Multi-objective Stochastic Programming Research Articles

Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems

This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology.

Integrated optimization of facility location, casualty allocation and medical staff planning for post-disaster emergency response

PurposeDisaster management and humanitarian logistics (HT) play crucial roles in large-scale events such as earthquakes, floods, hurricanes and tsunamis. Well-organized disaster response is crucial for effectively managing medical centres, staff allocation and casualty distribution during emergencies. To address this issue, this study aims to introduce a multi-objective stochastic programming model to enhance disaster preparedness and response, focusing on the critical first 72 h after earthquakes. The purpose is to optimize the allocation of resources, temporary medical centres and medical staff to save lives effectively.Design/methodology/approachThis study uses stochastic programming-based dynamic modelling and a discrete-time Markov Chain to address uncertainty. The model considers potential road and hospital damage and distance limits and introduces an a-reliability level for untreated casualties. It divides the initial 72 h into four periods to capture earthquake dynamics.FindingsUsing a real case study in Istanbul’s Kartal district, the model’s effectiveness is demonstrated for earthquake scenarios. Key insights include optimal medical centre locations, required capacities, necessary medical staff and casualty allocation strategies, all vital for efficient disaster response within the critical first 72 h.Originality/valueThis study innovates by integrating stochastic programming and dynamic modelling to tackle post-disaster medical response. The use of a Markov Chain for uncertain health conditions and focus on the immediate aftermath of earthquakes offer practical value. By optimizing resource allocation amid uncertainties, the study contributes significantly to disaster management and HT research.

Model for Working Capital Management of Micro, Small and Medium Enterprises in Indonesia by Using Multiple Objective Stochastic Programming

Micro, small and medium enterprises (MSME) have a big influence for the economy in Indonesia. But almost of this company don’t have an optimal working capital management because less knowledge and limitation of financial not only from the owner but also financial credit from bank. Working capital management plays an important role in the success or failure of a company its business activities. To achieve optimal use of working capital management managers the company must accurately control the trade-off between profitability and liquidity. The purpose of this research is to develop a model of working capital management where the sales are under uncertainty and the company has a limit financial. This study was tested using multiple linear regression analysis to see the correlation between profitability and liquidity with x1, x2, x3, x4, and x5 then find optimal solution by stochastic multi objective programming because we consider that sales is in under certainty. The main variables used in the analysis of return on assets to measure profitability, receivable turnover to measure liquidity, inventory turnover, accounts payable days, cash conversion. The results showed that account payable, inventory turnover, and cash turn over have a positive correlation for liquidity but inventory turnover and cash turnover have negative correlation to profitability.

Adaptation to seasonal drought in irrigation districts of south China: A copula-based fuzzy-flexible stochastic multi-objective approach for precise irrigation planning

The occurrence of seasonal drought has led to periodic water shortages in irrigation districts of south China, posing significant agricultural challenges on water and food security. Consequently, there is a pressing need for high-efficient water resources management from a sustainability perspective. To address this issue, a copula-based fuzzy-flexible stochastic multi-objective programming (CFSMP) model was proposed to facilitate irrigation planning under the combined influence of seasonal dry and wet conditions. The model was aimed to simultaneously achieve maximum economic benefit, water productivity and green water use efficiency, considering the economic, social, and environmental spheres of the irrigation district. The CFSMP model represented an innovative solution that was capable of (1) precisely describing the response of crop yield to water supply at ten-day time scale, which can be matched with practical irrigation demand; (2) characterizing joint distributions of seasonal dry and wet conditions of precipitation during different crop growth periods based on the copula function; (3) reconciling conflicts on objectives among economic, social, and environmental spheres of the irrigation district in complex and uncertain environments. The proposed model was applied to the Dongfeng Reservoir Irrigation District in south China. The downscaled ten-day Jensen water production functions of main grain and cash crops were fitted to recognize precise distributions of crop water demand and water sensitivity index. The Frank copula, with the smallest value of squared Euclidean distribution, was selected to describe the joint distribution of seasonal precipitation and gain insights into actual seasonal water availability and water scarcity. The results showed that the proposed model produced more water-saving and yield-promoting irrigation planning policies than the current quota. The average water allocation of rice, wheat, maize, rape, and citrus decreased by 352.6 mm, 10.6 mm, 67.7 mm, 7.44 mm, and 54.6 mm, respectively. Except for a yield reduction of 8.8% for rape, crop yields of rice, wheat, maize, and citrus were improved by 33.3%, 45.4%, 29.9%, and 12.3%, respectively. The coordination degree of the model reached 0.827, demonstrating excellent performance on generating coordinated and robust solutions. Therefore, the CSFMP model has the potential to alleviate seasonal drought in south China and can be applied in similar regions with comparable resources crisis.

Towards a responsive-sustainable-resilient tea supply chain network design under uncertainty using big data

Nowadays, issues such as limited natural resources, environmental problems, social matters, and significance of resilience in agricultural supply chain (ASC) have dragged considerable attention worldwide. In this research, a five-level multi-objective stochastic mixed-integer linear programming model is designed for tea supply chain (TSC) in Iran. The objective functions of the suggested network are minimizing total costs of the supply chain (SC), the total water consumption, and non-resilience measures, and maximizing job opportunities of facilities. Literally, considering uncertainty for SC networks is extremely beneficial due to the existence of some variations in different parameters like demand. As a consequence, a robust possibilistic optimization (RPO) is implemented to manage the uncertainty. Due to the nature of the multi-objective optimization problem, the weighted-normalized-extended goal programming (WNEGP) approach is employed to solve the model. In order to credit the model, real data is collected from the tea organization of Iran. It is worth mentioning that parameters are gathered according to three aspects of big data: volume, velocity, and variety. The results validated the functionality of the model regarding planning strategy. In addition, it showed applying more costs on SC triggers an effective sustainable-resilient-responsive network. In terms of managerial insights, this study offers a far-reaching perspective to managers especially in ASC to develop their industries. Finally, some sensitivity analyses are discussed on key parameters such as demand, robustness coefficients, and also the value of the objective functions in various states. It is worth mentioning that sensitivity analyses on different states of the problem show how sustainability and resiliency affect the supply chain efficiency.

Rice irrigation water efficiency improvement: An AquaCrop-based optimization modeling approach

Rice is the cereal crop that consumes the largest amount of water in the world. To improve the water use efficiency of rice farming and promote the sustainable development of rice production, this study proposes a novel AquaCrop-based optimization modeling approach. First, an AquaCrop-based multiobjective model is constructed to generate dynamic water production functions (WPFs). The NSGA-II algorithm is employed to solve the model, and quadratic dynamic WPFs for rice under different hydrological years (wet, normal and dry) are generated based on the obtained Pareto fronts, which can improve the modeling efficiency and help reflect the complicated reality of water flows. Second, a fuzzy credibility-constrained stochastic multiobjective programming (FCC-SMOP) model is developed for irrigation water allocation based on the acquired WPFs. The model addresses the randomness of precipitation and runoff, the fuzziness of decision-makers' preferences, and conflicting objectives of water savings, benefit increments, and water demand during the critical period of rice growth. The proposed simulation-optimization approach was applied to the Changgang irrigation district in northeast China. Optimal irrigation amounts under different decision-making preference scenarios (including conservative, moderate and positive) and different hydrological years were simultaneously generated. The following conclusions can be drawn: (1) The AquaCrop-based multiobjective method is capable of generating WPFs of different hydrological years with sparse discontinuous field experiments; (2) the decision-making preferences of decision-makers significantly impact the economic benefits, water use efficiency, and practicality of schemes; and (3) the FCC-SMOP model successfully makes tradeoffs among the three objectives under multiple uncertainties and can further improve the system efficiency and increase planting income in the Changgang irrigation district when its irrigation facilities become optimal.

A multi-objective stochastic programming approach with untrusted suppliers for green supply chain design by uncertain demand, shortage, and transportation costs

In recent decades, people are paying more attention to protecting the environment and biological resources. One of the most important issues of environmental pollution is air pollution, with production and transportation contributing a significant number of emissions. Considering the various warnings about the excessive increase in the amount of carbon dioxide on the planet, it is necessary to investigate the solutions to reduce the emission of carbon dioxide. On the other hand, in the production cycle, providing more comprehensive models and finding more optimal designs will play a significant role in reducing energy consumption and increasing profitability. Models with the most uncertain parameters are more practical and closer to the real world. In this paper, we consider a multi-objective stochastic programming approach for green supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage, and capacity expansion costs are all considered uncertain parameters. At the same time, environmental approaches to reduce air pollution, (specifically reducing carbon dioxide emissions), are presented. Our multi-objective model includes the minimization of the sum of the total cost, the minimization of the variance of the total cost, the minimization of the financial risk or the probability of not meeting a certain budget, and the minimization of the amount of pollution consequent of production and transportation machines. In the following case study, a three-tier supply chain with four suppliers, four production centers, and three product distribution centers with uncertain demand, suppliers, processing, transportation, cost shortages, and capacity development are examined. To solve the model, two meta-heuristic algorithms (multi-objective genetics with faulty sorting and particle swarming) have been developed. The computational results and optimal designs of the supply set were obtained after the implementation of the algorithms, and finally, by performing Sensitivity Analysis and statistical tests, showed that there are two algorithms with good performance and in most cases, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is superior to the Multi-Objective Particle Swarm Optimization (MOPSO).

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.

Scheduling an Energy-Aware Parallel Machine System with Deteriorating and Learning Effects Considering Multiple Optimization Objectives and Stochastic Processing Time

Currently, energy conservation draws wide attention in industrial manufacturing systems. In recent years, many studies have aimed at saving energy consumption in the process of manufacturing and scheduling is regarded as an effective approach. This paper puts forwards a multi-objective stochastic parallel machine scheduling problem with the consideration of deteriorating and learning effects. In it, the real processing time of jobs is calculated by using their processing speed and normal processing time. To describe this problem in a mathematical way, a multi-objective stochastic programming model aiming at realizing makespan and energy consumption minimization is formulated. Furthermore, we develop a multi-objective multi-verse optimization combined with a stochastic simulation method to deal with it. In this approach, the multi-verse optimization is adopted to find favorable solutions from the huge solution domain, while the stochastic simulation method is employed to assess them. By conducting comparison experiments on test problems, it can be verified that the developed approach has better performance in coping with the considered problem, compared to two classic multi-objective evolutionary algorithms.

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.

WEIGHTED ADDITIVE MODEL AND CHANCE CONSTRAINED TECHNIQUE FOR SOLVING NONSYMMETRICAL STOCHASTIC FUZZY MULTIOBJECTIVE LINEAR PROGRAM

The problems of linear programming are developing from time to time, and its complexity is constantly growing. Various problems can be viewed as a multi-objective fuzzy linear programming, multi-objective stochastic linear programming or a combination of both. This research is focused on examining Multi-Objective Fuzzy Stochastic Linear Programming (MOFSLP) with each of the objective functions has a different level of importance to decision makers, or better known as the nonsymmetrical model. The objective function of the linear program contains fuzzy parameters, while the constraint function contains the fuzzy parameters and random variables. The purpose of this study is to develop an algorithm to transform the MOFSLP be a Program of linear Single-Objective Deterministic Linear Programming (SODLP) so that it can be solved using simplex method. In the process of transforming MOFSLP to SODLP, several approaches have been used. They are; weighted additive model, analytic hierarchy process and chance constrained technique. An example of numerical computations has been provided at the end of the discussion in order to illustrate how the algorithm works. The resulted Model and algorithm are expected to help companies in the decision making process.

Design of a Knowledge Flow Network for the Personnel of an Organization under Various Scenarios and its Solution using Lagrangian Relaxation

Knowledge transfer can occur on two levels: intra-organizational and inter-organizational. Acquiring knowledge from outside an organization usually requires significant budget and considerable time. However, through awareness and reliance on knowledge already acquired by the personnel, and creating a knowledge flow network, knowledge level of the organization can be increased in the shortest possible time. The present paper addresses the design of a knowledge flow network between the personnel of an organization according to the professional and personal trust levels, teaching and learning capabilities, knowledge level of the personnel, organizational commitment level, type and importance of each knowledge, and the stochastic nature of the knowledge transfer duration. This problem was formulated as a stochastic multi-objective mixed-integer programming. The objectives of the proposed model were maximizing the knowledge level and minimizing the knowledge transfer time. The model was solved using the Lagrangian relaxation algorithm and the CPLEX solver. Results indicate the high efficiency of the Lagrangian relaxation algorithm specially in computational time of large-sized problems. Moreover, the results show that the organizational commitment parameter has more significant influence on the knowledge transfer duration, followed by teaching and learning capabilities.

Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

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.

Towards sustainable circular agriculture: An integrated optimization framework for crop-livestock-biogas-crop recycling system management under uncertainty

ContextGrowing socio-economic development and population poses unprecedented challenges for agriculture in meeting increasing demand of food, water, and energy. Rethinking the future agricultural production to simultaneously safeguard resources security and regulate environmental pollution is essential. Circular agriculture opens up a new path for the high-efficiency and environmental-friendly production. An integrated energy-water-food nexus optimization approach for managing agricultural resources and wastes in line with the principles of sustainable circular agriculture management is lacking. ObjectiveThis study therefore proposes an integrated uncertain optimization model to manage agricultural crop-livestock-biogas-crop recycling systems from a cross-sectoral energy-water-food nexus perspective in the changing environment. The aims are to: (1) balance objectives of input reduction, output promotion, ensuring equity, and global warming mitigation; (2) generate sustainable resources allocation strategies based on efficiency and recycling; (3) assess the global warming mitigation potential of the recycling systems from a life cycle perspective; and (4) deal with interactions, complexities, uncertainties, and risks existed in the recycling systems. MethodsThe proposed model framework is based on a stochastic multi-objective programming, while triangular fuzzy numbers, fuzzy credibility constrained programming, Stewart model, analytic hierarchy process, and opportunity carbon footprint are integrated to enhance its practicability and feasibility. The model is verified through a real-world case study in the Zhanghe Irrigation District, Hubei province, China. Results and conclusionsResults show that optimal water and land resources allocation solutions are more efficient than current strategies, with water consumption per unit area decreasing by 13.63% and rice production per unit area improving by 22.06%. Paddy field and biogas leakage are two of the largest sources of GHG emission, calling for agronomic and engineering measures to improve farmland management and biogas generation technology. Livestock breeding contributes 10% of the total GHG emission, along with generating 76% of the total biogas, indicating the great significance of manure recycle. Overall, 4.26 × 108 kg CO2 is reduced in the recycling system, contributed by chemical fertilizer reduction, agricultural wastes recycle, and non-renewable energy replacement. SignificanceThe study offers a potential nexus optimization approach for sustainable management of agricultural recycling systems from a holistic perspective. It can be used as a general model to extend to other agricultural systems suffering from similar resources and environmental crisis.

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 novel humanitarian and private sector relief chain network design model for disaster response

The private sector is widely regarded as a useful element in the emergency response to disasters. Humanitarian organizations tend to cooperate with the private sector to deliver aids to affected areas and mitigate the complexity of disasters. In this paper, we propose an efficient relief chain consisting of a humanitarian organization (HO) and third-party logistics providers (3PLPs) to tackle the issue of decentralized planning and decision-making in humanitarian logistics. The relief chain is expected to benefit both the HO and the 3PLPs. To this end, we developed a novel bi-level two-stage multi-objective stochastic programming model. The robust equivalent of the proposed model is also developed to cope with uncertainty. A Benders decomposition algorithm is tailored to solve large-scale problems. An actual earthquake is investigated as case-study to test the model's real-world applicability. Finally, a number of managerial insights are inferred by analyzing the findings of this research.

An optimal modeling approach for reducing carbon footprint in agricultural water-energy-food nexus system

Modern agriculture calls for efficient and environmental-friendly agricultural water and land management practice. Agricultural water and land utilization mode has a great impact on the amount of carbon emissions, and thus the aim of this work is to propose an optimal modeling approach for generating efficient agricultural water and land management alternatives and reducing carbon emission in agricultural water-energy-food nexus system. This study presents a novel approach consisting of carbon footprint lifecycle assessment method and bi-level multi-objective stochastic programming model. The proposed approach has contributions in following aspects: (1) the environmental impact of different resource allocation strategies can be measured in optimization (2) the spatial variability of spatial data (e.g., ET0 and precipitation); can be fully reflected via remote sensing information; (3) tradeoffs among two decision-making levels and their conflicting objectives under randomness of surface water availability can be addressed. The proposed approach was applied to the middle reaches of the Heihe River basin, northwest China. After solving the proposed model, the optimal water and land use alternatives under different hydrological years can be generated. Decision makers can plan agricultural production strategy according to optimization schemes, and reduce carbon emission through increasing vegetable cultivation and surface water utilization. Furthermore, the performance comparison of different models indicated that fierce conflicts exist between income fairness and economic benefits. The comprehensive evaluation value of bi-level multi-objective stochastic programming model is 0.7036, which is highest among single- and multi-objective models, showing that such model has obvious advantage in dealing with multiple decision-making levels and conflicting objectives. This approach can help decision makers of similar regions manage the agricultural production system in a more efficient and environment-friendly way.

A novel approach for solving stochastic problems with multiple objective functions

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.

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.