An equitable DEA-based approach for assigning fixed resources along with targets

A typical problem in organization management is how to divide a fixed resource along with a target among decision making units (DMUs) of an organization equitably. By using the data envelopment analysis technique, this paper concerns the problem from the perspective of efficiency analysis and proposes a new sharing model. In the proposed method, the fixed resource and target are divided among DMUs such that the efficiencies of DMUs remain unchanged after assigning the fixed cost and target. The proposed method is unit-invariant; it eliminates resource waste and target insufficiency brought by slacks. Also, every DMU is assigned a positive resource and a positive target under this method. Two corresponding algorithms are designed to yield a unique allocation. The proposed approach can be developed under both constant returns to scale and variable returns to scale. Two examples are presented to illustrate the validity and superiorities of our method.     

Allocating the fixed cost as a complement of other cost inputs: A DEA approach

In cost allocation problem, traditional DEA approaches allocate the fixed cost among a group of decision making units (DMUs), and treat the allocated cost as an extra input of each DMU. If costs except for the fixed cost are regarded as inputs in the cost allocation problem, then it is obvious that the fixed cost is a complement of other inputs rather than an extra independent input. Therefore it is necessary to combine the allocated cost with other cost measures in cost allocation problem. Based on this observation, this paper investigates the relationship between the allocated cost and the DEA efficiency score and develops a DEA-based approach to allocate the fixed cost among various DMUs. An example of allocating advertising expenditure between a car manufacturer and its dealers is presented to illustrate the method proposed in this paper.     

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.     

Characterizing an equitable allocation of shared costs: A DEA approach

In many applications to which DEA could be applied, there is often a fixed or common cost which is imposed on all decision making units. This would be the case, for example, for branches of a bank which can be accessed via the numerous automatic teller machines scattered throughout the country. A problem arises as to how this cost can be assigned in an equitable way to the various DMUs. In this paper we propose a DEA approach to obtain this cost allocation which is based on two principles: invariance and pareto-minimality. It is shown that the proposed method is a natural extension of the simple one-dimensional problem to the general multiple-input multiple-output case.     

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.     

基于DEA的二阶段网络系统的固定成本分摊方法

结合DEA和博弈的思想研究二阶段网络系统的固定成本分摊问题,将分摊成本作为新的投入,可以证明存在某种分摊使DMU整体效率达到最优,在此基础上考虑各个DMU之间以及DMU内部之间的博弈,首先建立讨价还价乘积最大化模型,求出各DMU唯一的分摊解,然后建立DMU子系统之间的讨价还价模型,给出子系统的分摊解,最终的分摊方案满足系统效率和子系统效率为1,与现有的方法相比具有一定的优势.     

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.     

Allocating fixed costs and common revenue via data envelopment analysis

An issue of considerable importance involves the allocation of fixed costs or common revenue among a set of competing entities in an equitable way. Based on the data envelopment analysis (DEA) theory, this paper proposes new methods for (i) allocating fixed costs to decision making units (DMUs) and (ii) distributing common revenue among DMUs, in such a way that the relative efficiencies of all DMUs remain unchanged and the allocations should reflect the relative efficiencies and the input-output scales of individual DMUs. To illustrate our methods, numerical results for an example are described in this paper.     

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.     

Fair resource allocation for different scenarios of demands

This paper considers a resource allocation problem, which objective is to treat fairly all the system users. Usually the requests cannot be entirely predicted, but the manager can forecast the request evolution, this leading to a set of possible scenarios. Such a problem arises for instance in network bandwidth allocation as well as in storage space management. It also appears in the management of computer systems, such as computational grids or in cloud computing, when teams share a common pool of machines. Problems of fair resource sharing arise among users with equal access right but with different needs.Here the problem is tackled by a multi-criteria model, where one criterion is associated to one scenario. A solution is a policy, which provides an allocation for each scenario. An algorithm is proposed and analysed that lists all solutions which are Pareto optimal with regard to the different possible user request scenarios. The algorithm is used offline, but can be adapted, with some additional hypothesis, to be used online.     

外源投入型两阶段制造系统网络DEA效率分析研究

制造过程评价是改善制造系统效率的重要一环,传统的评价方法将每个制造系统决策单元视为黑箱来研究整体效率,忽略了中间产品转化信息及投入要素在各子过程中的配置信息。针对两阶段(第二阶段有外源性新投入)制造系统的效率评估问题,分别在固定规模报酬和可变规模报酬假设下,充分利用制造系统中间产品的转化及外源投入要素的配置信息,建立了制造系统网络DEA效率测度及分解模型,建模方法遵循客观评价原则,无需事先主观确定子效率和系统效率之间的组合关系。并将其应用于钢铁制造系统效率测度与分解,研究结果表明该方法能够挖掘决策单元内部子单元的效率情况,帮助决策者发现复杂制造过程非有效的根源,为复杂制造过程的整体效率测度及分解提供了有效的分析方法。     

Spherical frontier DEA model based on a constant sum of inputs

In this paper, a Data Envelopment Analysis (DEA) model in which a fixed input needs to be assigned to a group of Decision-Making Units (DMUs) is presented. This is performed by assuming the existence of a geometric place represented by a sphere that characterizes the DEA frontier. It is shown that, under this assumption, it becomes relatively easy to find a way to distribute the fixed input to all DMUs, by considering that the individual assignments will be fair through the requirement that all DMUs be efficient or, in other words, be located on the spherically shaped efficiency frontier. A model is presented and results are compared to those obtained by using two different methods proposed in the literature within the same context.     

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.     

A polynomial expression for the Owen value in the maintenance cost game

The class of maintenance cost games was introduced in 2000 to deal with a cost allocation problem arising in the reorganization of the railway system in Europe. The main application of maintenance cost games regards the allocation of the maintenance costs of a facility among the agents using it. To that aim it was first proposed to utilize the Shapley value, whose computation for maintenance cost games can be made in polynomial time. In this paper, we propose to model this cost allocation problem as a maintenance cost game with a priori unions and to use the Owen value as a cost allocation rule. Although the computation of the Owen value has exponential complexity in general, we provide an expression for the Owen value of a maintenance cost game with cubic polynomial complexity. We finish the paper with an illustrative example using data taken from the literature of railways management.     

Scheduling non-critical activities using multicriteria approach

In many projects the problem of selecting the start time of a non-critical activity arises. Usually it is possible to use the “as soon as possible” or “as late as possible” rules. In some situations, however, the result of such a decision depends on external factors such as exchange rate. This leads to an approach in which the problem of scheduling non-critical activities is solved using an expanded Cox–Ross–Rubinstein (CRR) binomial tree method. In the paper a bi-criteria problem of determining the start time of a non-critical activity is considered. We assume that the early start and the late start of the activity have been identified using Critical Path Method, but the project manager is free to select the time when the activity will actually be started. This decision cannot, however, be changed later, as it is associated with the allocation of key resources. Two main criteria are considered: cost and risk. While cost depends on exchange rate, risk increases with the delay of the start of the activity. The problem can be described as a dynamic process. We propose a new interactive technique for solving such a bi-criteria decision making problem under risk. The procedure uses trade-offs to identify a candidate solution. The CRR binomial method is applied to evaluate the cost of the activity.

     

考虑非期望因素的决策单元排序:两阶段综合效率法

对所有平行级别上的同等类型的决策单元(DMUs)在绩效表现上的排序一直是管理决策领域研究的重要课题之一。基于数据包络分析的超效率理论和SBM模型,探讨考虑非期望因素的DMUs排序问题。首先构建新的考虑非期望因素的超效率SBM模型,此模型不仅能对有效DMUs排序,而且能够转化成线性规划问题求解,具有有界性、单调性等良好性质。然后将新模型与Tone的SBM模型结合提出了考虑非期望因素的SBM综合排序法,同时给出了相对应的多项式时间算法。该方法以SBM模型作为第一阶段完成非有效DMUs排序,以新模型作为第二阶段完成有效DMUs排序,两阶段综合即完成所有DMUs排序。研究结果表明,综合排序法能够完成对考虑非期望因素的DMUs的排序,为绩效评价的管理实践提供了重要的理论依据。选取中国2010年的30个省份为实证研究对象,应用所提出的综合效率排序法对其环境效率进行排序。分析结果与中国的现实情况的相吻合,表明该排序方法是合理的,能够完成对这些地区的环境效率进行排序,可以为决策者评价环境的绩效表现提供有效的决策支持。     

A variable neighbourhood search algorithm for the constrained task allocation problem

A variable neighbourhood search algorithm that employs new neighbourhoods is proposed for solving a task allocation problem whose main characteristics are: (i) each task requires a certain amount of resources and each processor has a capacity constraint which limits the total resource of the tasks that are assigned to it; (ii) the cost of solution includes fixed costs when using processors, task assignment costs, and communication costs between tasks assigned to different processors. A computational study shows that the algorithm performs well in terms of time and solution quality relative to other local search procedures that have been proposed.     

Efficiency evaluation model with constraint resource: an application to banking operations

Competition is often presented in a free market. Efficiency evaluation of decision-making units (DMUs) needs accommodation of such competition among various units due to constrained resources. This paper develops an innovative quantitative approach to address the above-mentioned performance evaluation problem with constrained resource using output-oriented DEA. The proposed model allows DMUs to identify the maximum input reduction and resource savings to achieve performance improvement. Relations between the proposed model and classical output-oriented DEA models are explored and some economic insights are derived from these models. The proposed approach is validated by use of computational examples.     

A fuzzy algorithm for continuous capacitated location allocation model with risk consideration

This paper presents a continuous capacitated location-allocation model with fixed cost as a risk management model. In the presented model, the fixed cost consists of production and installation costs. The model considers risk as percent of unsatisfied demands. The fixed cost is assigned to a zone with a predetermined radius from its center. Because of uncertain environment, demand in each zone is investigated as a fuzzy number. The model is solved by a fuzzy algorithm based on α-cut method. After solving the model based on different α-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved based on different α-values to determine best allocation values. Also, this paper proposes a Cross Entropy (CE) algorithm considering multivariate normal and multinomial density functions for solving large scale instances and is compared with GAMS. Finally, a numerical example is expressed to illustrate the proposed model.