Centralized resource allocation for enhanced Russell models

This paper proposes a centralized resource allocation (CRA) model for the enhanced Russell model. All the DMUs can be easily projected onto the efficient frontier by solving only one model. This projection can be made by transforming the proposed model to a linear programming problem. In this paper, instead of non-radially increasing or decreasing the inputs or outputs individually, we increase or decrease non-radially all of the inputs and outputs at the same time. By solving a single model, we can provide targets for all DMUs. By the proposed approximation, different targets can be found for all DMUs, as compared to those obtained by the previous approximations. The proposed model can be developed to CRA models. Finally, an applied example emphasizes the importance of the proposed model.     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

Centralized resource allocation with stochastic data

Data Envelopment Analysis (DEA) is a technique based on mathematical programming for evaluating the efficiency of homogeneous Decision Making Units (DMUs). In this technique inefficient DMUs are projected on to the frontier which constructed by the best performers. Centralized Resource Allocation (CRA) is a method in which all DMUs are projected on to the efficient frontier through solving just one DEA model. The intent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA) in order to allocate centralized resources where inputs and outputs are stochastic. The concept discussed throughout this paper is illustrated using the aforementioned example.     

A DEA approach for fair allocation of common revenue

An issue of considerable importance, how to allocate a common revenue in an equitable manner across a set of competing entities. This paper introduces a new approach to obtaining allocation common revenue on all decision making units (DMUs) in such a way that the relative efficiency is not changed. In this method for determining allocation common revenue dose not need to solving any linear programming. A numerical example is provided to illustrate the results of the analysis.     

Centralized DEA models with the possibility of downsizing

While traditional data envelopment analysis (DEA) models assess the relative efficiency of similar, independent decision making units (DMUs) centralized DEA models aim at reallocating inputs and outputs among the units setting new input and output targets for each one. This system point of view is appropriate when the DMUs belong to a common organization that allocates their inputs and appropriates their outputs. This intraorganizational perspective opens up the possibility that greater technical efficiency for the organization as a whole might be achieved by closing down some of the existing DMUs. In this paper, we present three centralized DEA models that take advantage of this possibility. Although these models involve some binary variables, we present efficient solution approaches based on Linear Programming. We also present some numerical results of the proposed models for a small problem from the literature.     

A generalized DEA model for centralized resource allocation

In this paper, we introduced a new generalized centralized resource allocation model which extends Lozano and Villa’s and Asmild et al.’s models to a more general case. In order to uncover the sources of such total input contraction in the generalized centralized resource allocation model, we applied the structural efficiency to further decompose it into three components: the aggregate technical efficiency, the aggregate allocative efficiency and re-transferable efficiency components. The proposed models are not only flexible enough for the central decision-maker to adjust the inputs and outputs to achieve the total input contraction but also identify the sources of such total input contraction, thereby giving rise to an important interpretation and understanding of the generalized centralized resource allocation model. Finally, an empirical example is used to illustrate the approach.     

The fair allocation of common fixed cost or revenue using DEA concept

The common fixed cost or revenue distribution amongst decision making units (briefly, DMUs) in an equitable way is one of the problems that can be solved by data envelopment analysis (DEA) concept. The motivation of this paper is common fixed cost or revenue allocation based on following three principles: First, allocation must be directly proportional to the elements (inputs and outputs) that are directly proportional to imposed common fixed cost or to obtained common fixed revenue. Second, allocation must be inversely proportional to the elements that are inversely proportional to common fixed cost or revenue. Finally, the elements that have no effect on common fixed cost or revenue must have no effect on allocation as well.     

Resource allocation based on the DEA model

The purpose of this paper is to develop an approach to a resource-allocation problem that typically appears in organizations with a centralized decision-making environment, for example, police stations, banks, and universities. The central unit is assumed to be interested in maximizing both the total efficiency and the efficiency of the individual unit by allocating available resources to them. Building upon this, we present a data envelopment analysis-based model for allocating input resources to DMUs (the decision-making units) under the framework of multiple objective programming. Numerical examples are used to illustrate the approach.     

DEA models for supply chain efficiency evaluation

An appropriate performance measurement system is an important requirement for the effective management of a supply chain. Two hurdles are present in measuring the performance of a supply chain and its members. One is the existence of multiple measures that characterize the performance of chain members, and for which data must be acquired; the other is the existence of conflicts between the members of the chain with respect to specific measures. Conventional data envelopment analysis (DEA) cannot be employed directly to measure the performance of supply chain and its members, because of the existence of the intermediate measures connecting the supply chain members. In this paper it is shown that a supply chain can be deemed as efficient while its members may be inefficient in DEA-terms. The current study develops several DEA-based approaches for characterizing and measuring supply chain efficiency when intermediate measures are incorporated into the performance evaluation. The models are illustrated in a seller-buyer supply chain context, when the relationship between the seller and buyer is treated first as one of leader-follower, and second as one that is cooperative. In the leader-follower structure, the leader is first evaluated, and then the follower is evaluated using information related to the leader's efficiency. In the cooperative structure, the joint efficiency which is modelled as the average of the seller's and buyer's efficiency scores is maximized, and both supply chain members are evaluated simultaneously. Non-linear programming problems are developed to solve these new supply chain efficiency models. It is shown that these DEA-based non-linear programs can be treated as parametric linear programming problems, and best solutions can be obtained via a heuristic technique. The approaches are demonstrated with a numerical example.     

Resource allocation based on cost efficiency

In this paper, we consider a resource allocation (RA) problem and develop an approach based on cost (overall) efficiency. The aim is to allocate some inputs among decision making units (DMUs) in such way that their cost efficiencies improve or stay unchanged after RA. We formulate a multi-objective linear programming problem using two different strategies. First, we propose an RA model which keeps the cost efficiencies of units unchanged. This is done assuming fixed technical and allocative efficiencies. The approach is based on the assumption that the decision maker (DM) may not have big changes in the structure of DMUs within a short term. The second strategy does not impose any restrictions on technical and allocative efficiencies. It guarantees that none of the cost efficiencies of DMUs get worse after RA, and the improvement for units is possible if it is feasible and beneficial. Two numerical examples and an empirical illustration are also provided.     

The overall efficiency of the dynamic DEA models

Central European Journal of Operations Research - This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA...     

Additive DEA based on MCDA with imprecise information

This work exploits links between Data Envelopment Analysis (DEA) and multicriteria decision analysis (MCDA), with decision making units (DMUs) playing the role of decision alternatives. A novel perspective is suggested on the use of the additive DEA model in order to overcome some of its shortcomings, using concepts from multiattribute utility models with imprecise information. The underlying idea is to convert input and output factors into utility functions that are aggregated using a weighted sum (additive model of multiattribute utility theory), and then let each DMU choose the weights associated with these functions that minimize the difference of utility to the best DMU. The resulting additive DEA model with oriented projections has a clear rationale for its efficiency measures, and allows meaningful introduction of constraints on factor weights.     

运用DEA方法评价地区科技资源配置的相对有效性

本文针对我国东部、中部和西部地区科技资源状况的差异性,运用数据包络分析方法(DEA方法)来评价区域科技资源配置的相对有效性,指出了区域科技资源配置状况的非均衡性,并揭示了影响科技资源配置相对效率的原因。     

DEA models for the explicit maximisation of relative efficiency

It has recently been demonstrated that incorporating weight bounds and other non-homogeneous restrictions in DEA models may lead to underestimation of the maximum relative efficiency of decision making units. This paper suggests a way of avoiding this by replacing the objective function in DEA models by the relative efficiency of the assessed unit and converting the resulting models to linear forms. An alternative approach based on incorporating weight restrictions in the recently introduced maximin DEA model is also considered. It is shown that imposing weight bounds in the maximin model is equivalent to imposing bounds on ratios of individual weights.     

Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

Mathematical programming models for revenue management under customer choice

We study a network airline revenue management problem with discrete customer choice behavior. We discuss a choice model based on the concept of preference orders, in which customers can be grouped according to a list of options in decreasing order of preference. If a customer’s preferred option is not available, the customer moves to the next choice on the list with some probability. If that option is not available, the customer moves to the third choice on the list with some probability, and so forth until either the customer has no other choice but to leave or his/her request is accepted. Using this choice model as an input, we propose some mathematical programs to determine seat allocations. We also propose a post-optimization heuristic to refine the allocation suggested by the optimization model. Simulation results are presented to illustrate the effectiveness of our method, including comparisons with other models.     

Asset allocation under threshold autoregressive models

We discuss the asset allocation problem in the important class of parametric non‐linear time series models called the threshold autoregressive model in (J. Roy. Statist. Soc. Ser. A 1977; 140 :34–35; Patten Recognition and Signal Processing. Sijthoff and Noordhoff: Netherlands, 1978; and J. Roy. Statist. Soc. Ser. B 1980; 42 :245–292). We consider two specific forms, one self‐exciting (i.e. the SETAR model) and the other smooth (i.e. the STAR) model developed by Chan and Tong (J. Time Ser. Anal. 1986; 7 :179–190). The problem of maximizing the expected utility of wealth over a planning horizon is considered using a discrete‐time dynamic programming approach. This optimization approach is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system, which includes the SETAR model and the STAR model as particular cases. Numerical studies are conducted to demonstrate the practical implementation of the proposed model. We also investigate the impacts of non‐linearity in the SETAR and STAR models on the optimal portfolio strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

Proposing a method for fixed cost allocation using DEA based on the efficiency invariance and common set of weights principles

One of the applications of data envelopment analysis is fixed costs allocation among homogenous decision making units. In this paper, we first prove that Beasley’s method (Eur J Oper Res 147(1):198–216, 2003), whose infeasibility has been claimed by Amirteimoori and Kordrostami (Appl Math Comput 171(1):136–151, 2005), always has a feasible solution and the efficiency invariance principle does not necessarily satisfy in Amirteimoori and Kordrostami’s method (Appl Math Comput 171(1):136–151, 2005). Hence, we present two equitable methods for fixed cost allocation based on the efficiency invariance and common set of weights principles such that, if possible, they help meet these two principles. In the first method, the costs are allocated to DMU in such a way that the efficiency score of DMUs does not change, and simultaneously this allocation has the minimum distance from the allocation that has been obtained with a common set of weights. However, in the second method, the costs are allocated in such a way that input and output of all units have a common set of weights and it has the minimum distance from the allocation that satisfies the efficiency invariance principle. Moreover, both methods, consider the satisfaction of each unit of the allocated cost. Finally, the proposed method is illustrated by two real world examples.     

DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.     

A framework for optimization under limited information

In many real world problems, optimisation decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of data points. The scarcity of data may be due to high cost of observation or fast-changing nature of the underlying system. This paper presents a “black-box” optimisation framework that takes into account the information collection, estimation, and optimisation aspects in a holistic and structured manner. Explicitly quantifying the observations at each optimisation step using the entropy measure from information theory, the often nonconvex-objective function to be optimised is modelled and estimated by adopting a Bayesian approach and using Gaussian processes as a state-of-the-art regression method. The resulting iterative scheme allows the decision maker to address the problem by expressing preferences for each aspect quantitatively and concurrently.