Fuzzy Chance-constrained Programming Approach Research Articles

Chance-Constrained Optimization for a Green Multimodal Routing Problem with Soft Time Window under Twofold Uncertainty

This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.

A novel two-phase approach for a sustainable p-hub median problem with multiple service levels and carbon cap-and trade policy under uncertainty

ABSTRACT To reduce the carbon emissions for society's sustainable development and satisfy customers' personalized delivery service, this paper addresses the cap-and-trade policy and multiple service levels into a p-hub median problem. In the hub network designing, single-assignment patterns between hubs and demand nodes, the choice of transportation mode for each O-D pair and the uncertainties of carbon emission and price are taken into account. Based on a fuzzy chance-constrained programming approach, a fuzzy mathematical model under an expected cost-minimization context with some fuzzy constraints is first presented. Then a two-phase approach is proposed to solve the proposed model. Finally, in view of the comparative analysis with small- and large-scale Turkish instances, serval managerial insights are finally obtained for government and logistics companies in the reduction of carbon emission and the hub network's total designing cost for the sustainable development.

Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach

An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.

Sustainable fuzzy multi-trip location-routing problem for medical waste management during the COVID-19 outbreak

The performance of waste management system has been recently interrupted and encountered a very serious situation due to the epidemic outbreak of the novel Coronavirus (COVID-19). To this end, the handling of infectious medical waste has been particularly more vital than ever. Therefore, in this study, a novel mixed-integer linear programming (MILP) model is developed to formulate the sustainable multi-trip location-routing problem with time windows (MTLRP-TW) for medical waste management in the COVID-19 pandemic. The objectives are to concurrently minimize the total traveling time, total violation from time windows/service priorities and total infection/environmental risk imposed on the population around disposal sites. Here, the time windows play a key role to define the priority of services for hospitals with a different range of risks. To deal with the uncertainty, a fuzzy chance-constrained programming approach is applied to the proposed model. A real case study is investigated in Sari city of Iran to test the performance and applicability of the proposed model. Accordingly, the optimal planning of vehicles is determined to be implemented by the municipality, which takes 19.733 h to complete the processes of collection, transportation and disposal. Finally, several sensitivity analyses are performed to examine the behavior of the objective functions against the changes of controllable parameters and evaluate optimal policies and suggest useful managerial insights under different conditions.

A fuzzy chance-constrained programming model for integrated planning of the wheat supply chain considering wheat quality and sleep period: a case study

Wheat is a staple food in many countries, and as a result, the first most cultivated crop worldwide. Since wheat is a vital product in terms of food security, and its supply chain needs to be studied and planned carefully. This paper proposes a mixed-integer linear programming model for integrated planning of imported and domestically-produced wheat that addresses supplier selection, order planning, transportation, storage, and distribution problems at the same time. Specifically, this model focuses on the wheat quality and wheat sleep period. Moreover, differentiation of long-term and short-term storage facilities and consideration of intra-layer flows between storage facilities are other characteristics of this model. A fuzzy chance-constrained programming approach is employed to cope with the uncertainties associated with domestic supply, demand, and global wheat prices. Applicability and advantages of the developed model are demonstrated using real data from the wheat supply chain of Iran. Results show that the current status of the wheat supply chain of Iran is far from being optimal, and there are many opportunities for improvement.

QFD-Based Product Design for Multisegment Markets: A Fuzzy Chance-Constrained Programming Approach

Modern companies are moving rapidly toward more customer-oriented approaches for new product design and development. In real-world applications, customer requirements are more diverse and rather heterogeneous in practice, which requires the targeted market to be multisegmented. In this article, employing the quality function deployment (QFD) and assuming that parameter uncertainty exists, we propose a new fuzzy QFD model for use in multisegment markets, to search for optimal engineering characteristics by maximizing the overall customer satisfaction score. Under that framework, and when the credibility measure is employed, we adopt a fuzzy chance-constrained programming setting to convert the fuzzy model into its crisp counterpart. Afterwards, an analytical method based on fuzzy operational law is proposed to further transform the chance-constrained programming into an equivalent explicit model that can be solved directly by a standard commercial software. For a targeted group of customers, a new yoghurt design is presented to illustrate the effectiveness and superiority of our treatment. We report that our methodology not only permits the selection of the preferred solution based on an acceptable level of risk, which is very important in practice, but also guarantees higher customer satisfaction scores. This fact extends the fuzzy QFD methodology to a wider range of applications.

A Hybrid Heuristic Based on a Particle Swarm Algorithm to Solve the Capacitated Location-Routing Problem With Fuzzy Demands

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered, which simultaneously solves two problems: locating the facilities and designing the vehicle routes among the established facilities and customers. In the CLRP-FD, the capacities of the employed vehicles and established facilities cannot exceed, and the demands of the customers are assumed to be triangular fuzzy variables. To model the CLRP-FD, a fuzzy chance constrained programming approach is designed using fuzzy credibility theory. To solve this problem, a hybrid particle swarm optimization (HPSO) algorithm, which includes a stochastic simulation and a local search strategy based on the variable neighborhood search algorithm, is proposed. Finally, the influence of the value of the dispatcher preference index ( DPI ) on the total distribution cost is analyzed by conducting numerical experiments. To evaluate the efficiency of the proposed HPSO and the performance of the CLRP-FD model, the results obtained using the HPSO were compared with their corresponding lower bound provided using the CPLEX solver. Moreover, we also evaluated the performance of HPSO through computational experiments on some well-known benchmark CLRP instances. The numerical results show that the proposed HPSO is competitive, and can give a satisfactory solution in a reasonable amount of time.

Optimal groundwater security management policies by control of inexact health risks under dual uncertainty in slope factors

Groundwater remediation is a complicated system with time-consuming and costly challenges, which should be carefully controlled by appropriate groundwater management. This study develops an integrated optimization method for groundwater remediation management regarding cost, contamination distribution and health risk under multiple uncertainties. The integration of health risk into groundwater remediation optimization management is capable of not only adequately considering the influence of health risk on optimal remediation strategies, but also simultaneously completing remediation optimization design and risk assessment. A fuzzy chance-constrained programming approach is presented to handle multiple uncertain properties in the process of health risk assessment. The capabilities and effectiveness of the developed method are illustrated through an application of a naphthalene contaminated case in Anhui, China. Results indicate that (a) the pump-and-treat remediation system leads to a low naphthalene contamination but high remediation cost for a short-time remediation, and natural attenuation significantly affects naphthalene removal from groundwater for a long-time remediation; (b) the weighting coefficients have significant influences on the remediation cost and the performances both for naphthalene concentrations and health risks; (c) an increased level of slope factor (sf) for naphthalene corresponds to more optimal strategies characterized by higher environmental benefits and lower economic sacrifice. The developed method could be simultaneously beneficial for public health and environmental protection. Decision makers could obtain the most appropriate remediation strategies according to their specific requirements with high flexibility of economic, environmental, and risk concerns.

A Fuzzy Goal Programming Approach for Solid Waste Management Under Multiple Uncertainties

In this study a fuzzy chance constrained programming approach is developed for municipal solid waste management to minimize the net system cost and maximize the revenue generated from different treatment facilities. Most of the parameters involved with this model are imprecisely defined and probabilistically uncertain. A fuzzy chance programming model is developed to minimize the net system cost of sorting and transporting the wastes and to maximize the revenue generated from different treatment facilities. To resolve the cases arising due to the multiple occurrences of fuzzy goals, a fuzzy goal programming has been adopted. To expound the potential use of the approach, modified version of a case example, studied previously, has been considered and solved. The achieved model solution is compared with the existing technique for waste management, studied earlier.