Fuzzy Stochastic Programming Model Research Articles

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.

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.

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.

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.

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.

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.

Sustainable allocation of water resources in water-scarcity conditions using robust fuzzy stochastic programming

Economic, social, and demographic development has globally led to an increased demand for water, consequently forcing some countries to face the shortage of water resources. In Iran, the problem of water scarcity is such a serious challenge that the sustainable allocation of water resources is sought after so as to help deal with this crisis. To this aim, the present paper proposes a new Robust Fuzzy Stochastic Programming model for the allocation of water resources. For the first time in the literature of stochastic water allocation problem, we applied the sustainability index to the optimization model and considered different levels of groundwater in an allocation system. Another feature of this model is its capability in considering a hybrid uncertainty in the parameters of the model, i.e. fuzzy stochastic scenarios, in a robust fuzzy stochastic programming model. Our proposed model considers three objective functions, namely maximizing the profits of different consumption sectors, minimizing the loss of different sectors caused by water shortage in different scenarios, and minimizing the allocation of salt water from ground water. The model has been applied in Mashhad city, northeastern Iran, which has long had water scarcity as an issue. We studied the allocation of water from surface, ground, and recycled wastewater resources to the three sectors of agricultural, municipal, and industrial; the results indicated that water allocation patterns and water shortages were affected by different scenarios. In fact, the municipal and agricultural sectors did not face water shortage in all scenarios, whereas the industrial sector encountered water scarcity in a drought year. Moreover, the assessment of optimality and feasibility robustness of the model indicated that the proposed model is robust.

A genetic algorithm for fuzzy random and low-carbon integrated forward/reverse logistics network design

Considering the influence of carbon emissions trading, the fuzzy stochastic programming model was established to cut back the total cost of carbon trading balance. Modeling this chain is carried out by accounting for carbon cap-and-trade considerations and total cost optimization. In this paper, we analyze the low-carbon integrated forward/reverse logistics network and made relevant simulation tests. The results show that the changes of the confidence level and carbon emission limits have obvious influences on logistics costs. If the emission limit is large, carbon trading mechanism has little effect on the total logistics cost in the same scenario. Therefore, the government needs to use the appropriate emission limits to guide enterprises to reduce carbon emissions, and enterprises can make coping strategies according to the different limit at the same time. Therefore, the fuzzy random programming model proposed in this paper is practical. Its decision making applying the proposed algorithm is reasonable and applicable and could provide decision basis for enterprise managers.

Integrated relief pre-positioning and procurement planning in humanitarian supply chains

Humanitarian organizations typically pre-position relief items in strategic locations whose optimum levels are affected by the amounts of pre-disaster contractual agreements and post-disaster procurements. To account for these interrelationships, this paper proposes a novel two-stage scenario-based mixed fuzzy-stochastic programming model for integrated relief pre-positioning and procurement planning based on a quantity flexibility (QF) contract under a mixture of uncertain data. An effective multi-step solution method is also devised to solve the problem in real-sized instances. Applicability of the proposed model is examined through a real case study. Finally, a number of sensitivity analyses are conducted to provide helpful managerial insights.

A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network

ABSTRACTRecently, governmental legislations, limitation of natural resources and adverse effects of End-of-Life products on ecological system have spurred researchers to design closed-loop supply chains (CLSCs). Accordingly, designing green supply chains (SCs) that manage greenhouse gas emissions and prevent air pollution can be helpful for companies to heighten profitability and customer loyalty, besides, uncertainty of parameters and disruption strikes could adversely affect performance of SCs and lower quality of output decisions. Effective planning prevents great losses and increases reliability of manager's decisions against uncertainties. Therefore, this paper is proceeding to design a reliable bi-objective green CLSC that minimizes total costs of network aside with minimizing harmful gas emissions. The proposed model is capable of controlling adverse effects of disruptions via applying scenario-based stochastic programming approach. Also, an effective hybrid robust fuzzy stochastic programming method is extended to effectively control uncertainty of parameters and risk-aversion level of output decisions. Extended model analyzing is based on lead-acid battery SC case study that output results approve applicability and effectiveness of model.

An inexact fixed-mix fuzzy-stochastic programming model for heat supply management in wind power heating system under uncertainty

To better utilize electricity generated by wind power in northern China and ease the strain on local energy grids in the winter, the National Energy Administration (NEA) is committed to promoting the development of wind power heating projects in areas where conditions are suitable. However, multiple uncertainties and complexities that exist in the processes of wind power generation and heat supply present substantial challenges to the stability of wind power heating system and put its operation into risk. Therefore, an inexact fixed-mix fuzzy-stochastic programming (IFFSP) method was developed and applied to the heat supply management of an actual wind power heating system under uncertainties presented as interval values, random variables and fuzzy sets within a multi-stage context. Interval solutions associated with plausibility degrees of constraint violation can help decision makers identify the optimal heat supply management strategies and gain a comprehensive tradeoff between economic objectives and reliability risks of system. Moreover, the feasibility of wind power heating project in promoting wind power consumption and relieving wind curtailment is studied, and the results indicated that the effect is limited. Finally, suggestions aimed on resolving issues of integration and consumption of wind energy are proposed.

A fuzzy stochastic model for telecommunications bandwidth brokers under probabilistic QoS measures

In this paper, we model and solve profit maximization problem of a telecommunications Bandwidth Broker (BB) under uncertain market and network infrastructure conditions. The BB may lease network capacity from a set of Backbone Providers (BPs) or from other BBs in order to gain profit by leasing already purchased capacity to end-users. BB’s problem becomes harder to deal with when bandwidth requests of end-users, profit and cost margins are not known in advance. The novelty of the proposed work is the development of a mechanism via combining fuzzy and stochastic programming methodologies for solving complex BP selection and bandwidth demand allocation problem in communication networks, based on the fact that information needed for making these decisions is not available prior to leasing capacity. In addition, suggested model aims to maximize BB’s decision maker’s satisfaction ratio rather than just profit. As a solution strategy, the resulting fuzzy stochastic programming model is transformed into deterministic crisp equivalent form and then solved to optimality. Finally, the numerical experiments show that on the average, proposed approach provides 14.30% more profit and 69.50% more satisfaction ratio compared to deterministic approaches in which randomness and vagueness in the market and infrastructure are ignored.

A stochastic-fuzzy programming model with soften constraints for electricity generation planning with greenhouse-gas abatement

SUMMARY Increased atmospheric CO2 concentration is widely being considered as the main driving factor that causes the phenomenon of global warming, due to the ever-boosting use of fossil fuels. In this study, a fuzzy-stochastic programming model with soft constraints (FSP-SC) is developed for electricity generation planning and greenhouse gas (GHG) abatement in an environment with imprecise and probabilistic information. The developed FSP-SC is applied to a case study of long-term planning of a regional electricity generation system, where integer programming technique is employed to facilitate dynamic analysis for capacity expansion within a multi-period context to satisfy increasing electricity demand. The results indicate different relaxation levels can lead to changed electricity generation options, capacity expansion schemes, system costs, and GHG emissions. Several sensitivity analyses are also conducted to demonstrate that relaxation of different constraints have different effects on system cost and GHG emission. Tradeoffs among system costs, resource availabilities, GHG emissions, and electricity-shortage risks can also be tackled with the relaxation levels for the objective and constraints. Copyright © 2012 John Wiley & Sons, Ltd.

Management of Uncertain Information for Environmental Systems Using a Multistage Fuzzy-Stochastic Programming Model with Soft Constraints

In this study, a multistage fuzzy-stochastic programming model with soft constraints (FSPM-SC) is developed for managing environmental systems associated with uncertain information. The developed model can deal with uncertainties expressed as probability distributions and fuzzy sets; it can also reflect the dynamics in terms of decisions for waste-flow allocation and capacity expansion, through transactions at discrete points of a complete scenario set over a multistage context. The results indicate that solutions have been generated for binary and continuous decision variables under fuzzy and random information. They can be used for generating waste-flow-allocation pattern and facility-capacity-expansion scheme with a cost-effective manner. Sensitivity analyses are also conducted to demonstrate that the violation of waste-disposal-demand constraint has significant effect on reducing system cost.

A new method for redundancy optimisation problem with fuzzy random lifetime

In this paper, a redundancy optimisation problem, in which element lifetimes are fuzzy random variables (FRVs), is formulated by using fuzzy stochastic programming model. Subsequently, a new method is developed to solve the model based on the concepts of mean value of FRVs, chance-constrained programming and binary integer programming. Furthermore, an illustrative numerical example is also solved to clarify the methods discussed in this paper and major types of system performance are investigated.

A multistage fuzzy-stochastic programming model for supporting sustainable water-resources allocation and management

In this study, a multistage fuzzy-stochastic programming (MFSP) model is developed for tackling uncertainties presented as fuzzy sets and probability distributions. A vertex analysis approach is proposed for solving multiple fuzzy sets in the MFSP model. Solutions under a set of α-cut levels can be generated by solving a series of deterministic submodels. The developed method is applied to the planning of a case study for water-resources management. Dynamics and uncertainties of water availability (and thus water allocation and shortage) could be taken into account through generation of a set of representative scenarios within a multistage context. Moreover, penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The modeling results can help to generate a range of alternatives under various system conditions, and thus help decision makers to identify desired water-resources management policies under uncertainty.

An Inexact Two-stage Fuzzy-stochastic Programming Model for Water Resources Management

An inexact two-stage fuzzy-stochastic programming (ITFSP) method is developed for water resources management under uncertainty. Fuzzy sets theory is introduced to represent various punishment policies under different water availability conditions. As an extension of conventional two-stage stochastic programming (TSP) method, two special characteristics of the proposed approach make it unique compared with existing approaches. One is it could handle flexible penalty rates, which are much reasonable for both of the authorities and users, and have seldom been considered in the TSP framework. The other is uncertain information expressed as discrete intervals and probability distribution functions can be effectively reflected in the optimization processes and solutions. After formulating the model, a hypothetical case is employed for demonstrating its applicability under two scenarios, where the inflow is divided into four and eight intervals, respectively. The results indicate that reasonable solutions have been obtained. They provide desired allocation patterns with maximized system benefit under two feasibility levels. The solutions present as stable intervals with different risk levels in violating the water demands, and can be used for generating decision alternatives. Comparisons of the solution from the ITFSP with that from the ITSP (inexact two-stage stochastic programming) and TSP approach are also undertaken. It shows that the ITFSP could produce more system benefit than existing methods and deal with flexible penalty policies for better water management and utilization.