Time-cost trade-off via optimal control theory in Markov PERT networks

We develop a new analytical model for the time-cost trade-off problem via optimal control theory in Markov PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. Then, we construct a multi-objective optimal control problem, in which the first objective is the minimization of the total direct costs of the project, in which the direct cost of each activity is a non-decreasing function of the resources allocated to it, the second objective is the minimization of the mean of project completion time and the third objective is the minimization of the variance of project completion time. Finally, two multi-objective decision techniques, viz, goal attainment and goal programming are applied to solve this multi-objective optimal control problem and obtain the optimal resources allocated to the activities or the control vector of the problem     

水资源持续利用的多目标决策模型的建立

可持续发展战略的实施,资源的可持续利用是关键.针对日趋短缺的淡水资源,根据多目标决策理论,以同时追求经济、环境、社会效益为主要目标提出了其可持续利用的多目标决策模型,并举例说明了模型的应用,旨在为决策者提供淡水利用规划的依据.     

不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化

项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。     

Resource allocation in dynamic PERT networks with finite capacity

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.     

A multi-objective optimal allocation model for irrigation water resources under multiple uncertainties

This paper proposed a multi-objective optimal water resources allocation model under multiple uncertainties. The proposed model integrated the chance-constrained programming, semi-infinite programming and integer programming into an interval linear programming. Then, the developed model is applied to irrigation water resources optimal allocation system in Minqin’s irrigation areas, Gansu Province, China. In this study, the irrigation areas’ economic benefits, social benefits and ecological benefits are regarded as the optimal objective functions. As a result, the optimal irrigation water resources allocation plans of different water types (surface water and groundwater) under different hydrological years (wet year, normal year and dry year) and probabilities are obtained. The proposed multi-objective model is unique by considering water-saving measures, irrigation water quality impact factors and the dynamic changes of groundwater exploitable quantity in the irrigation water resources optimal allocation system under uncertain environment. The obtained results are valuable for supporting the adjustment of the existing irrigation patterns and identify a desired water-allocation plan for irrigation under multiple uncertainties.     

城市公共设施事故应急资源配置优化模型

城市公共设施事故发生时,迅速调动应急资源,尽早展开救援,对促进社会发展和保持社会稳定具有重要意义。本文根据城市公共设施突发事故中资源配置问题的特点,运用多目标规划的思想,建立了应急资源配置的多目标规划模型,并通过实验模拟对模型进行了求解验证。此模型可以成功实现城市公共设施事故应急资源的有效配置,为相关部门的决策提供理论指导。     

考虑双方感知满意度的应急资源再配置方法

突发事件常诱发次生灾害,在外界大规模应急资源配送前,发挥区域互救优势,共享原生灾害点应急资源进行资源再配置是及时响应次生灾害的重要手段之一。本文尝试将灾民心理因素融入到应急资源的再配置问题中,基于前景理论提出了原生灾害点灾民的感知满意度模型,结合生存概率曲线对次生灾害点灾民感知满意度进行刻画,构建了考虑双方灾民感知满意度的多目标优化模型。此外,引入缩放系数和违反约束检查函数,改进多目标粒子群算法以加快算法初始化,进而提升模型求解效率。最后,本文通过算例验证了模型和算法的可行性和科学性,并与传统资源配置问题进行了对比,为具有连锁反应的突发事件应急管理提供决策支持。     

基于直觉模糊规划的多目标投资组合选择模型

将直觉模糊集合的概念引入投资组合模型中,并将多目标投资组合模型中的收益、方差和偏度三个目标模糊化,用隶属函数与非隶属函数作为新的目标函数.针对该模糊多目标投资组合模型,提出了一个动态遗传算法,算例给出了该模型的一个实例的最优解.     

兼顾效率和成本的ARMA控制图多目标优化设计

ARMA控制图是一种有效的自相关过程质量监控方法,为了能够同时对ARMA控制图监控方案的效率和成本进行优化,本文分别研究了ARMA控制图的平均运行长度和质量成本的计算方法,并由此建立了ARMA控制图的多目标优化设计模型。采用NSGA-Ш智能优化算法,通过一个具体的算例对该模型的计算方法进行了说明,针对不同程度的过程偏移给出了多目标优化设计的非劣解解集。然后通过灵敏度分析的方法研究了模型中的主要设计参数对监控方案的效率和成本的影响程度。最后,通过与其它几种ARMA控制图优化设计方案的比较分析,说明了本文提出的设计方法的优势。     

资源受限下森林火灾应急救援多目标调度优化

许多森林火灾由于救援资源受限而不能在第一时间扑灭,导致火灾扩大蔓延,进而造成更大的森林资源损失。因此,在救援资源受限情形下,如何对消防救援车辆进行合理的调度安排以快速和低成本地扑灭火灾已成为亟待解决的现实问题。本文研究了一类资源受限下森林火灾应急救援多目标调度优化问题,为该问题构建了多目标混合整数非线性规划模型,优化目标为同时最小化总灭火救援时间和救援车辆总行驶距离。为有效求解该问题,首先将上述非线性模型等价转化为线性模型。然后提出ε-约束法和模糊逻辑相结合的算法对问题进行求解。最后,以大兴安岭山发生的火灾案例和随机生成仿真算例对模型和算法有效性进行验证,结果表明所提出的模型和算法能够有效解决资源受限下森林火灾应急救援问题,并为决策者提供最优的消防调度方案。     

A dynamic multi-objective optimization model with interactivity and uncertainty for real-time reservoir flood control operation

Despite the successes of both multi-objective optimization and uncertainty handling techniques in reservoir flood control operation, no work has been done yet on developing and investigating dynamic multi-objective optimization models for this problem. In this work, a dynamic multi-objective optimization model with interactivity and uncertainty was developed for the real-time reservoir flood control operation. Accordingly, a dynamic multi-objective optimization algorithmic framework with two newly designed change reaction strategies was proposed for solving the proposed dynamic model. Following the proposed algorithmic framework, any evolutionary multi-objective optimization algorithm can be converted into a dynamic optimizer. After investigating the difficulty variation of the proposed dynamic model, the effectiveness and robustness of the proposed algorithmic framework have been validated based on experiential studies on two typical floods of Ankang reservoir.     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-II and Monte Carlo simulation

The present study extends a multi-objective mathematical model in the context of industrial hazardous waste management, which covers the integrated decisions of three levels with locating, vehicle routing, and inventory control. Analyzing these decisions simultaneously not only may lead to the most effective structure in the waste management network, but also may reduce the potential risk of managing the hazardous waste. Furthermore, because of the inherent complexity of the waste management system, uncertainty is inevitable and should be acknowledged to guarantee reliability in the decision-making process. From this perspective, the proposed model is novel in the following three aspects: (1) shifting from a deterministic to stochastic environment; (2) considering a multi-period planning horizon; and (3) incorporating the inventory decisions into the problem. The problem is formulated as a multi-objective stochastic Mixed-Integer Nonlinear Programming (MINLP) model, which can be easily converted into a MILP one. In terms of methodological contribution, a new simheuristic approach that is an integration of Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and Monte Carlo simulation is developed to overcome the stochastic combinatorial optimization problem of this study. Our findings verify the efficiency of the proposed approach as it is able to find a high-quality solution within a relatively reasonable computational time.     

A multi-objective mathematical optimization model for process targeting using 100% inspection policy

The selection of the optimal process target is an important problem in production planning and quality control. Such process targeting problems are usually modeled in the literature using a single objective optimization model. In this paper multi-objective optimization is introduced in the process targeting area. The quality characteristic under consideration is normally distributed with unknown mean and known standard deviation, and has two market specification limits. 100% inspection is used as the mean of product quality control. Product satisfies the first specification limit is sold in a primary market at a regular price and products fails the first specification limit and satisfies the second one is sold in a secondary market at a reduced price. The product is reworked if it does not satisfy both specification limits. The developed multi-objective optimization model consists of three objective functions, which are to maximize profit, income and product uniformity using Taguchi quadratic function as a surrogate for product uniformity. An algorithm is proposed to obtain and rank the set of Pareto optimal points. The utility of the model has been demonstrated using a numerical example from the literature with some additional data the new model requires. Sensitivity analysis was conducted and showed that the results of the model are sensitive to changes in process variance. In addition the optimal objectives of the profit function and product uniformity are more sensitive to changes in model parameters than the income function.     

基于D-S证据理论的水资源合理配置方案综合评价

由于水资源合理配置具有多目标性、模糊性和不确定性的特点,其方案的综合评价可作为一个数据融合问题.利用改进的D-S证据理论合成公式,并考虑不同指标之间权重,给出了水资源合理配置方案综合评价模型.石羊河流域水资源配置方案评价的实例研究表明,D-S证据理论在水资源合理配置方案评价中有较好的实用性.     

Optimizing of bullwhip effect and net stock amplification in three-echelon supply chains using evolutionary multi-objective metaheuristics

In this article, we intend to model and optimize the bullwhip effect (BWE) and net stock amplification (NSA) in a three-stage supply chain consisting of a retailer, a wholesaler, and a manufacturer under both centralized and decentralized scenarios. In this regard, firstly, the causes of BWE and NSA are mathematically formulated using response surface methodology (RSM) as a multi-objective optimization model that aims to minimize the BWE and NSA on both chains. The simultaneous analysis of the BWE and NSA is considered as the main novelty of this paper. To tackle the addressed problem, we propose a novel multi-objective hybrid evolutionary approach called MOHES; MOHES is a hybrid of two known multi-objective algorithms i.e. multi-objective electro magnetism mechanism algorithm (MOEMA) and population-based multi-objective simulated annealing (PBMOSA). We applied a co-evolutionary strategy for this purpose with eligibility of both algorithms. Proposed MOHES is compared with three common and popular algorithms (i.e. NRGA, NSGAII, and MOPSO). Since the utilized algorithms are very sensitive to parameter values, RSM with the multi-objective decision making (MODM) approach is employed to tune the parameters. Finally, the hybrid algorithm and the singular approaches are compared together in terms of some performance measures. The results indicate that the hybrid approach achieves better solutions when compared with the others, and also the results show that in a decentralized chain, the order batching factor and the demand signal processing in wholesaler are the most important factors on BWE. Conversely, in a centralized chain, factors such as rationing, shortage gaming, and lead time are the most effective at reducing the BWE.     

A united search particle swarm optimization algorithm for multiobjective scheduling problem

The performance of a scheduling system, in practice, is not evaluated to satisfy a single objective, but to obtain a trade-off schedule regarding multiple objectives. Therefore, in this research, I make use of multiple objective decision-making method, a global criterion approach, to develop a multi-objective scheduling problem model with different due-dates on parallel machines processes, in which consider three performance measures, namely minimum run time of every machine, earlierness time (no tardiness) and process time of every job, simultaneously. According to this special multi-objective scheduling problem, the method of reverse order drawing GATT will be proposed, at the same time, bring forward a united search particle swarm optimization algorithm (USPSOA) solves this multi-objective scheduling problem. The validity and adaptability of the USPSOA is investigated through experimental results.     

地震期间应急资源调度方案的优化选取

应急资源的调度是地震救援工作的重点,为解决这个难题,本文构建了以时效性、伤亡性和经济性为三大分量的多目标函数,然后经过无量纲和Delphi加权处理,将其转化为单目标函数,并将其中的决策效用函数看成运筹学中指派问题的效率函数,最后运用匈牙利法计算出最大的目标函数值,从而得出最优的资源调度方案.与其他多目标的应急资源调度方法相比,本文构建的这种算法具有简易、实用的优点,可以说为地震期间应急资源调度方案的优化选取工作提供了一种切实、可行的途径.     

Three-person multi-objective conflict decision in reservoir flood control

Reservoir flood control decisions are often compromised by various parties with conflicting benefits. In this paper, a three-person multi-objective conflict decision model is presented for reservoir flood control. In order to obtain the group decision, the ideal bargaining solution is first sought by two stages satisfying programming and then the decision alternative is chosen using the fuzzy pattern recognition. The advantages of this model are simple and more adaptable to the real problem. The model is demonstrated by application to Fengman Reservoir in China.     

A multi-objective heuristic approach for the casualty collection points location problem

In this paper, we formulate the casualty collection points (CCPs) location problem as a multi-objective model. We propose a minimax regret multi-objective (MRMO) formulation that follows the idea of the minimax regret concept in decision analysis. The proposed multi-objective model is to minimize the maximum per cent deviation of individual objectives from their best possible objective function value. This new multi-objective formulation can be used in other multi-objective models as well. Our specific CCP model consists of five objectives. A descent heuristic and a tabu search procedure are proposed for its solution. The procedure is illustrated on Orange County, California.