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Given the importance of estimating the demand for relief items in earthquake disaster, this research studies the complex nature of demand uncertainty in a vehicle routing problem in order to distribute first aid relief items in the post disaster phase, where routes are subject to disruption.

To cope with such kind of uncertainty, the demand rate of relief items is considered as a random fuzzy variable and a robust scenario-based possibilistic-stochastic programming model is elaborated. The results are presented and reported on a real case study of earthquake, along with sensitivity analysis through some important parameters.

The results show that the demand satisfaction level in the proposed model is significantly higher than the traditional scenario-based stochastic programming model.

In reality, in the occurrence of a disaster, demand rate has a mixture nature of objective and subjective and should be represented through possibility and probability theories simultaneously. But so far, in studies related to this domain, demand parameter is not considered in hybrid uncertainty. The worth of considering hybrid uncertainty in this study is clarified by supplementing the contribution with presenting a robust possibilistic programming approach and disruption assumption on roads.

This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered.

At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models.

The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models.

This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.

The number of natural and man-made disasters is remarkable and threatened human lives at the time of occurrence and also after that. Therefore, an efficient response following a disaster can eliminate or mitigate the adverse effects. This paper aims to help address those challenges related to humanitarian logistics by considering disaster network design under uncertainty and the management of emergency relief volunteers simultaneously.

In this paper, a robust fuzzy stochastic programming model is proposed for designing a relief commodity supply chain network in a disaster by considering emergency relief volunteers. To demonstrate the practicality of the proposed model, a case study is presented for the 22 districts of Tehran and solved by an exact method.

The results indicate that there are many parameters affecting the design of a relief commodity supply chain network in a disaster, and also many parameters should be controlled so that, the catastrophe is largely prevented and the lives of many people can be saved by sending the relief commodity on time.

This model helps decision-makers and authorities to explore optimal location and allocation decisions without using complex optimization algorithms.

To the best of the authors’ knowledge, employee workforce management models have not received adequate attention despite their role in relief and recovery efforts. Hence, the proposed model focuses on the problem of managing employees and designing a disaster logistics network simultaneously. The robust fuzzy stochastic programming method is applied for the first time for controlling the uncertainties in the design of humanitarian relief supply chains.

This paper aims to introduce a novel structure for the physical internet (PI)–enabled sustainable supplier selection and inventory management problem under uncertain environments.

To address hybrid uncertainty both in the objective function and constraints, a novel interactive hybrid multi-objective optimization solution approach combining Me-based fuzzy possibilistic programming and interval programming approaches is tailored.

Various numerical experiments are introduced to validate the feasibility of the established model and the proposed solution method.

Due to its interconnectedness, the PI has the opportunity to support firms in addressing sustainability challenges and reducing initial impact. The sustainable supplier selection and inventory management have become critical operational challenges in PI-enabled supply chain problems. This is the first attempt on this issue, which uses the presented novel interactive possibilistic programming method.

This study aims to design a proper supply chain network for the vaccine industry in Iran, which considers several features such as uncertainties in demands and cost, perishability of vaccines, wastages in storage, limited capacity and different priorities for demands.

This study presents a mixed-integer linear programming (MILP) model and using a robust counterpart approach for coping with uncertainties of model.

The presented robust model in comparison with the deterministic model has a better performance and is more reliable for network design of vaccine supply chain.

This study considers uncertainty in the network design of vaccine supply chain for the first time in the vaccine context It presents an MILP model where strategic decisions for each echelon and tactical decisions among different echelons of supply chain are determined. Further, it models the difference between high- and low-priority demands for vaccine.

One of the practical issues in the area of location and allocation is the location of the hub. In recent years, exchange rates have fluctuated sharply for a number of reasons such as sanctions against the country. Natural disasters that have occurred in recent years caused delays in hub servicing. The purpose of this study is to develop a mathematical programming model to minimize costs, maximize social responsibility and minimize fuel consumption so that in the event of a disruption in the main hub, the flow of materials can be directed to its backup hub to prevent delays in flow between nodes and disruptions in hubs.

A multi-objective mathematical programming model is developed considering uncertainty in some parameters, especially cost as fuzzy numbers. In addition, backup hubs are selected for each primary hub to deal with disruption and natural disasters and prevent delays. Then, a robust possibilistic method is proposed to deal with uncertainty. As the hub location-allocation problem is considered as NP-Hard problems so that exact methods cannot solve them in large sizes, two metaheuristic algorithms including a non-dominated sorting genetic algorithm non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) are applied to tackle the problem.

Numerical results show the proposed model is valid. Also, they demonstrate that the NSGA-II algorithm outperforms the MOPSO algorithm.

The proposed model was implemented in one of the largest food companies in Iran, which has numerous products manufactured in different cities, to seek the hub locations. Also, due to several reasons such as road traffic and route type the difference in the rate of fuel consumption between nodes, this model helps managers and decision-makers to choose the best locations to have the least fuel consumption. Moreover, as the hub set up increases the employment rate in that city and has social benefits as it requires hiring some staff.

This paper investigates the hub location problem considering backup hubs with multiple objective functions to deal with disruption and uncertainty. Also, this study examines how non-hub nodes are assigned to hub nodes.

This paper aims to minimize the mean-risk cost of sustainable and resilient supplier selection, order allocation and production scheduling (SS,OA&PS) problem under uncertainty of disruptions. The authors use conditional value at risk (CVaR) as a risk measure in optimizing the combined objective function of the total expected value and CVaR cost. A sustainable supply chain can create significant competitive advantages for companies through social justice, human rights and environmental progress. To control disruptions, the authors applied (proactive and reactive) resilient strategies. In this study, the authors combine resilience and social responsibility issues that lead to synergy in supply chain activities.

The present paper proposes a risk-averse two-stage mixed-integer stochastic programming model for sustainable and resilient SS,OA&PS problem under supply disruptions. In this decision-making process, determining the primary supplier portfolio according to the minimum sustainable-resilient score establishes the first-stage decisions. The recourse or second-stage decisions are: determining the amount of order allocation and scheduling of parts by each supplier, determining the reactive risk management strategies, determining the amount of order allocation and scheduling by each of reaction strategies and determining the number of products and scheduling of products on the planning time horizon. Uncertain parameters of this study are the start time of disruption, remaining capacity rate of suppliers and lead times associated with each reactive strategy.

In this paper, several numerical examples along with different sensitivity analyses (on risk parameters, minimum sustainable-resilience score of suppliers and shortage costs) were presented to evaluate the applicability of the proposed model. The results showed that the two-stage risk-averse stochastic mixed-integer programming model for designing the SS,OA&PS problem by considering economic and social aspects and resilience strategies is an effective and flexible tool and leads to optimal decisions with the least cost. In addition, the managerial insights obtained from this study are extracted and stated in Section 4.6.

This work proposes a risk-averse stochastic programming approach for a new multi-product sustainable and resilient SS,OA&PS problem. The planning horizon includes three periods before the disruption, during the disruption period and the recovery period. Other contributions of this work are: selecting the main supply portfolio based on the minimum score of sustainable-resilient criteria of suppliers, allocating and scheduling suppliers orders before and after disruptions, considering the balance constraint in receiving parts and using proactive and reactive risk management strategies simultaneously. Also, the scheduling of reactive strategies in different investment modes is applied to this problem.

This study aims to develop a model for project portfolio selection considering organizational goals such as budgets, sustainability cash flow and reinvestment strategy under an uncertain environment.

A multi-objective mathematical programming model is proposed for project selection, which takes the social, environmental and financial aspects into account as the objectives of the project portfolio selection problem. The project evaluation and selection process in one of the large capitals in the Middle East with numerous urban construction projects was considered as a real case study, in which the subjects of environmental and social sustainability are of great importance. Then, the most significant criteria for project evaluation and selection based on sustainability were identified and ranked using the fuzzy best-worst method (BWM).

The criterion of “defining clear and real objectives” was ranked first, “project investment return period” was ranked second, “minimum changes in the predicted range” was ranked third, and the other ten sustainability indicators were ranked as well. Next, the presented mathematical programming model was solved using the augmented e-constraint method. The sensitivity analysis indicated that increasing the amount of investments in projects would increase their net present value. Also, increased investment had no effect on sustainability, while decreased investment caused sustainability to not being optimal.

This study focuses on the impact of the amount of investments on projects, and the associated costs of sustainable projects. Further to the authors' knowledge, there has been no relevant study taking uncertainty into account. Also, very few studies proposed a mathematical programming model for the project portfolio selection problem. Moreover, this research uses the brainstorming and Delphi method to identify the sustainability indicators influencing the organization and screens the evaluation indicators. Furthermore, the weights of the evaluation indicators are determined using the fuzzy BWM based on the consistency of opinions.

The purpose of this study is to develop a holistic optimization model for an integrated sustainable fleet planning and closed-loop supply chain (CLSC) network design problem under uncertainty.

A novel mixed-integer programming model that is able to consider interactions between vehicle fleet planning and CLSC network design problems is first developed. Uncertainties of the product demand and return fractions of the end-of-life products are handled by a chance-constrained stochastic program. Several Pareto optimal solutions are generated for the conflicting sustainability objectives via compromise and fuzzy goal programming (FGP) approaches.

The proposed model is tested on a real-life lead/acid battery recovery system. By using the proposed model, sustainable fleet plans that provide a smaller fleet size, fewer empty vehicle repositions, minimal CO₂ emissions, maximal vehicle safety ratings and minimal injury/illness incidence rate of transport accidents are generated. Furthermore, an environmentally and socially conscious CLSC network with maximal job creation in the less developed regions, minimal lost days resulting from the work's damages during manufacturing/recycling operations and maximal collection/recovery of end-of-life products is also designed.

Unlike the classical network design models, vehicle fleet planning decisions such as fleet sizing/composition, fleet assignment, vehicle inventory control, empty repositioning, etc. are also considered while designing a sustainable CLSC network. In addition to sustainability indicators in the network design, sustainability factors in fleet management are also handled. To the best of the authors' knowledge, there is no similar paper in the literature that proposes such a holistic optimization model for integrated sustainable fleet planning and CLSC network design.

This study aims to address the inherent uncertainties within closed-loop supply chain (CLSC) networks through the application of a multi-objective approach, specifically focusing on the optimization of integrated production and transportation processes. The primary purpose is to enhance decision-making in supply chain management by formulating a robust multi-objective model.

In dealing with uncertainty, this study uses Pythagorean fuzzy numbers (PFNs) to effectively represent and quantify uncertainties associated with various parameters within the CLSC network. The proposed model is solved using Pythagorean hesitant fuzzy programming, presenting a comprehensive and innovative methodology designed explicitly for handling uncertainties inherent in CLSC contexts.

The research findings highlight the effectiveness and reliability of the proposed framework for addressing uncertainties within CLSC networks. Through a comparative analysis with other established approaches, the model demonstrates its robustness, showcasing its potential to make informed and resilient decisions in supply chain management.

This study successfully addressed uncertainty in CLSC networks, providing logistics managers with a robust decision-making framework. Emphasizing the importance of PFNs and Pythagorean hesitant fuzzy programming, the research offered practical insights for optimizing transportation routes and resource allocation. Future research could explore dynamic factors in CLSCs, integrate real-time data and leverage emerging technologies for more agile and sustainable supply chain management.

This research contributes significantly to the field by introducing a novel and comprehensive methodology for managing uncertainty in CLSC networks. The adoption of PFNs and Pythagorean hesitant fuzzy programming offers an original and valuable approach to addressing uncertainties, providing practitioners and decision-makers with insights to make informed and resilient decisions in supply chain management.