Multi-objective Stochastic Programming Model Research Articles

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.

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.

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.

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.

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 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.

A multi-objective stochastic programming model to configure a sustainable humanitarian logistics considering deprivation cost and patient severity

As the occurrence of disasters has increased frequently and has resulted in growing concern about their adverse effects on the environment, Sustainable Humanitarian Logistics (SHL) has received great attention recently. SHL aims to reduce disaster damages in an environmentally-friendly manner in the shortest possible time. The terms including ‘environmentally-friendly’ and ‘shortest possible time’ refer to the environmental and social aspects of sustainability. This research proposes a stochastic multi-objective mixed-integer programming model to configure an SHL network during the response phase. Having compared to the research literature, this is the first study that considers economic, social, and environmental aspects of sustainability by incorporating relief cost, deprivation cost, and carbon emissions, respectively. Then, the improved multi-choice goal programming approach is applied to solve the proposed multi-objective model. To indicate the validity of the proposed model, an earthquake that occurred in a region of Kermanshah, Iran, in 2017 is investigated as a real case study. Finally, sensitivity analysis is performed and several managerial and theoretical insights are provided. The results show that exerting environmental issues in humanitarian logistics does not necessarily increase the relief costs, but can be in contrast with the social aspect. Furthermore, a minor increase in the budget of the preparedness phase drastically decreases the response costs.

A new scheduling method based on sequential time windows developed to distribute first-aid medicine for emergency logistics following an earthquake.

After an earthquake, affected areas have insufficient medicinal supplies, thereby necessitating substantial distribution of first-aid medicine from other supply centers. To make a proper distribution schedule, we considered the timing of supply and demand. In the present study, a "sequential time window" is used to describe the time to generate of supply and demand and the time of supply delivery. Then, considering the sequential time window, we proposed two multiobjective scheduling models with the consideration of demand uncertainty; two multiobjective stochastic programming models were also proposed to solve the scheduling models. Moreover, this paper describes a simulation that was performed based on a first-aid medicine distribution problem during a Wenchuan earthquake response. The simulation results show that the methodologies proposed in this paper provide effective schedules for the distribution of first-aid medicine. The developed distribution schedule enables some supplies in the former time windows to be used in latter time windows. This schedule increases the utility of limited stocks and avoids the risk that all the supplies are used in the short-term, leaving no supplies for long-term use.

Multi-Objective Two-Stage Stochastic Programming Model for a Proposed Casualty Transportation System in Large-Scale Disasters: A Case Study

Disaster management is a process that includes mitigation, preparedness, response and recovery stages. Operational strategies covering all stages must be developed in order to alleviate the negative effects of the disasters. In this study, we aimed at minimizing the number of casualties that could not be transported to the hospitals after the disaster, the number of additional ambulances required in the response stage, and the total transportation time. Besides, we assumed that a data-driven decision support tool is employed to track casualties and up-to-date hospital capacities, so as to direct the ambulances to the available hospitals. For this purpose, a multi-objective two-stage stochastic programming model was developed. The model was applied to a district in Istanbul city of Turkey, for a major earthquake. Accordingly, the model was developed with a holistic perspective with multiple objectives, periods and locations. The developed multi-objective stochastic programming model was solved using an improved version of the augmented ε-constraint (AUGMECON2) method. Hence, the Pareto optimal solutions set has been obtained and compared with the best solution achieved according to the objective of total transportation time, to see the effect of the ambulance direction decisions based on hospital capacity availability. All of the decisions examined in these comparisons were evaluated in terms of effectiveness and equity. Finally, managerial implication strategies were presented to contribute decision-makers according to the results obtained. Results showed that without implementing a data-driven decision support tool, equity in casualty transportation cannot be achieved among the demand points.

Towards sustainable water management in an arid agricultural region: A multi-level multi-objective stochastic approach

Water-shortage crisis is threatening the food production and sustainable development around the world. Especially for arid agricultural regions, it is necessary to plan sustainable agricultural water management strategies for improving water use efficiency. But there are many complexities in it, such as multiple decision-making levels, objectives, water users and uncertainties. To effectively tackle these complexities, this study presents a novel optimization-modeling approach consisting of a multi-level multi-objective stochastic programming (MLMOSP) model and weighting quantification method for formulating sustainable water-allocation schemes in arid agricultural regions. The MLMOSP model incorporates multi-level programming, multi-objective programming, and stochastic expectation programming into a general framework. The proposed approach is capable of: 1) quantifying key factors affecting water-allocation systems through weighting quantification methods; 2) describing the main conflicting objectives of each decision-making level, including economic benefits, environment impacts, fairness, effectiveness, and crop yield; 3) considering tradeoffs among conflicting objectives, and 4) reflecting the leader-follower relationship under different scenarios of surface water availability at a regional scale and a monthly temporal resolution. The proposed approach is applied to a real-world case in a typical arid agricultural region of northwest China for verifying its validity. From this real-world case, it is found that: 1) optimization results corresponding to different flow-level scenarios of surface runoff can provide upper-, middle-, and lower-level decision makers with a set of decision alternatives to help identify the most appropriate management strategy; and 2) multiple model comparisons show that the MLMOSP approach can not only give more practical results guaranteeing the achievement of decision-making goals at different decision-making levels, but also help reduce groundwater extraction under different flow level scenarios of surface runoff.

Decentralized rainwater harvesting program for rural cities considering tax incentive schemes under stakeholder interests and purchasing power restrictions

Abstract This paper focuses on implementing a decentralized rainwater harvesting (DRH) program for rural cities under stakeholder interests and purchasing power restrictions. The study is conducted by considering: (1) a no tax incentive scheme (NTIS); (2) a flat rate tax incentive scheme (FTIS); and (3) a progressive tax incentive scheme (PTIS). A three-stage decision framework is proposed. In the first stage, a water balance simulation model is developed to estimate the amount of rainwater that can be collected at individual households using different capacity rain barrels and to determine the threshold rain barrel capacity. In the second stage, the water balance simulation model is run multiple times with varying input parameters to obtain the probability distributions for rainwater used and water demand for different households using different capacity rain barrels, which are then used to generate scenarios for the third stage optimization model. In the third stage, a multi-objective stochastic mixed integer linear programming (Mo-SMILP) model is proposed that aims to determine the household participation rate and cumulative city-wide DRH capacity considering tax incentive schemes, stakeholder interests, and purchasing power restrictions. The proposed Mo-SMILP model is solved by using an improved augmented epsilon constraint method (AUGMECON 2) in order to understand the trade-off between city-wide household reliability, city-wide household savings, and city government savings. A case study of a small rural city in the State of Texas in the US is used to illustrate the effectiveness of the proposed decision framework. The results shows a significant decrease in city-wide household reliability when stakeholder interests and purchasing power are considered. In addition, the PTIS is best at improving city-wide household reliability and savings. NTIS and FTIS are best at improving city government savings depending on the household preference for reliability and savings.

A bi-level multiobjective stochastic approach for supporting environment-friendly agricultural planting strategy formulation

In this study, integration of analytic hierarchy process method and entropy method (AHP-EW) for quantifying the knowledge and experience accumulated by regional managers as well as the socioeconomic situation, the partial least squares regression (PLS) for reflecting the relationship between irrigation water use efficiency and agronomic inputs, and the ecosystem service value for measuring environmental impacts of changing crop planting area were considered in one framework simultaneously. With help of these efforts, a bi-level multiobjective stochastic approach to improve irrigation water use efficiency and decrease the pollution production of agronomic measures in the process of agricultural production. The proposed framework integrate bi-level multiobjective programming and stochastic expectation programming to not only make tradeoffs among multiple concerns from two-level decision makers, but also deal with the randomness of runoff. Then, the proposed approach was applied to a real-world case in the middle reaches of the Heihe River basin, northwest China. Results show that the developed approach can improve irrigation water use efficiency, reduce CO2 emission, expand ecosystem service values, and provide more profitable and environment-friendly agricultural planting strategies to decision makers, which can further contribute to the sustainable development of agriculture. Furthermore, by comparing the bi-level multiobjective stochastic programming (BMSP) model with the other six models originated from developed model, it can be found that 1) the single objective model can obtain the best value of that objective, but cannot readily consider other important aspects; 2) the multiobjective models can make tradeoffs among multiple objectives; 3) the BMSP model can reflect the leader-follower relationship in the optimization process. The approach is applicable for arid and semiarid regions that face similar problems to determine agricultural planting strategies.

Incorporating risk aversion and fairness considerations into procurement and distribution decisions in a supply chain

This paper considers a three-tier supply chain in which a manufacturer uses raw materials sourced from multiple suppliers to produce an item and sells it through multiple distributors. We develop an integrated optimisation model to study supply chain procurement and distribution decisions incorporating the manufacturer’s aversion to risk and the distributors’ concern for fairness in a climate of uncertain supply and demand. Resilient strategies, such as alternative sourcing and transshipment, are also considered when optimising the supply chain cost and service level. To solve the problem, a Monte Carlo simulation-based multi-objective stochastic programming model is built. It uses the CVaR (Conditional Value-at-Risk) and unfairness aversion utility function to reflect the decision maker’s risk aversion and the customer’s concern for fairness, respectively. A Normalised Normal Constraint based algorithm is adopted to obtain the Pareto Frontier. In addition, the numerical analysis provides some valuable insights for supply chain managers.

Towards sustainable water regulation based on a distributed hydrological model for a heavily polluted urban river, northwest China

Abstract The Qinling Mountains are located in a transition zone between (semi)-arid regions in north China and humid regions in south China. The water resource and water ecology of regional rivers are strongly affected by climate change and human activity. In this paper, the stochastic simulation of river water regulation was performed and an optimal water regulation scheme of rubber dam projects was developed by establishing a multi-objective stochastic constraint water regulation model of rubber dam projects based on the coupling of a distributed hydrological model and a water balance model. Results show that a ∼40% reduction of water occurred in the lower river channel due to the operation of water supply project in the upper reach and impoundment by rubber dam projects in the lower reaches. This water reduction was associated with decreased water environment self-purification capacity and serious deterioration of water quality for smaller ecological basic flow and mean flow velocity. By establishing a multi-objective stochastic constraint programming model, the average velocity and the ecological basic flow at different adjusting heights of rubber dams are determined. The regulation scheme of rubber dam projects we propose in this paper may optimize the current river water management strategies and help to improve the river water quality environment in urban rivers.

A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics

To improve the sustainable rescue ability in emergency relief management, this paper addresses the emergency resource allocation problem by simultaneously considering primary and secondary disasters. A conditional probability based scenario tree is proposed to define the correlation between primary and secondary disasters. A multi-objective three-stage stochastic programming model to minimize transportation time, transportation cost and unsatisfied demand. An alternative single-objective model based on fuzzy auxiliary variables of membership is employed to cope with the multi-objective functions. To improve the computational tractability for large-scale cases, we propose an approximation single-stage stochastic programming by taking the worst-case scenario. Our results based on Wenchuan Earthquake show that the solution in this paper outperforms some normal ways. Moreover, by considering secondary disasters, we find that the sustainable rescue ability can be greatly improved than others only considering primary disasters.

A robust optimisation model for sustainable blood supply chain network design under uncertainty

Blood is a perishable, scarce and lifesaving product. While the demand for blood products has been increased over the past few decades, there has been no specified artificial alternative for this critical product yet. In this context, it is of paramount importance to design efficient, agile and effective blood supply chain networks. This paper presents a multi-objective stochastic programming model for blood supply chain network design by considering the following objectives: minimising total cost, minimising delivery time and maximising two important social measures including the indicator of consumer's health and the rate of regular blood donors. A robust optimisation approach is employed to incorporate different sources of uncertainties in demand and supply parameters. To investigate the performance and utility of the proposed formulation, the model is implemented using real data of blood transfusion network of Tehran.

A multi-objective stochastic programming model for project-oriented human-resource management optimization

ABSTRACTHuman resource policy is one of the key factors in managing a project. The cost associated with the individuals assigned to a project and the quality of the tasks completed by the assigned individuals are two of the main concerns in developing a project team. In this study, we present a new multi-objective mathematical model for developing a project team for multi-disciplinary projects under uncertainty. The objective functions optimize cost and competency simultaneously. To cope with the uncertainty and the multiple objectives in the presented model, we applied the two-stage stochastic programming approach and the Augmented Epsilon Constraint Method, respectively. The presented model and its solution methodology can be applied to different types of projects. In this study, a project that involves an overhaul of a set of aircrafts is presented as a case study.

Designing a sustainable stochastic electricity generation network with hybrid production strategies

This paper aims to design a sustainable stochastic electricity production network where fossil fuels-based, biomass-based, and co-firing-based production strategies are simultaneously considered in order to take advantage of all the three production strategies. A multi-objective stochastic mixed integer linear programming model is proposed to achieve economic feasibility, as well as environmental and social benefits under multiple uncertainties. The model is solved by using the improved augmented epsilon constraint method. A case study is used to illustrate the effectiveness of the proposed model. Pareto optimal analysis is conducted to understand the trade-off between economic, environmental, and social aspects of sustainability.