An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty

Planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities, where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist. With the purpose of tackling such difficulties, this paper presents the development of an interval-fuzzy nonlinear programming (IFNP) model for water quality management under uncertainty. Methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left- and right-hand sides of the nonlinear constraints. Uncertainties in water quality, pollutant loading, and the system objective were reflected through the developed IFNP model. The method of piecewise linearization was developed for dealing with the nonlinearity of the objective function. A case study for water quality management planning in the Changsha section of the Xiangjiang River was then conducted for demonstrating applicability of the developed IFNP model. The results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels. It was also indicated that the proposed linearization method was effective in dealing with IFNP problems; uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives; the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals. It also suggested that the linearized method should be used under detailed error analysis in tackling IFNP problems.     

A hybrid inexact-stochastic water management model

An inexact-stochastic water management (ISWM) model is proposed and applied to a case study of water quality management within an agricultural system. The model is based on an inexact chance-constrained programming (ICCP) method, which improves upon the existing inexact and stochastic programming approaches by allowing both distribution information in B and uncertainties in A and C to be effectively incorporated within its optimization process. In its solution process, the ICCP model (under a given pi level) is first transformed into two deterministic submodels, which correspond to the upper and lower bounds for the desired objective function value. This transformation process is based on an interactive algorithm, which is different from normal interval analysis or best/worst case analysis. Interval solutions, which are feasible and stable in the given decision space, can then be obtained by solving the two submodels sequentially. Thus, decision alternatives can be generated by adjusting decision variable values within their solution intervals. The obtained ICCP solutions are also useful for decision makers to obtain insight regarding tradeoffs between environmental and economic objectives and between increased certainties and decreased safeties (or increased risks). Results of the case study indicate that useful solutions for the planning of agricultural activities in the water quality management system have been obtained. A number of decision alternatives have been generated and analyzed based on projected applicable conditions. Generally, some alternatives can be considered when water quality objective is given priority, while the others may provide compromises between environmental and economic considerations. The above alternatives represent various options between environmental and economic tradeoffs. Willingness to accept low agricultural income will guarantee meeting the water quality objectives. A strong desire to acquire high agricultural income will run into the risk of violating water quality constraints.     

Optimal Liquidity management and Hedging in the presence of a non-predictable investment opportunity

In this paper, we develop a dynamic model that captures the interaction between a firm’s cash reserves, the risk management policy and the profitability of a non-predictable irreversible investment opportunity. We consider a firm that has assets in place generating a stochastic cash-flow stream. The firm has a non-predictable growth opportunity to expand its operation size by paying a sunk cost. When the opportunity is available, the firm can finance it either by cash or by costly equity issuance. We provide an explicit characterization of the firm strategy in terms of investment, hedging, equity issuance and dividend distribution.     

Composing medical crews with equity and efficiency

The quality of the health care is directly connected to the equity and to the efficiency of the service delivered. Usually, the health care is delivered by crews composed of individuals working together sharing knowledge, experiences and skills. We consider the problem of composing medical crews in such a way that the health care service provided follows the principles of equity and efficiency. We present a general mathematical programming model for this problem and a solution algorithm based on Tabu Search methodology. Computational analysis proves the effectiveness of the proposed algorithm.     

Asset-liability management for Czech pension funds using stochastic programming

It is possible to model a wide range of portfolio management problems using stochastic programming. This approach requires the generation of input scenarios and probabilities, which represent the evolution of the return on investment, the stream of liabilities and other random phenomena of the problem and respect the no-arbitrage properties. The quality of the recommended capital allocation depends on the quality of the input scenarios and a validation of results is necessary. Appropriate scenario generation techniques and output analysis methods are described in the context of defined contribution pension fund and applied to the specific model of a Czech pension fund. The numerical results indicate various components that influence the recommended investment decisions and the fund’s achievements. In particular, the initial balance sheet position of the pension fund is important for the optimal investment strategy because of the accounting rules embedded in the model and tracking of both the market and purchasing value of assets.     

Application of nonlinear optimization to water quality

Two formulations for nonlinear optimization (minimize variance and fractile programming formulations) are presented for the solution of water quality planning problems. The optimization algorithms are applied to the problem of determining the optimal waste removal to mitigate the deleterious impacts of the waste discharges on the dissolved oxygen concentration in a water body. The pollutant loading and transport in the stream are considered as random variables with the first two moments of the resulting distributions included in the models.     

Reliable method for water reuse in multicontaminant batch plants: NIS policy

This paper presents a mathematical technique for minimisation of freshwater and wastewater in operations characterised by multiple contaminants. The minimisation of wastewater is achieved through the exploitation of recycle and reuse opportunities using a superstructure that entails all possible recycle and reuse possibilities. This eventually forms the basis for the mathematical formulation. The existence of an optimal production schedule, which provides starting and finishing times for water using operations, is not necessary in this formulation. The paper addresses the case where central reusable water storage is nonexistent, which implies that recycle and reuse opportunities are effected by direct stream routing. The contaminants in any given water stream need not be limiting at the same time which is characteristic of practical situations. This condition enforces the overall model to be cast as a mixed integer nonlinear programming (MINLP) problem which global optimality cannot be guaranteed for complex problems. A solution procedure to overcome structural problems and guarantee global optimality is also presented.     

A multiple objective programming approach for determining faculty salary equity adjustments

A multiple objective programming approach is proposed as a new analytical tool to fit a model which is used to project faculty salaries. The projected salaries are used as a basis to allocate the available budget for faculty salary equity adjustments. The model is also used to classify all faculty members into two categories with one category consisting of those faculty members being underpaid and the other consisting of those being overpaid. The multiple objective programming approach is much more powerful than regression analysis for this purpose because budgetary and policy restrictions can be included in the model as constraints. It is also more flexible than the goal programming approach because it has desirable solution properties. Salary data from a public university are used as an example to demonstrate the use of the approach. In addition, determinants of faculty salaries and variables to be included in the model are briefly discussed.     

考虑路网可靠性和空间公平性的次优拥挤收费模型

根据随机路网环境下出行者规避风险的路径选择行为,提出了一种考虑路网可靠性和空间公平性的次优拥挤收费双层规划模型。其中,上层模型以具有空间公平性约束条件下最大化路网的社会福利为目标,下层模型是实施拥挤收费条件下考虑行程时间可靠性的弹性需求用户平衡模型。鉴于双层规划模型的复杂性,设计了基于遗传算法和FrankWolfe算法的组合式算法来求解提出的模型。算例结果表明:考虑行程时间可靠性的次优拥挤收费会产生不同于传统次优拥挤收费的平衡流量分布模式,表明出行者的路径选择行为对拥挤收费结果会产生直接影响;此外,算例结果还说明遗传算法对参数设置具有很强的鲁棒性。     

Non-linear equity portfolio variance reduction under a mean–variance framework—A delta–gamma approach

To examine the variance reduction from portfolios with both primary and derivative assets we develop a mean–variance Markovitz portfolio management problem. By invoking the delta–gamma approximation we reduce the problem to a well-posed quadratic programming problem. From a practitioner’s perspective, the primary goal is to understand the benefits of adding derivative securities to portfolios of primary assets. Our numerical experiments quantify this variance reduction from sample equity portfolios to mixed portfolios (containing both equities and equity derivatives).     

避难场所生活物资政府—企业联合储备优化问题研究

应急避难场所是地震等大型自然灾害发生后人员安置的重要场所。用于救灾的生活物资如食品、饮用水等既是应急资源,同时也是日用消费品,在一定保质期内需要定期更新,因此这种特殊应急资源储备需同时兼顾应急供应保障度和日常管理成本。文章以应急避难场所的一个存储周期为研究对象,将避难所及其周围的超市作为可选存储地点,避难所自行储备的供应保障度高,但日常管理成本较大,周边超市则相反,建立混合整数规划模型,选择周边超市和避难所一同存储一定数量的生活物资,在满足政府预算的条件下,使得应急状态下物资保障程度最大化。文章设计了启发式算法,最后给出算例说明算法的有效性。     

Optimal Operations Management and Network Planning of a District Heating System with a Combined Heat and Power Plant

District heating plants are becoming more common in European cities. These systems make it possible to furnish users with warm water while locating the production plants in the outskirts having the double benefit of lowering the impact of pollution on the center of the city and achieving better conversion performances. In order to amortize the costs throughout the year, the system often includes a combined heat and power (CHP) plant, to exploit the energy during the summer as well, when the demand for warm water decreases. A linear programming model for the optimal resource management of such a plant is presented and some results for a real case are reported. A distribution network design problem is also addressed and solved by means of mixed integer linear programming.     

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.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

基于基尼系数的停车换乘拥挤收费定价模型

许多大城市提倡停车换乘的组合出行方式,目的是减少出行车辆,缓解交通拥挤状况.应用双层规划模型对停车换乘拥挤收费进行研究.下层模型采用弹性需求SUE模型,上层模型考虑了交通公平因素.以各出行方式占用的道路资源为公平指标,应用基尼系数对传统上层模型进行改造,构建一个用户盈余尽可能大而基尼系数尽可能小的上层模型,并利用基尼系数控制参数,实现在不同公平要求下的拥挤收费设计.算例表明,基于基尼系数的停车换乘拥挤收费设计,能改善道路的拥挤状况,且兼顾了用户盈余与公平.     

Multiobjective management of mining under water hazard by game theory

The management of an aquifer is studied under the assumption that the solution of the multiobjective programming model describing the management problem should satisfy a certain set of axioms. It is shown that a certain class of multiobjective problems may be solved by a game-theoretical concept leading to a single objective quasiconvex programming problem. The method is generalization of Nash's cooperative game theoretical model, and may lean on Zeuther's bargaining process. The methodology is applied to the Transdanubian Karstic region in Hungary where three objectives are present: mining costs, water supply and environmental protection. Results are compared with the solution previously obtained by compromise programming with an l₁-norm. It is found that results obtained by the two methods are comparable.     

服务管理目标优化配置的Fuzzy-QFD线性规划模型构建与求解

由于服务管理的复杂性和模糊性,现有方法难以有效解决基于主观语言评价的服务质量改进问题。本文拓展了质量功能展开(QFD)方法在服务业中的应用,通过构建一个模糊线性规划模型,以求解最大化提高顾客需求综合满意度的企业能力优化配置问题。首先基于顾客感知-期望差距的模糊评估确定顾客需求、需求权重和边界约束等模型参数,接着运用模糊线性回归和非对称三角模糊数的隶属函数,将含有模糊变量的模糊线性规划问题转化为经典线性规划问题,进而求得不同模糊条件下的模型解。最后通过网购平台的实例验证了模型的有效性和可行性。     

Optimizing Asset and Capital Adequacy Management in Banking

This paper considers the application of stochastic optimization theory to asset and capital adequacy management in banking. Our study is motivated by new banking regulation that emphasizes risk minimization practices associated with assets and regulatory capital. Our analysis depends on the dynamics of the capital adequacy ratio (CAR), which we compute in a stochastic setting, by dividing regulatory bank capital (RBC) by risk weighted assets (RWAs). Furthermore, we demonstrate how the CAR can be optimized in terms of bank equity allocation and the rate at which additional debt and equity is raised. In either case, the dynamic programming algorithm for stochastic optimization is employed to verify the results. Also, we provide an illustration of aspects of bank management practice in relation to this regulation. Finally, we make a few concluding remarks and discuss possibilities for further research. The research was supported by a generous grant from the National Research Foundation of South Africa under GUN 2069031.     

The Joint Problem of Investment and Financing

A programming model of project selection is extended to include the issue of new equity as one of the activities.This allows the marginal cost of capital, in each year up to a planning horizon, to be determined within the model.It also allows pre-horizon decisions to be uncoupled, under plausible assumptions, from the consideration of post-horizon opportunities.The model is used to specify optimal joint strategies for financing and investment, and to analyse complex projects-e.g. acquisitions-which affect both financial structure and the supply of profitable opportunities. Interactions between project selection, financing policy and dividend policy are illustrated and the results are contrasted with those derived from familiar decision-rules.     

Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known ε-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.