Fuzzy Stochastic Programming Research Articles

Compromising allocation for optimising agri-food supply chain distribution network: a fuzzy stochastic programming approach

Compromising allocation for optimising agri-food supply chain distribution network: a fuzzy stochastic programming approach

Designing a sustainable, resilient, and responsive wheat supply chain under mixed uncertainty: A multi-objective approach

The stability and long-term viability of agri-food supply chains are at risk due to factors such as rapid population growth and global disruptions like the COVID-19 pandemic. This study develops a multi-objective robust fuzzy stochastic programming model to integrate sustainability, resilience, and responsiveness in designing agri-food supply chains operating under uncertain conditions. The sustainability-related objectives of the proposed model aim to reduce the overall cost and negative environmental and social effects. The resilience-related objectives in this model focus on decreasing the node criticality, complexity, and customer dissatisfaction. Additionally, minimizing the total delivery time serves as a measure of responsiveness. In this study, the Torabi and Hassini (TH) interactive fuzzy programming method and the Best-Worst Method (BWM) are applied as a solution approach to handle the multi-objective model. The proposed multi-objective model is applied to a Canadian wheat supply chain, considering its distinct features like blending, wheat quality, weather, and intermodal transport. Moreover, comprehensive sensitivity analyses are carried out to examine the effects of changing the model's parameters on the objective functions. Finally, the performance of the presented model is evaluated by conducting a comparative analysis. The results demonstrate the model's ability to handle hybrid uncertainty and provide tradeoffs between various objectives, which can benefit decision-makers.

A New Fuzzy Stochastic Integrated Model for Evaluation and Selection of Suppliers

In light of the rapid rate of change and unforeseen occurrences seen in the realms of technology, market dynamics, and the wider business landscape, there is a growing need for the inclusion of uncertainty and risk factors in the realm of supply chain planning. Supplier evaluation and selection (SES) is a major strategic decision area where the impact of uncertainty and risk can be more proactively dealt with. A review of extant literature reveals that there is a strong need for developing practitioner-oriented and more comprehensive frameworks and models to mitigate both the capability- and performance-related risks, in the context of SES decisions. This paper presents an integrated model to support SES decisions involving quantity discounts and multiple planning periods under stochastic conditions. The proposed model employs the Fuzzy Analytical Hierarchy Process (FAHP), Fuzzy Evaluation Based on Distance from Average Solution EDAS (EDAS-F), and fuzzy stochastic goal programming (FSGP) to effectively address the above requirements. A case study from a garment manufacturing industry is used to demonstrate the efficacy of the proposed model. The findings of the study provide confirmation that the suggested FSIM has the ability to provide substantial advantages in the context of making choices related to quantity discounts in SES. The proposed FSIM model incorporates the use of FAHP and EDAS-F techniques to effectively reduce the number of suppliers to a manageable level, taking into consideration capability-based risks. Additionally, fuzzy stochastic goal programming (FSGP) is employed to mitigate performance-based risks, enabling the selection of suppliers and the allocation of orders among them. The paper contributes to the literature by proposing a comprehensive framework to solve the SES problem, considering certain practical situations faced by organizations.

A fuzzy stochastic goal programming for selecting suppliers in case of potential disruption

ABSTRACT Due to globalization and the new characteristics of the business, companies face various challenges to ensure their continuity and competitive advantages. COVID-19 pandemic can be an extreme event that will eventually force many businesses and all industries to redesign and transform their global supply chain model? Challenges concerning mainly reducing the operating cost which is based on selecting the optimal suppliers to provide a reliable product. This study contributes to solving a supplier selection problem under disruption risk due to the lack of literature reviews with a lack of multi-methodological perspective for the fuzzy stochastic notions and quantitative techniques for the quantification of risk alternatives. Prior studies are neglecting to consider the value of risk and prefer to discover chances for optimizing anticipated costs or profits. This study proposed a fuzzy stochastic goal programming approach for selecting the optimal supplier under disruption risk. The proposed model incorporates multiple criteria such as capacity, stochastic demand, and probability of disturbance. The problem of stochastic combinatorial optimization obtained is presented as a program of fuzzy random aim by integrating techniques of value at risk and conditional risk value. Numeric samples and calculation results are included. The results of the models help the decision-maker to optimize the selection of suppliers in the event of a disturbance risk problem by an estimated value at risk and by simultaneously minimizing the conditional value of the risk and demonstrate the efficacy and acceptability of the created risk-averse technique as well as the effects of risk factors on our model behavior.

Supply portfolio selection for lead-time sensitive manufacturers under operational and disruption risks

PurposeThis paper proposes a two-level supply chain including suppliers and manufacturers. The purpose of this paper is to design a resilient fuzzy risk-averse supply portfolio selection approach with lead-time sensitive manufacturers under partial and complete supply facility disruption in addition to the operational risk of imprecise demand to minimize the mean-risk costs. This problem is analyzed for a risk-averse decision maker, and the authors use the conditional value-at-risk (CVaR) as a risk measure, which has particular applications in financial engineering.Design/methodology/approachThe methodology of the current research includes two phases of conceptual model and mathematical model. In the conceptual model phase, a new supply portfolio selection problem is presented under disruption and operational risks for lead-time sensitive manufacturers and considers resilience strategies for risk-averse decision makers. In the mathematical model phase, the stages of risk-averse two-stage fuzzy-stochastic programming model are formulated according to the above conceptual model, which minimizes the mean-CVaR costs.FindingsIn this paper, several computational experiments were conducted with sensitivity analysis by GAMS (General algebraic modeling system) software to determine the efficiency and significance of the developed model. Results show that the sensitivity of manufacturers to the lead time as well as the occurrence of disruption and operational risks, significantly affect the structure of the supply portfolio selection; hence, manufacturers should be taken into account in the design of this problem.Originality/valueThe study proposes a new two-stage fuzzy-stochastic scenario-based mathematical programming model for the resilient supply portfolio selection for risk-averse decision-makers under disruption and operational risks. This model assumes that the manufacturers are sensitive to lead time, so the demand of manufacturers depends on the suppliers who provide them with services. To manage risks, this model also considers proactive (supplier fortification, pre-positioned emergency inventory) and reactive (revision of allocation decisions) resilience strategies.

Sustainable management of water-agriculture-ecology nexus system under multiple uncertainties

The shrinkage and ecological degradation of the Aral Sea resulting from the uncontrolled use of water resources and the unregulated expansion of agriculture activities call for sustainable management of water-agriculture-ecology (WAE) nexus from a basin perspective. However, managers face thorny challenges brought by multiple uncertainties in the management and planning processes. In this study, an interval stochastic fuzzy programming (ISF) method is developed for tackling multiple uncertainties presented as probability distributions, flexible variables and interval parameters. Then, an ISF-WAE model is formulated for Aral Sea Basin, which considers 108 planning scenarios that reflect different food-security and ecology-restoration requirements, as well as risk-response attitudes of decision maker over a long-term planning horizon (2021–2050). Results reveal that for Aral Sea Basin: (i) managers should set strict acreage benchmarks for cereal crops, in which wheat would account for a range of [29.1, 31.2] % of the total agricultural area; (ii) for promoting ecological restoration, the proportion of agricultural water allocation should decrease by a range of [12.7, 16.1] % during the planning horizon; (iii) due to low water requirement and high ecological value of grassland, it is recommended to expand grassland area to improve the sustainability of the Aral Sea Basin in the case of limited water resources.

A novel multi-objective robust fuzzy stochastic programming model for sustainable agri-food supply chain: case study from an emerging economy

On the one hand, supply chain management of agri-food products under uncertain conditions has a significant impact on food security and, on the other hand, increases the profits of supply chain components. Moreover, considering the sustainability concepts leads to more social and environmental benefits. The present study investigates the canned food supply chain under uncertain conditions and sustainability concepts by considering strategic and operational decisions and different characteristics. The proposed model is a multi-echelon, multi-period, multi-product, multi-objective location-inventory-routing problem (LIRP) in which the vehicle fleet is considered heterogeneously. The objectives of this model are to (1) minimize costs, (2) minimize customer dissatisfaction, (3) maximize production throughput, and (4) maximize job opportunities. In this study, carbon cap and trade mechanism are used to minimize environmental damage. Robust fuzzy stochastic programming (RFSP) is employed to cope and control uncertainties. The multi-objective optimization problem is implemented on a real case and solved using the Torabi and Hassini (TH) method. The results of this study showed that with increasing confidence levels, the severity of the problem increased and the values of the objective functions worsened. Also, using the relative value of stochastic solution (RVSS) criterion demonstrated that the effect of utilizing the RFSP approach on the first and second objective functions was higher than that the nominal approach showed itself. Finally, sensitivity analysis is performed on two parameters: the selling price of products to foreign customers and the cost of purchasing products from farms. The results of this study showed that changing these two parameters had a significant effect on the first and second objective functions.

Pareto Optimal Solution of a Fuzzy Newsboy Problem

In this paper, a multi-item classical newsboy problem is formulated, occurring both fuzziness and randomness with floor space constraint. Here, the demand is considered as a random variable in fuzzy sense and also the purchase cost, salvage value, and selling price are fuzzy numbers. Initially, a method is explained for solving such a problem by using the minimization of a FN by Buckley [Buckley, JJ (2003). Fuzzy probabilities: New approach and applications]. Then the fuzzy programming technique, [Formula: see text]-constraint, and the weighted sum methods are applied to handle the multiobjective programming problem. The basic idea for transforming the fuzzy stochastic programming problem into a deterministic equivalent has been discussed. Finally, the deterministic model is solved by the LINGO package and is illustrated numerically.

Improved managerial decisions for fuzzy stochastic bi-objective linear programming models: A Trade-off ratio-based autonomized approach

Improved managerial decisions for fuzzy stochastic bi-objective linear programming models: A Trade-off ratio-based autonomized approach

Sustainable inventory management in blood banks considering health equity using a combined metaheuristic-based robust fuzzy stochastic programming

This study examines the challenges of healthcare systems toward sustainable inventory management of blood products. In this regard, three main goals are pursued; First, promoting social equity in providing medical services to various patients and reducing the risk to lives. Second, the optimal management of medical products in a way that minimizes economic costs. Third, optimal management of biological waste due to inventory corruption and reduction of greenhouse gas emissions caused by transportation, to the least environmental pollution. To achieve these purposes, a practical demand-driven multi-objective inventory model is presented by utilizing hybrid policies in an uncertain environment. In the proposed model, the demands are in two types, including elective and non-elective. These demands are classified according to their medical urgency, substitution allowance, and product freshness. A hybrid robust fuzzy stochastic programming approach is applied to capture real-world uncertainties. The proposed model is implemented for blood platelet. The solution is obtained using a combined metaheuristic technique established on genetic algorithms and simulated annealing according to global and local search paradigms. To create a proper perspective for decision-makers, sensitivity analysis is performed. Besides, the performance of the model is proved by the realization. The results show that the performance of the proposed RFSP model is better than the Nominal model. Also, it performs well in minimizing the overall system costs and environmental degradation, besides reducing shortage and wastage. It is also effective for taking steps toward equity in health and suggests a proper strategy for dealing with emergencies.

A hybrid machine learning-optimization approach to pricing and train formation problem under demand uncertainty

Due to the complexity of pricing in the service industry, it is important to provide an efficient pricing framework for real-life and large-sized applications. To this end, we combined an optimization approach with a regression-based machine learning method to provide a reliable and efficient framework for integrated pricing and train formation problem under hybrid uncertainty. To do so, firstly, a regression-based machine learning model is applied to forecast the ticket price of the passenger railway, and then, the obtained price in is used as the input of a train formation optimization model. Further, in order to deal with the hybrid uncertainty of demand parameters, a robust fuzzy stochastic programming model is proposed. Finally, a real transportation network from the Iran railway is applied to demonstrate the efficiency of the proposed model. The analysis of numerical results indicated that the proposed framework is able to state the optimal price with less complexity in comparison to traditional models.

Power distribution network design considering the distributed generations and differential and dynamic pricing

In this study, a power distribution network design model is developed considering voltage control, as well as differential and dynamic pricing schemes. The objective is to maximize power distribution network profits under uncertain demands and parameters, such as power generation capacity, investment and generation cost of renewable distributed generation units, and the penalty budget for unsatisfied demands. The model determines the percentage of the power supply to the customer groups, the amount of power supplied to each customer group, the technology and capacity of renewable distributed generation units, and the prices offered. The proposed pricing scheme is differential for different types of customers with allowable voltage limits. The price is dynamic according to the planning time, including low, medium, and peak times. A fuzzy stochastic programming approach is developed to solve this problem. By simultaneously using triangular crisp numbers and probabilistic variables, the fuzzy stochastic programming integrates the fuzzy and stochastic approaches to deal with the uncertainty of demand and parameters. The numerical analysis shows that, as the confidence level decreases, the capacity of renewable distributed generation units and the profit increase. The results also show that when the decision maker responds to the uncertainty in demand with a high confidence level, the optimum profit can be obtained; approximately 55.90% of the power is supplied to low-demand customers.

Design of control strategies to help prevent the spread of COVID-19 pandemic

This paper proposes control strategies to allocate COVID-19 patients to screening facilities, health facilities, and quarantine facilities for minimizing the spread of the virus by these patients. To calculate the transmission rate, we propose a function that accounts for contact rate, duration of the contact, age structure of the population, susceptibility to infection, and the number of transmission events per contact. Moreover, the COVID-19 cases are divided into different groups according to the severity of their disease and are allocated to appropriate health facilities that provide care tailored to their needs. The multi-stage fuzzy stochastic programming approach is applied to cope with uncertainty, in which the probability associated with nodes of the scenario tree is treated as fuzzy variables. To handle the probabilistic model, we use a more flexible measure, Me measure, which allows decision-makers to adopt varying attitudes by assigning the optimistic-pessimistic parameter. This measure does not force decision-makers to hold extreme views and obtain the interval solution that provides further information in the fuzzy environment. We apply the proposed model to the case of Tehran, Iran. The results of this study indicate that assigning patients to appropriate medical centers improves the performance of the healthcare system. The result analysis highlights the impact of the demographic differences on virus transmission, and the older population has a greater influence on virus transmission than other age groups. Besides, the results indicate that behavioral changes in the population and their vaccination play a key role in curbing COVID-19 transmission.

A stochastic modeling approach for analyzing water resources systems

Many uncertain factors exist in the water resource systems, leading to dynamic characteristics of the water distribution process. Especially for the watershed including irrigation area with multiple water sources and water users, it is complicated that the joint risk among available water from each water source and multi-uncertainties under water resource allocation among multiple water users. In this research, an approach is developed that a copula-based interval multi-stage fuzzy stochastic programming (CIMFSP) model. This research aims at figuring out the planning of a case study for water-resources management. In the multi-sources water supply subsystem, the copula function is introduced to tackle the interaction of water availability between two water sources (i.e., A &B). Joint risk was set 0.05, 0.10, 0.15 to reflect the shortage risk of total available water at diverse levels. An interval parameter multi-stage fuzzy stochastic programming (IMFSP) model is developed for water resource distribution in a multi-users water-demand subsystem. Through this model, uncertainties presented as interval numbers and probability distributions, as well as fuzzy sets, were handled. The dynamics of the entire water resource system can be reflected by multi-stage discrete trees. A series of solutions can be generated under multiple scenarios (i.e., joint risk and α-cut levels). The modeling results will produce a series of alternatives under a battery of scenarios and help the decision-makers get an insight into the tradeoff between the system economic benefit and financial penalties under the corresponding risk level. This approach is valuable for improving the feasibility of optimal results in the watershed with irrigation region water resource management.

A disaster relief commodity supply chain network considering emergency relief volunteers: a case study

PurposeThe 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.Design/methodology/approachIn 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.FindingsThe 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.Practical implicationsThis model helps decision-makers and authorities to explore optimal location and allocation decisions without using complex optimization algorithms.Originality/valueTo 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.

Designing a Sustainable Green Closed-Loop Supply Chain under Uncertainty and Various Capacity Levels

The ever-increasing concerns of the growth in the volume of waste tires and new strict government legislations to reduce the environmental impact of the end-of-life (EOL) tires have increased interest among companies to design a sustainable and efficient closed-loop supply-chain (CLSC) network. In the real world, the CLSC network design is subject to a variety of uncertainties, such as random and fuzzy (epistemic) uncertainties. Designing a reliable and environmentally cautious CLSC with consideration of risks and the uncertainty of the parameters in the network is necessary for a successful supply-chain network. This study proposes a sustainable and environmentally cautious closed-loop supply-chain network for the tire industry, by considering several recovery options, including retreading, recycling, and energy recovery. This study aims to design and develop a robust multi-objective, multi-product, multi-echelon, multi-cycle, multi-capacity, green closed-loop supply-chain network under hybrid uncertainty. There are two types of uncertainties associated with the parameters in the network. There is an uncertainty associated with the demand, which is expressed in some future scenarios according to the probability of their occurrences, as well as fuzzy-based uncertainty associated with return rates, retreading rates, recycling rates, procurement, and production costs, which are expressed with possibilistic distributions. In order to deal with this hybrid uncertainty, a robust fuzzy stochastic programming approach has been proposed, and the proposed mixed integer programming model is applied to a case study in the tire industry to validate the model. The result indicates the applicability of the proposed model and its efficiency to control the hybrid uncertainties and the risk level in the network.

Light robustness model for the bidding strategy of an electric vehicle aggregator

Considering the uncertainties of the behaviour of electric vehicles (EVs) and the bidding of other participants in the market, the light robustness bidding model for the EV aggregator in the day-ahead market is constructed. The model is a bilevel model, with the upper-level model representing cost minimisation of the EV aggregator, whereas the lower-level model represents market clearing providing market price and bidding energy for the upper-level model. Bids of other market participants and EV driving pattern were not known to the EV aggregator in advance. They were seen as uncertain variables. A numerical example was used to illustrate the feasibility of the proposed method. Through the example analysis, the costs of the EV aggregator under different circumstances are compared and, under the same uncertainties, the results of the method proposed herein are also compared with the traditional robust optimisation method and stochastic fuzzy programming method.

Robust Fuzzy-Stochastic Programming Model and Meta-Heuristic Algorithms for Dual-Resource Constrained Flexible Job-Shop Scheduling Problem Under Machine Breakdown

Resource scheduling, job sequencing, and assigning them to available resources are the most critical issues in manufacturing systems, such as flexible job-shop systems. In addition, scheduling uncertainties have attracted significant attention in this field. This study investigates the dual-resource constrained flexible job-shop scheduling (DRCFJSS) problem under machine breakdown and operational uncertainty. Stochastic scenario-based methods were utilized to study the uncertain nature of the problem. Because process times have inherent uncertainty, they are considered fuzzy numbers and are controlled by a credibility-based measure. Robust scheduling must be developed to address unexpected disruptions, such as machine breakdowns and operational risks, such as uncertain process times. Accordingly, a novel robust fuzzy stochastic programming (RFSP) model is presented to solve this problem. In the proposed RFSP model, the objective function is formulated using a hybrid measure (i.e., a combined average-case and worst-case performance of the manufacturing system) under probable machine breakdown scenarios. Because the DRCFJSS problem is NP-hard, two types of meta-heuristic algorithms, evolutionary population-based, genetic algorithm (GA), and vibration damping optimization (VDO) algorithm, are used for large-size problems. Then, the proposed RFSP model was applied to a case study, and numerical experiments with randomly generated test problems were used. In small-sized problems, the proposed model is solved using the CPLEX solver, GA, and VDO algorithms. Computational studies indicate a higher performance of the GA compared with the other algorithms in terms of the objective function.

A risk-sharing-based resilient renewable energy supply network model under the COVID-19 pandemic.

Over the past few months, the COVID-19 pandemic has postponed many renewable energy projects because of disruptions in the technology and finance supply. Additionally, the existing power plants are inefficient because of a record drop in demand for goods and services caused by lockdowns in cities. This situation poses huge challenges to the resilience of renewable energy supply networks in the face of deeply hazardous events, such as the COVID-19 pandemic. Therefore, the purpose of this study was to design a resilient renewable energy supply network considering supply, demand, and payment risks caused by COVID-19. The objective of the proposed model was to determine the optimal amount of electric power generated and stored to meet the demands and the risk-sharing effort index to maximize the total resilient profit of the power plant and determine the optimal price adjustment index to minimize the cost to consumers. A government subsidy-based risk-sharing model was developed to enhance the resilience of the concerned renewable energy supply network under the pandemic. To overcome uncertainties in both random and risk events, a robust fuzzy-stochastic programming model was proposed to solve these research problems. Computational experiments were conducted on the test supply network in Vietnam. The results showed that the resilient energy supply network with the risk-sharing model tended to stabilize the total profit with the different impact levels of COVID-19 compared to the network without risk-sharing. The proposed model efficiently tackled both uncertainties in random and hazardous events and had a higher profit and shorter CPU time compared to the robust optimization mode.

Solving fuzzy stochastic multi-objective programming problems based on a fuzzy inequality

Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic orfuzzy problem. By using a special type of fuzzy inequality, wetransform the problem into a convenient stochastic problem. Thensome known methods are applied to obtain the optimal solution.Finally, the equivalent multi-objective problem is solved by aninteractive approach. A numerical example is provided to illustrate the procedure.