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 multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management

This paper presents a multi-level Taguchi-factorial two-stage stochastic programming (MTTSP) approach for supporting water resources management under parameter uncertainties and their interactions. MTTSP is capable of performing uncertainty analysis, policy analysis, factor screening, and interaction detection in a comprehensive and systematic way. A water resources management problem is used to demonstrate the applicability of the proposed approach. The results indicate that interval solutions can be generated for the objective function and decision variables, and a variety of decision alternatives can be obtained under different policy scenarios. The experimental data obtained from the Taguchi’s orthogonal array design are helpful in identifying the significant factors affecting the total net benefit. Then the findings from the multi-level factorial experiment reveal the latent interactions among those important factors and their curvature effects on the model response. Such a sequential strategy of experimental designs is useful in analyzing the interactions for a large number of factors in a computationally efficient manner.     

A fuzzy inexact two-phase programming approach to solving optimal allocation problems in water resources management

Inappropriate agricultural activities are the main reasons of water shortage and environmental pollution in many rural areas. How to generate preferred decision schemes for agricultural activities is a critical issue for decision makers. In this study, a two-phase programming approach is advanced for regional water resources allocation in a rural region of China. The approach shows applicability when the uncertain inputs are provided as intervals and such uncertainty is desired to be delivered to the corresponding solutions. Multiple control variables are introduced both in the objective function and constraints of the programming model, which make it possible for the constraints being relaxed under respective levels. A more satisfactory objective value can thus be expected as well as the impact of each constraint on the modeling outputs can be clarified effectively. The decision variables are useful for decision makers to justify and/or adjust the decision schemes for agricultural activities through incorporation of their implicit knowledge on water allocation management.     

An approach to measuring the quality of maintenance performance

^** Email: sa_oke{at}yahoo.com This paper presents an approach that quantifies the performanceof the maintenance system in terms of the quality of service,offered by maintenance to the production system. Maintenanceis discussed as involving both technical and economic issues.This influences the definition of maintenance quality and maintenanceperformance used in this work. This is because maintenance canbe considered of high quality if the latter is measured (orevaluated) by only technical terms such as quality rate. However,this does not necessarily mean that maintenance is so when itsperformance is measured in economic terms. This issue is importantand is highlighted in the paper. The motivation for writingthe paper is the need for a scientific means of conflict resolutionbetween the maintenance and production department. There arefrequently complaints from the production department that thequality of the machines soon after maintenance is sometimespoor, thus leading to a shortened period of production. Themethodology adopted hinges on the framework in which scrap generation,rework and reject are partly due to the malfunction of the machine.Thus, if a machine has a deteriorated state soon after maintenance,it is likely to produce rejects, scrap or reworked materials.It is argued that the measurement of performance using thisapproach is helpful and could be used for planning purposes.The approach utilized in this work is new, and represents acontribution to the maintenance performance literature.     

Project management with time,cost, and quality considerations

In the project management literature, quantitative models were developed for project crashing to determine the appropriate activities for crashing at minimal cost. In this paper, we suggest that the project quality may be affected by project crashing and develop linear programming models to study the tradeoffs among time, cost, and quality. Each of the three models developed optimizes one of these entities by assigning desired bounds on the other two. An illustrative example with a project network consisting of 13 nodes, 14 activities, and 2 dummy activities is provided. The computational study includes tabulation of the interrelationships among time, cost, and quality.     

A stochastic programming approach to cash management in banking

The treasurer of a bank is responsible for the cash management of several banking activities. In this work, we focus on two of them: cash management in automatic teller machines (ATMs), and in the compensation of credit card transactions. In both cases a decision must be taken according to a future customers demand, which is uncertain. From historical data we can obtain a discrete probability distribution of this demand, which allows the application of stochastic programming techniques. We present stochastic programming models for each problem. Two short-term and one mid-term models are presented for ATMs. The short-term model with fixed costs results in an integer problem which is solved by a fast (i.e. linear running time) algorithm. The short-term model with fixed and staircase costs is solved through its MILP equivalent deterministic formulation. The mid-term model with fixed and staircase costs gives rise to a multi-stage stochastic problem, which is also solved by its MILP deterministic equivalent. The model for compensation of credit card transactions results in a closed form solution. The optimal solutions of those models are the best decisions to be taken by the bank, and provide the basis for a decision support system.     

An optimization approach to gene stacking

We present a multi-objective integer programming model for the gene stacking problem, which is to bring desirable alleles found in multiple inbred lines to a single target genotype. Pareto optimal solutions from the model provide strategic stacking schemes to maximize the likelihood of successfully creating the target genotypes and to minimize the number of generations associated with a stacking strategy. A consideration of genetic diversity is also incorporated in the models to preserve all desirable allelic variants in the target population. Although the gene stacking problem is proved to be NP-hard, we have been able to obtain Pareto frontiers for smaller sized instances within one minute using the state-of-the-art commercial computer solvers in our computational experiments.     

Inexact joint-probabilistic chance-constrained programming with left-hand-side randomness: An application to solid waste management

In practical waste management systems, amounts of waste transported and treated are not always equal on a daily basis. To distinguish between these two kinds of amounts and reflect their random relationships effectively, an inexact joint-probabilistic left-hand-side chance-constrained programming (IJLCP) method was developed and applied to a municipal solid waste management problem under dual uncertainties. Dual uncertainties are defined as two kinds of uncertainties existing in the same programming model. Improving upon conventional right-hand-side chance-constrained programming, the IJLCP can not only reflect uncertainties presented in terms of interval parameters (unit transportation/treatment costs, capacities of waste treatment facilities, waste generation rates, waste transportation/treatment amounts and so on) and left-hand-side random variables (the relationship between waste transportation and treatment amounts), but also examine the reliability of satisfying (or risk of violating) the entire system constraints. A non-equivalent but sufficient linearization form of IJLCP for solving this type of problem was proposed and proved in a straightforward manner. The performance of IJLCP was analyzed under scenarios at joint and individual probabilities and compared with the corresponding internal-parameter programming model. The results indicated that the net system costs would both decrease with increasing joint probability levels and decrease slightly at different individual probabilities with the same joint probabilities. The two types of dual uncertainties were discussed as well.     

A comparison of multiple criteria analysis techniques for water resource management

Multiple criteria analysis (MCA) is a framework for evaluating decision options against multiple criteria. Numerous techniques for solving an MCA problem are available. This paper applies MCA to six water management decision problems. The MCA methods tested include weighted summation, range of value, PROMTHEE II, Evamix and compromise programming. We show that different MCA methods were in strong agreement with high correlations amongst rankings. In the few cases where strong disagreement between MCA methods did occur it was due to presence of mixed ordinal-cardinal data in the evaluation matrix. The results suggest that whilst selection of the MCA technique is important more emphasis is needed on the initial structuring of the decision problem, which involves choosing criteria and decision options.     

A fuzzy-robust stochastic multiobjective programming approach for petroleum waste management planning

This paper proposes a fuzzy-robust stochastic multiobjective programming (FRSMOP) approach, which integrates fuzzy-robust linear programming and stochastic linear programming into a general multiobjective programming framework. A chosen number of noninferior solutions can be generated for reflecting the decision-makers’ preferences and subjectivity. The FRSMOP method can effectively deal with the uncertainties in the parameters expressed as fuzzy membership functions and probability distribution. The robustness of the optimization processes and solutions can be significantly enhanced through dimensional enlargement of the fuzzy constraints. The developed FRSMOP was then applied to a case study of planning petroleum waste-flow-allocation options and managing the related activities in an integrated petroleum waste management system under uncertainty. Two objectives are considered: minimization of system cost and minimization of waste flows directly to landfill. Lower waste flows directly to landfill would lead to higher system costs due to high transportation and operational costs for recycling and incinerating facilities, while higher waste flows directly to landfill corresponding to lower system costs could not meet waste diversion objective environmentally. The results indicate that uncertainties and complexities can be effectively reflected, and useful information can be generated for providing decision support.     

A multiple criteria decision making approach to manure management systems in the Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers’ conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems.     

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.     

A stochastic approach to professional services firms’ revenue optimization

Regarding professional service time as perishable goods, it should be possible to directly migrate the successful airline revenue management techniques to professional services firms (PSFs) for their analogous business characters. However, there are salient differences between airlines and PSFs should be highlighted—the network structure of length-of-continuance and capacity allocation of multifunctional staff. Customers booking to be served from a first continuance time to a last continuance time in consecutive time continuance. Multifunctional professionals should be properly allocated to maximize the benefit. The arrival demands and lengths of service are stochastic in nature.     

An algebraic approach to integer portfolio problems

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model.     

The relationship between quality management practices and their effects on quality outcomes

Recent research into quality management has examined the relationship between quality management and performance. The purpose of this study is to identify the relationships between quality management practices, and to examine the direct and indirect effects of these practices on quality outcomes by means of replication research. The paper uses a path analysis and a research model is tested using cross-section data collected from 106 certified firms in Spain. The findings support the relationships between quality management practices and the positive impact of these practices on quality outcomes. Evidence is also found confirming previous research showing that a firm could transfer the organizational forms and behaviours underlying quality management to other countries with similar cultures. However, as minor differences emerge, managers should consider the cultural issues. The contribution of the paper is that it provides empirical support for direct and indirect effects of quality management on performance in Spain compared to previous studies carried out in USA and Korea.     

An evolutionary programming approach to mixed-variable optimization problems

Many engineering optimization problems frequently encounter discrete variables as well as continuous variables and the presence of nonlinear discrete variables considerably adds to the solution complexity. Very few of the existing methods can find a globally optimal solution when the objective functions are non-convex and non-differentiable. In this paper, we present a mixed-variable evolutionary programming (MVEP) technique for solving these nonlinear optimization problems which contain integer, discrete, zero-one and continuous variables. The MVEP provides an improvement in global search reliability in a mixed-variable space and converges steadily to a good solution. An approach to handle various kinds of variables and constraints is discussed. Some examples of mixed-variable optimization problems in the literature are tested, which demonstrate that the proposed approach is superior to current methods for finding the best solution, in terms of both solution quality and algorithm robustness.     

Cost/risk balanced management of scarce resources using stochastic programming

We consider the situation when a scarce renewable resource should be periodically distributed between different users by a Resource Management Authority (RMA). The replenishment of this resource as well as users demand is subject to considerable uncertainty. We develop cost optimization and risk management models that can assist the RMA in its decision about striking the balance between the level of target delivery to the users and the level of risk that this delivery will not be met. These models are based on utilization and further development of the general methodology of stochastic programming for scenario optimization, taking into account appropriate risk management approaches. By a scenario optimization model we obtain a target barycentric value with respect to selected decision variables. A successive reoptimization of deterministic model for the worst case scenarios allows the reduction of the risk of negative consequences derived from unmet resources demand. Our reference case study is the distribution of scarce water resources. We show results of some numerical experiments in real physical systems.     

Probability density functions based weights for ordered weighted averaging (OWA) operators: An example of water quality indices

This paper explores the application of ordered weighted averaging (OWA) operators to develop water quality index, which incorporates an attitudinal dimension in the aggregation process. The major thrust behind selecting the OWA operator for aggregation of multi-criteria is its capability to encompass a range of operators bounded between minimum and maximum. A new approach for generating OWA weight distributions using probability density functions (PDFs) is proposed in this paper. The basic parameters (mean and standard deviation) of the probability density functions can be determined using the number of criteria (e.g., water quality indicators) in the aggregation process.     

A rolling horizon approach for disruption management of railway rolling stock

This paper deals with real-time disruption management of rolling stock in passenger railway transportation. We describe a generic framework for dealing with disruptions of railway rolling stock schedules. The framework is presented as an online combinatorial decision problem, where the uncertainty of a disruption is modeled by a sequence of information updates. To decompose the problem and to reduce the computation time, we propose a rolling horizon approach: rolling stock decisions are only considered if they are within a certain time horizon from the time of rescheduling. The schedules are then revised as time progresses and new information becomes available. We extend an existing model for rolling stock scheduling to the specific requirements of the real-time situation, and we apply it in the rolling horizon framework. We perform computational tests on instances constructed from real-life cases of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. We explore the consequences of different settings of the approach for the trade-off between solution quality and computation time.     

An integrated approach for supplier selection in multi-item/multi-supplier environment

One of the important stages in supply chain management which regards all the activities from the purchasing of raw material to final delivery of the product is the supplier selection process. Since it is the first stage of the supply chain management, it is a critical process affecting the consecutive stages. It is simply desired to select the best supplier for a specific product. But since there are a lot of criteria and alternatives to be considered, numerous decision making models have been proposed to provide a solution to this problem. Within this study, an integrated approach including fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a mixed integer linear programming model is developed to select the best supplier in a multi-item/multi-supplier environment. The importance value of each supplier with respect to each product is obtained via fuzzy TOPSIS in the first stage. Then in the second stage, these values are used as an input in the mathematical model which determines the suppliers and the quantities of products to be provided from the related suppliers. So as to validate the proposed methodology, an application is performed in air filter sector.