Uncertain Flows Research Articles

An $$\alpha $$-risk appetite cost minimizing model for multi-commodity capacitated p-hub median problem with time windows and uncertain flows

An $$\alpha $$-risk appetite cost minimizing model for multi-commodity capacitated p-hub median problem with time windows and uncertain flows

Entropy calculation for networks with determined values of flows in nodes

The paper analyses a network with given input and output flows in each of its nodes. The basis of this analysis is the algorithm for determining the set of solutions of the linear equations system, using the Gaussian method. The power of the set determines the structural entropy of the system. By introducing uncertainty into the value of part of the information flows, the deviation of the network from its equilibrium state is simulated. The set of potential solutions, as a part of the total set of the system solutions, determines the statistical entropy of the system. The probability entropy is calculated for a network with four nodes and a total flow of 10 erlangs with a sampling step of 1 erlang. Calculated entropy values for 1, 2, 3, and 4 uncertain flows out of a total of 16 flows that are transmitted between nodes of the fully connected network. As a result of the conducted statistical analysis of entropy values, the optimal number of statistical intervals for entropy values is determined: 4, 11, 24, and 43 intervals for 1, 2, 3, and 4 uncertain flows, respectively. This makes it possible to highlight the set of flows in the system that have the greatest influence on the entropy value in the system. The obtained results are of practical importance, as they enable the detection of deviations of the network from its equilibrium state by monitoring the passage of traffic on individual branches of a complex telecommunication network. Since, as shown in our previous works, the task of determining the complete set of solutions of the system for the number of nodes greater than 4 has a significant computational complexity, the application of the algorithm to such networks requires an increase in the discretization step of the values of information flows in the network. Another way to reduce computational complexity can be to reduce the set of analysed solutions to a subset of solutions close to the equilibrium state of the system.

Reservoir fertilisation and fishery response in a highly managed reservoir with uncertain flows: Ecosystem‐based management using decision analysis

AbstractInland fisheries managers must account for multiple competing uses for aquatic resources; using methods such as ecosystem‐based management allows for different priorities for aquatic ecosystems to be accounted for. Declining abundance of kokanee salmon Oncorhynchus nerka (Walbaum) in Arrow Lakes Reservoir in the 1990s led to the use of large‐scale nutrient addition to improve productivity of kokanee and large piscivores. However, it is unclear what effect these measures had on the system given high discharge and highly variable annual flow regime throughout the watershed. An Ecopath with Ecosim model of the ecosystem was fitted to the available data and used to predict ecosystem structure and reservoir objectives under different nutrient addition strategies and varying annual flow regimes. Results from the model indicate that nutrient addition is an important driver in the system, with lower flows resulting in higher biomass for higher trophic levels. Decision analysis demonstrated the importance of maintaining nutrient additions to achieve management objectives despite losses in some high‐flow years.

Fund Flows, Liquidity, and Asset Prices

This paper tests whether mutual funds on aggregate matter for the equilibrium stock returns due to (i) uncertain fund flows, which directly affect fund size and managers' income; and (ii) time-varying liquidity costs of assets. I find the aggregate shocks to fund flows enter the pricing kernel in equilibrium and price 100 liquidity, fund flow beta, size, book-to-market, profitability, and investment portfolio returns net of liquidity costs. The risk prices for the aggregate flow shocks are similar across the separate portfolios and different model specifications, supporting the prediction that one pricing kernel of mutual funds prices a range of cross-sections.

Path planning in uncertain flow fields using ensemble method

An ensemble-based approach is developed to conduct optimal path planning in unsteady ocean currents under uncertainty. We focus our attention on two-dimensional steady and unsteady uncertain flows, and adopt a sampling methodology that is well suited to operational forecasts, where an ensemble of deterministic predictions is used to model and quantify uncertainty. In an operational setting, much about dynamics, topography, and forcing of the ocean environment is uncertain. To address this uncertainty, the flow field is parametrized using a finite number of independent canonical random variables with known densities, and the ensemble is generated by sampling these variables. For each of the resulting realizations of the uncertain current field, we predict the path that minimizes the travel time by solving a boundary value problem (BVP), based on the Pontryagin maximum principle. A family of backward-in-time trajectories starting at the end position is used to generate suitable initial values for the BVP solver. This allows us to examine and analyze the performance of the sampling strategy and to develop insight into extensions dealing with general circulation ocean models. In particular, the ensemble method enables us to perform a statistical analysis of travel times and consequently develop a path planning approach that accounts for these statistics. The proposed methodology is tested for a number of scenarios. We first validate our algorithms by reproducing simple canonical solutions, and then demonstrate our approach in more complex flow fields, including idealized, steady and unsteady double-gyre flows.

Planning the Minimum Time and Optimal Survey Trajectory for Autonomous Underwater Vehicles in Uncertain Current

The authors develop an approach to a “best” time path for Autonomous Underwater Vehicles conducting oceanographic measurements under uncertain current flows. The numerical optimization tool DIDO is used to compute hybrid minimum time and optimal survey paths for a sample of currents between ebb and flow. A simulated meta-experiment is performed where the vehicle traverses the resulting paths under different current strengths per run. The fastest elapsed time emerges from a payoff table. A multi-objective function is then used to weigh the time to complete a mission versus measurement inaccuracy due to deviation from the desired survey path.

Robust quadratic assignment problem with budgeted uncertain flows

We consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.

A stochastic programming model for hub-and-spoke network with uncertain flows

Hub-and-spoke network (HSN) exploits economy of scale in transportation and reduces logistics operational cost through collaborations among nodes. Because of the uncertainty of origin-destination (OD) flows between nodes, the uncertainty increases the risk of selecting capacities for nodes and affects the analysis of contribution of the nodes to the HSN. First, considering the characteristics of the uncertainty of OD flows, the throughput capacities of spoke nodes are determined based on stochastic programming approach and expectation theory; then, a stochastic mixed-integer linear programming model for designing hub-and-spoke network is established based on the capacities of spokes, and the structure of the HSN and throughput capacities of the hubs are designed. Second, the classification method of nodes is formulated based on the transportation flows between spokes, resource utilisation degree, and the branch and trunk convective equilibrium degree. A multi-attribute utility evaluation function for evaluating contribution rates of nodes to the HSN is established based on the proposed evaluation indices. Finally, the existing problems about network operational and adjustment strategies are analysed based on the contribution rates of the nodes to the HSN.

Uncapacitated $$p$$ p -hub location problem with fixed costs and uncertain flows

Hub location problem is an important problem and has many applications in various areas, such as transportation and telecommunication. Since the problem involves long-term strategic decision, the future flows will change with time. However, it is difficult or costly to obtain the data of flows, which implies that it is necessary to consider hub location problems in the absence of data. A commonly used way is to estimate future flows by experts' subjective information. As a result, this paper presents a new uncapacitated $$p$$p-hub location problem, in which the flows are described by uncertain variables. Two uncertain programming models are formulated to respectively minimize the expected cost and the $$\alpha $$ź-cost with the corresponding constraints. Equivalent forms are given when the information about uncertainty distributions of flows is further provided. A genetic algorithm is designed to solve the proposed models and its effectiveness is illustrated by numerical examples.

Streamflow rating uncertainty: Characterisation and impacts on model calibration and performance

Common streamflow gauging procedures require assumptions about the stage-discharge relationship (the ‘rating curve’) that can introduce considerable uncertainties in streamflow records. These rating uncertainties are not usually considered fully in hydrological model calibration and evaluation yet can have potentially important impacts. We analysed streamflow gauge data and conducted two modelling experiments to assess rating uncertainty in operational rating curves, its impacts on modelling and possible ways to reduce those impacts. We found clear evidence of variance heterogeneity (heteroscedasticity) in streamflow estimates, with higher residual values at higher stage values. In addition, we confirmed the occurrence of streamflow extrapolation beyond the highest or lowest stage measurement in many operational rating curves, even when these were previously flagged as not extrapolated. The first experiment investigated the impact on regional calibration/evaluation of: (i) using two streamflow data transformations (logarithmic and square-root), compared to using non-transformed streamflow data, in an attempt to reduce heteroscedasticity and; (ii) censoring the extrapolated flows, compared to no censoring. Results of calibration/evaluation showed that using a square-root transformed streamflow (thus, compromising weight on high and low streamflow) performed better than using non-transformed and log-transformed streamflow. Also, surprisingly, censoring extrapolated streamflow reduced rather than improved model performance. The second experiment investigated the impact of rating curve uncertainty on catchment calibration/evaluation and parameter estimation. A Monte-Carlo approach and the nonparametric Weighted Nadaraya-Watson (WNW) estimator were used to derive streamflow uncertainty bounds. These were later used in calibration/evaluation using a standard Nash-Sutcliffe Efficiency (NSE) objective function (OBJ) and a modified NSE OBJ that penalised uncertain flows. Using square-root transformed flows and the modified NSE OBJ considerably improved calibration and predictions, particularly for mid and low flows, and there was an overall reduction in parameter uncertainty.

Energy-saving-oriented group-elevator dispatching strategy for multi-traffic patterns

Energy-saving elevator dispatching has been recognized as a challenging issue in building transportation, and we develop a novel energy-saving dispatching strategy for regenerative group-elevator system. Group-elevator dispatching is a typical combinatorial optimization problem, and three keys of the dispatching optimization are optimization method, objective, and model. The three keys of energy-saving-oriented elevator dispatching are studied in this paper. First, robust optimization method is introduced to handle dispatching optimization under uncertain elevator traffic flows; uncertain flows influence energy-saving dispatching seriously. Second, dispatching energy-objective function for regenerative group-elevator system is derived both schedule energy for four traffic patterns (up-peak, down-peak, up/down-mixed, and night) and return energy for two peak patterns (up-peak and down-peak) are considered. Third, four robust optimization-dispatching models for four traffic patterns are built, and optimization objectives of four models are minimizing the energy-objective function. Moreover, because we cannot solve robust optimization models with uncertain parameters directly, model counterpart transformation is studied. Finally, we solve the four transformed models by Linear Interactive and General Optimizer software and obtain robust optimization-dispatching solutions. In practice, four energy-saving-dispatching robust optimization models are switched according to real-time traffic patterns, and elevators are dispatched based on the dispatching solutions. We reduce elevator system-energy consumption effectively and keep average waiting time of the passengers acceptable under multi-traffic patterns. Simulation results demonstrate the validity of our strategy. Practical application: Group-elevator system spends much unnecessary energy because of the uncertainty of elevator passenger-traffic flows. This paper develops an energy-saving elevator-dispatching optimization strategy, which is immune to the uncertainty of four typical traffic flows. In practice, we update the group-elevator controller by our algorithm to realize energy-saving dispatching of regenerative group-elevator system under multi-traffic patterns.

Institutional response to external disturbances in spate irrigation systems of Punjab, Pakistan

Social ecological systems (SESs) – spate irrigation system in our case – operate under an environment of stress due to several external and contextual factors. Spate irrigation systems are more complex due to uncertain flows and can exhibit unexpected changes due to novel shocks. Therefore, actions directed at enhancing robustness to a particular set of disturbances can trigger changes in ecological dynamics that may, in turn, alter the set of disturbances faced by irrigators. This paper looks on the institutional change and resulting water rights and operational rules-in-use in such a context in spate irrigation systems in Punjab province. The sustainability framework (Anderies et al., 2004) has been used for analysis of entities involved in case studies of SESs. The study has important policy implications about how the institutional arrangements imposed from external agencies fail to address new disturbance regimes as the mechanisms remain in place for longer time horizons.

Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.

Champ de spécialisation et revenu

An earnings function is defined for the highly qualified manpower in Canada in 1973. Education, experience and field of study, instead of occupation, are the arguments. By use of regression techniques it is shown that the third independent variable adds significantly to the explanation of the variance of earnings. Even when years of schooling and experience are accounted for, the contribution of the so-called traditional fields of study—medicine, law, accounting and engineering—remains considerable. The first of the three interpretations suggested refers to different "innate" abilities associated with choice of a field of study but it is promptly dismissed. The second interpretation deals with differences in work organization leading to either more uncertain flows of earnings or to longer hours of work. It is shown to be plausible in the case of graduates of law schools but it does not hold in the case of graduates of medical schools. In the latter case a third interpretation is hinted at: medical doctors, either through their association or individually, do exert some significant influence on both the supply of and the demand for their own services.

Perturbation Growth and Structure in Uncertain Flows. Part I

Perturbation growth in uncertain systems is examined and related to previous work in which linear stability concepts were generalized from a perspective based on the nonnormality of the underlying linear operator. In this previous work the linear operator, subject to an initial perturbation or a stochastic forcing distributed in time, was either fixed or time varying, but in either case the operator was certain. However, in forecast and climate studies, complete knowledge of the dynamical system being perturbed is generally lacking; nevertheless, it is often the case that statistical properties characterizing the variability of the dynamical system are known. In the present work generalized stability theory is extended to such uncertain systems. The limits in which fluctuations about the mean of the operator are correlated over time intervals, short and long, compared to the timescale of the mean operator are examined and compared with the physically important transitional case of operator fluctuation on timescales comparable to the timescales of the mean operator. Exact and asymptotically valid equations for transient ensemble mean and moment growth in uncertain systems are derived and solved. In addition, exact and asymptotically valid equations for the ensemble mean response of a stable uncertain system to deterministic forcing are derived and solved. The ensemble mean response of the forced stable uncertain system obtained from this analysis is interpreted under the ergodic assumption as equal to the time mean of the state of the uncertain system as recorded by an averaging instrument. Optimal perturbations are obtained for the ensemble mean of an uncertain system in the case of harmonic forcing. Finally, it is shown that the remarkable systematic increase in asymptotic growth rate with moment in uncertain systems occurs only in the context of the ensemble.

Perturbation Growth and Structure in Uncertain Flows. Part II

Perturbation growth in uncertain systems associated with fluid flow is examined concentrating on deriving, solving, and interpreting equations governing the ensemble mean covariance. Covariance evolution equations are obtained for fluctuating operators and illustrative physical examples are solved. Stability boundaries are obtained constructively in terms of the amplitude and structure of operator fluctuation required for existence of bounded second-moment statistics in an uncertain system. The forced stable uncertain system is identified as a primary physical realization of second-moment dynamics by using an ergodic assumption to make the physical connection between ensemble statistics of stable stochastically excited systems and observations of time mean quantities. Optimal excitation analysis plays a central role in generalized stability theory and concepts of optimal deterministic and stochastic excitation of certain systems are extended in this work to uncertain systems. Remarkably, the optimal excitation problem has a simple solution in uncertain systems: there is a pure structure producing the greatest expected ensemble perturbation growth when this structure is used as an initial condition, and a pure structure that is most effective in exciting variance when this structure is used to stochastically force the system distributed in time. Optimal excitation analysis leads to an interpretation of the EOF structure of the covariance both for the case of optimal initial excitation and for the optimal stochastic excitation distributed in time that maintains the statistically steady state. Concepts of pure and mixed states are introduced for interpreting covariances and these ideas are used to illustrate fundamental limitations on inverting covariances for structure in stochastic systems in the event that only the covariance is known.

The Demand for Excess Reserves

This paper provides an estimate of the demand for reserves in the United States. It finds that reserves are negatively related to the Federal funds rate and positively related to transactions deposits. It also finds that clearing needs significantly affect the demand for reserves with increases in reserves coming in response to lower required reserve balances and higher clearing volume. Some implications for monetary policy are discussed. The demand for reserves is at the center of a number of issues in monetary economics. While at one time it was featured primarily in the calculation of money multipliers, more recently it has figured in Federal Reserve policy through its connection to the targeting of the Federal funds rate. Each week, the open market desk is obligated to forecast the demand for reserves, including the demand for reserves, to determine the amount of reserves to supply through open market operations. This shift in the role of reserves is reflected worldwide; a number of countries have abandoned reserve requirements altogether, and the entire connection between monetary policy and the economy is through the demand for excess reserves. This paper looks at recent data on reserves in the United States to determine the sensitivity of demand to changes in interest rates and other variables affecting the willingness to hold reserves. The standard approach to modeling the demand for reserves is to treat it as part of a bank's liquidity management decision. Banks want to hold reserves to avoid overdraft or reserve deficiency penalties on their account at the central bank when facing uncertain flows of funds. This general model of the precautionary demand for reserves was given by Poole (1968). Two basic propositions fall out of this approach. The first is that the quantity of reserves demanded should vary inversely with short-term interest rates, which are the opportunity cost of holding reserves, assuming that reserves pay no interest. The second proposition is that since reserves are providing a buffer against uncertainty about reserve balances, demand should increase with uncertainty. The textbook model of reserve demand assumes that this uncertainty increases proportionately with the level of transactions deposits. This paper finds support for both of these propositions. In recent years, reserves have increased with the growth in transactions deposits and were negatively related to interest rates, decreasing roughly $120 million for each percentage-point increase in the Federal funds rate. The role of reserves in monetary policy depends on the particular operational strategy adopted by the central bank. The approach in the United States shifted in 1982, when the

The effect of systematic risk factors on counterparty default and credit risk of interest rate swaps

This research investigates the effect of specific systematic risk factors on credit risk pricing and capital allocation of interest rate swaps. Because of the stochastic nature of uncertain future cash flows and interest rates, practitioners typically employ the Black-Scholes option pricing model in combination with a simulation analysis to establish capital requirements and estimate the shadow price of an interest rate swap. However, this practice of pricing swap risk excludes systematic risk factors that affect the risk shadow price, thereby underestimating the capital allocation required for financial institutions. This research demonstrates the effect of risk mispricing when simulation models ignore systematic risk factors such as model risk, convexity risk, and parameter risk on the pricing of interest rate swaps.

Capital budgeting strategies with uncertain cash flows

In financial planning problems the selection of project investment when cash flows are certain has been the subject of considerable work. This paper considers optimal project sets with practical aspects involving the effect of uncertain flows using simulation to determine the confidence limit for required available funds and the probability that a chosen project set is not the best.