Harvesting discrete nonlinear age and stage structured populations

A natural extension of age structured Leslie matrix models is to replace age classes with stage classes and to assume that, in each time period, the transition from one stage class to the next is incomplete; that is, diagonal terms appear in the transition matrix. This approach is particularly useful in resource systems where size is more easily measured than age. In this linear setting, the properties of the models are known; and these models have been applied to the analysis of population problems. A more applicable setting is to assume that the reproduction, survival, and transition parameters in the model are density dependent. The behavior of such models is determined by the form of this density dependence. Here, we focus on models in which the parameters depend on the value of an aggregated variable, defined to be the weighted sum of the number of individuals in each stage class. In forestry models, for example, this aggregated variable may represent a basal area index; in fisheries models, it may represent a spawning stock biomass. Current age structured nonlinear stock-recruitment fisheries models are a special case of the models considered here. Certain results that apply to age structured models can be extended to this broader class of models. In particular, the questions addressed relate to the minimum number of age classes that need to be harvested to obtain maximum sustainable yield policies and to managing resources under nonequilibrium and stochastic conditions. Application of the model to problems in fisheries, forestry, pest, and wildlife management is also discussed.The author would like to thank R. G. Haight for comments and discussions relating to the material presented here. This work was supported by NSF Grant DMS-85-11717.     

Transparent prioritisation,budgeting and resource allocation with multi-criteria decision analysis and decision conferencing

Managers in both for-profit and not-for-profit organisations continually face the task of allocating resources by balancing costs, benefits and risks and gaining commitment by a wide constituency of stakeholders to those decisions. This task is complex and difficult because many options are present, benefits and risks are rarely expressed as single objectives, multiple stakeholders with different agendas compete for limited resources, individually optimal resource allocations to organisational units are rarely collectively optimal, and those dissatisfied with the decisions taken may resist implementation. We first explain three current approaches to resource allocation taken from corporate finance, operational research and decision analysis, and we identify a common mistake organisations make in allocating resources. The paper then presents a technical process, multi-criteria portfolio analysis, for balancing the conflicting elements of the problem, and a social process, decision conferencing, which engages all the key players during the modelling process, ensuring their ownership of the model and the subsequent implementation. This socio-technical process improves communication within the organisation, develops shared understanding of the portfolio and generates a sense of common purpose about those projects that will best realise the organisation’s objectives. The paper concludes with lessons we have learned from actual practice. The authors want to thank Allergan and FCT (Portuguese Science Foundation) for their support.     

Augmentation of the Generalised n×n Eigenvalue Equation to a Generalised (n+1)×(n+1) Eigenvalue Equation

Generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) where B and S ^b are n×n Hermitian matrices while S ^b is in addition positive definite is considered. This equation is augmented to a generalised (n+1)(n+1) eigenvalue equation H| _k = _k S| _k (k=1,...,n+1) where Hermitian matrices H and S represent matrices B and S ^b , respectively, augmented by one additional row and one additional column. It is shown how the eigenvalues _k and the eigenvectors | _k of the augmented eigenvalue equation can be expressed in terms of the eigenvalues _i and the eigenvectors | _i of the original eigenvalue equation. Operation count to obtain by this method all augmented eigenvalues and eigenvectors is of the order O(n ²). Unless matrices involved are of some special kind such as sparse matrices or alike, this operation count is one order of magnitude smaller than operation count required by other presently known methods. In many practical cases operation count to obtain a single selected eigenvalue and/or eigenvector by this method is of the order O(n). In the case of the generalised eigenvalue equation, all other methods usually require again O(n ³) operations, even if only a single eigenvalue and/or eigenvector is required. Thus in many cases of interest operation count to obtain a selected eigenvalue and/or eigenvector by this method is two orders of magnitude smaller than operation count required by other methods.     

TREATMENT AND RESOURCE REUSE OF 1，2，4—ACID PRODUCING EFFLUENT WITH MACROPOROUS POLYMERIC ADSORBENT

The treatment and resource reuse of 1,2,4-acid producing wastewater by self-mademacroporous adsorption resin ND,A-107 was studied in this paper. Optimum adsorption anddesorption process parameters were acquired by systematically study. The polymeric resin NDA-10 7indicated good adsorption & desorption of 1,2, 4-acid in the wastewater. The removal efficiency of1,2,4-acid, CODer is about 78%, 72% respectively. It is evident that this adsorption process is anefficient treatment method for 1,2,4-acid producing wastewater. At the same time, the accumulationand resource reuse of l,2, 4-acid can be realized in this process.     

A practical prioritization by multi-level group decision support

Military capability is proposed to be defined according to the DYNPOT scoring method. Multiobjective resource allocation of shared resources by group decision-making can combine analytic and qualitative modeling. Recently it has been pointed out that the goal programming model is superior to other models though it remained to be answered how to take into account hierarchy of decision makers (and objectives) (Stummer and Vetschera in Cent Eur J Oper Res 11:3–260, 2003). In this article it is tried to present, that the quantitative model can be easily adapted to the qualitative STT/QFD model of objectives of top-level group of decision-makers. The subsequent phases of the qualitative and the analytic solution of a multiobjective cooperative resource allocation problem can be applied within the group decision-making framework of defence requirements capability-based planning.     

Allocation of flexible and indivisible resources with decision postponement and demand learning

We consider a firm that uses two perishable resources to satisfy two demand types. Resources are flexible such that each resource can be used to satisfy either demand type. Resources are also indivisible such that the entire resource must be allocated to the same demand type. This type of resource flexibility can be found in different applications such as movie theater complexes, cruise lines, and airlines. In our model, customers arrive according to independent Poisson processes, but the arrival rates are uncertain. Thus, the manager can learn about customer arrival rates from earlier demand figures and potentially increase the sales by postponing the resource allocation decision. We consider two settings, and derive the optimal resource allocation policy for one setting and develop a heuristic policy for the other. Our analysis provides managerial insights into the effectiveness of different resource allocation mechanisms for flexible and indivisible resources.     

Dynamic resource allocation: A flexible and tractable modeling framework

This paper presents a binary optimization framework for modeling dynamic resource allocation problems. The framework (a) allows modeling flexibility by incorporating different objective functions, alternative sets of resources and fairness controls; (b) is widely applicable in a variety of problems in transportation, services and engineering; and (c) is tractable, i.e., provides near optimal solutions fast for large-scale instances. To justify these assertions, we model and report encouraging computational results on three widely studied problems – the Air Traffic Flow Management, the Aircraft Maintenance Problems and Job Shop Scheduling. Finally, we provide several polyhedral results that offer insights on its effectiveness.     

An experimental investigation of heat transfer characteristics for turbulent flow over staggered ribs in a square duct

An experimental study of developing and fully developed turbulent air flow in a square duct with two opposite rib-roughened walls in which the ribs are attached in a staggered fashion was conducted to determine the heat transfer characteristics. The rib height-to-hydraulic diameter ratio (e/D_H) was 0.19, the rib pitch-to-height ratio (p/e) was 5.31. The streamwise temperature distribution was measured, and a law of the wall for the thermal boundary layer at each free-stream turbulence level was obtained. The effects of free-stream turbulence intensity with variations of 4–11% on heat transfer coefficients were also examined. Finally, the relationship between Nusselt number and Reynolds number was correlated. The results might be used in the design of turbine blade cooling channels.     

Multilevel augmentation methods for solving the Burgers' equation

In this article, multilevel augmentation method (MAM) for solving the Burgers' equation is developed. The Crank–Nicolson–Galerkin scheme of the Burgers' equation results in nonlinear algebraic systems at each time step, the computational cost for solving these nonlinear systems is huge. The MAM allows us to solve the nonlinear system at a fixed initial lower level and then compensate the error by solving a linear system at the higher level. We prove that the method has the same optimal convergence order as the projection method, while reducing the computational complexity greatly. Finally, numerical experiments are presented to confirm the theoretical analysis and illustrate the efficiency of the proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1665–1691, 2015