stochastic multi-objective mixed integer programming model is solved using a hybrid approach based on chance- and epsilon-constraint methods. Given the NP-hard quality of the model, we introduce a hybrid meta-heuristic method based on genetic algorithm (GA) and simulated annealing (SA). This novel technique, named MOGASA, combines the global and local search capacities of both meta-heuristic algorithms, providing an intuitive solution approach that allows to solve problem instances considering large distribution networks with multiple types of vehicles in reasonable CPU time. We illustrate how MOGASA improves upon the hybrid chance- and epsilon-constraint exact solution method, particularly when dealing with large problem instances that cannot be solved by the latter. A medium instance scenario is used to analyze the reaction of the objective functions and the subsequent Pareto frontiers to modifications in the main structural parameters defining the transportation network. Potential applications of our stochastic framework to different types of logistic structures and retail supply chains are highlighted.

Robust optimization of risk-aware, resilient and sustainable closed-loop supply chain network design with Lagrange relaxation and fix-and-optimize

ABSTRACT This study explores a Robust, Risk-aware, Resilient, and Sustainable Closed-Loop Supply Chain Network Design (3RSCLSCND) to tackle demand fluctuation like COVID-19 pandemic. A two-stage robust stochastic multiobjective programming model serves to express the proposed problems in formulae. The objective functions include minimising costs, CO2 emissions, energy consumption, and maximising employment by applying Conditional Value at Risk (CVaR) to achieve reliability through risk reduction. The Entropic Value at Risk (EVaR) and Minimax method are used to compare with the proposed model. We utilise the Lp-Metric method to solve the multiobjective problem. Since this model is complex, the Lagrange relaxation and Fix-and-Optimise algorithm are applied to find lower and upper bounds in large-scale, respectively. The results confirm the superior power of the model offered in estimating costs, energy consumption, environmental pollution, and employment level. This model and algorithms are applicable for other CLSC problems.

Nested Bilevel Optimization for DERA Operation Strategy: A Stochastic Multiobjective IGDT Model With Hybrid Endogenous/Exogenous Scenarios

An aggregation of distributed energy resources (DERs) can bring economic and technical benefits for the DER owners and system operator. However, the operation of DERs encounters various uncertainties, which can seriously impact the benefits of DER aggregation. This article presents a new operation optimization approach for an aggregator of DERs considering the unavailability of DERs (as discrete uncertainty sources) as well as forecast uncertainties of electricity prices, solar powers, and wind powers (as continuous uncertainty sources). The proposed approach for DER aggregator (DERA) operation optimization comprises stochastic multiobjective information-gap decision theory (IGDT) to model these discrete and continuous uncertain variables. Moreover, a hybrid endogenous/exogenous scenario generation method is incorporated into the proposed approach to enhance the efficiency of the stochastic programming part by producing decision-dependent scenario trees. The proposed approach is formulated as a nested bilevel optimization model. The proposed approach is compared with other DERA operation optimization models using an out-of-sample analysis method. The comparative results illustrate the superiority of the proposed stochastic multiobjective IGDT approach over various deterministic, stochastic, and IGDT methods. In addition, the high tractability of the proposed solution method is illustrated, while its linearization error for the stochastic multiobjective IGDT problem is well below 1%.

Agricultural water and land resources allocation considering carbon sink/source and water scarcity/degradation footprint

There is an urgent need for scientific management of agricultural water and land resources to cope with global warming and water shortages. Therefore, a stochastic multi-objective non-linear programming model was established under the society-economy-ecology framework in this study, which is capable of (1) considering the carbon sink function of farmland vegetation and the carbon emissions produced from the input of production materials; (2) dealing with the potential impact of agricultural water use on ecology by the indexes of water scarcity and degradation footprint (3) weighing the conflicts and contradictions among different developing targets with economic benefits, and water productivity as well as ecological considerations; (4) obtaining the planting structure, irrigation water allocation schemes and irrigation schedules. In order to verify the applicability and effectiveness of the model, it was applied to Huangyang Irrigation District in Shiyang River Basin, northwest China. After optimization, the net carbon sink increased by 2.55 × 104 t of which fertilizer contributed nearly 50% of carbon emission, while the water footprint reduced by 0.48 × 108 m3. To analyze the impact of the different allocation schemes of water and land resources on the ecological, economic and social subsystems as well as their interaction, coupling coordination degree (CCD) models were introduced to evaluate status quo and the optimization results of different models. The results showed that, compared with the single-objective models and the status quo, the proposed model has improved the value of CCD from 0.428 to 0.674. The proposed model can promote the harmonious and sustainable development of agricultural production and is equally applicable to agricultural management systems in the regions with similar conditions.

A Stochastic Multi-Objective Model for a Sustainable Closed-Loop Supply Chain Network Design in the Automotive Industry

A Stochastic Multi-Objective Model for a Sustainable Closed-Loop Supply Chain Network Design in the Automotive Industry

A multi-objective stochastic programming model for post-disaster management

This paper develops a mathematical model for post-disaster planning with human casualties, which can be considered as operational guidance for the proper use of emergency resources. For this purpose, a stochastic mixed-integer programming model is provided to formulate the problem. The objective functions of the model are (1) maximizing the survival probability of patients, (2) minimizing the maximum of completion time of treatment of all patients, and (3) minimizing the total cost of operations. The model is solved with the ϵ-constraint method. Due to the NP-hardness of the problem which is a significant challenge in the literature, two innovative meta-heuristic algorithms are proposed, i.e. a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective simulated annealing (MOSA). Finally, a comprehensive computational analysis is performed for evaluation purposes. Also, a case study is made on the earthquake in Iran, which illustrates the real-world application of the model. Highlights A stochastic multi-objective mathematical programming model to allocate patients to hospitals and treat them. NSGA-II and MOSA are proposed, in addition to ϵ-constraint method as solution methods. Performance of two meta-heuristic algorithms is measured with five evaluation metrics. The study showed that NSGA-II is more effective than MOSA. The model was implemented on a real-world case, Tabriz earthquake in Iran.

A multi-objective stochastic programming model to configure a sustainable humanitarian logistics considering deprivation cost and patient severity

As the occurrence of disasters has increased frequently and has resulted in growing concern about their adverse effects on the environment, Sustainable Humanitarian Logistics (SHL) has received great attention recently. SHL aims to reduce disaster damages in an environmentally-friendly manner in the shortest possible time. The terms including ‘environmentally-friendly’ and ‘shortest possible time’ refer to the environmental and social aspects of sustainability. This research proposes a stochastic multi-objective mixed-integer programming model to configure an SHL network during the response phase. Having compared to the research literature, this is the first study that considers economic, social, and environmental aspects of sustainability by incorporating relief cost, deprivation cost, and carbon emissions, respectively. Then, the improved multi-choice goal programming approach is applied to solve the proposed multi-objective model. To indicate the validity of the proposed model, an earthquake that occurred in a region of Kermanshah, Iran, in 2017 is investigated as a real case study. Finally, sensitivity analysis is performed and several managerial and theoretical insights are provided. The results show that exerting environmental issues in humanitarian logistics does not necessarily increase the relief costs, but can be in contrast with the social aspect. Furthermore, a minor increase in the budget of the preparedness phase drastically decreases the response costs.