Gabriel Villa

CENTRALIZED RESOURCE ALLOCATION USING DATA ENVELOPMENT ANALYSIS

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.

Measuring the performance of nations at the Summer Olympics using data envelopment analysis

In this paper a well known tool for relative efficiency assessment, namely Data Envelopment Analysis (DEA), is used to measure the performance of the nations participating at the last five Summer Olympic games. The proposed approach considers two inputs (GNP and population) and three outputs (number of gold, silver and bronze medals won). To increase the consistency of the results, weight restrictions are included, guaranteeing a higher valuation for gold medals than for silver medals and higher for the latter than for bronze medals. Variable returns to scale are assumed. The results for the last five Summer Olympics are analysed. For each of them, a performance index as well as benchmarks are computed for each country. In addition, plotting the performance of a specific country for the different games can help identify trends as well as objective successes and disappointments.

Centralised reallocation of emission permits using DEA

In this paper a data envelopment analysis (DEA) approach to the problem of emission permits reallocation is presented. It can be used with conventional command and control as well as with an allowance market. It uses a centralized point of view, which represents the common good. In the model it is assumed that firms produce two types of outputs: desirable outputs (i.e. good outputs with positive value for consumers) and undesirable outputs (i.e. bad outputs with negative value for consumers, such as emissions of pollutants). The proposed approach has three phases, which correspond to three objectives that are pursued lexicographically. The three objectives are maximizing aggregated desirable production, minimizing undesirable total emissions and minimizing the consumption of input resources. The relative priority of these objectives is defined by the regulator. The whole approach is units-invariant and does not require information on input and output prices. The approach is applied on a dataset from the Swedish pulp and paper industry.

Data envelopment analysis of integer-valued inputs and outputs

This paper addresses DEA scenarios whose inputs and outputs are naturally restricted to take integer values. Conventional DEA models would project the DMU onto targets that generally do not respect such type of integrality constraints. Although integer-valued inputs and outputs can be considered as a special case of ordinal inputs and outputs, the use of that type of models has many drawbacks. In this paper a MILP DEA model that guarantees the required integrality of the computed targets is proposed.

Application of centralised DEA approach to capital budgeting in Spanish ports

In this paper, we propose a number of non-radial, output-oriented, centralised DEA models to determine individual and collective output target levels, input slacks and input reallocations as well as additional inputs acquisitions under a capital budget constraint. The application of the proposed approach to the Spanish Port Agency is presented. The overall amount of inefficiency currently found in the system allows for the determination of potential total output increases ranging from 24% to 114% without additional resources. Considering inputs reallocation would allow for an additional 20% output expansion. The acquisition of additional input resources would make feasible to expand outputs further, to levels whose exact values monotonously depend on the capital budget considered.

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.

Multiobjective target setting in data envelopment analysis using AHP

In this paper two new target setting DEA approaches are proposed. The first one is an interactive multiobjective method that at each step of the process asks the decision maker (DM) which inputs and outputs he wishes to improve, which ones are allowed to worsen and which ones should stay at their current level. The local relative priorities of these inputs and outputs changes are computed using the analytic hierarchy process (AHP). After obtaining the candidate target, the DM can update his preferences for improving, worsening or maintaining current inputs and outputs levels and obtain a new candidate target. Thus continuing, until a satisfactory operating point is computed. The second method proposed uses a lexicographic multiobjective approach in which the DM specifies a priori a set of priority levels and, using AHP, the relative importance given to the improvements of the inputs and outputs at each priority level. This second approach requires solving a series of models in order, one model for each priority level. The models do not allow for worsening of neither inputs nor outputs. After the lowest priority model has been solved the corresponding target operating point is obtained. The application of the proposed approach to a port logistics problem is presented.

Determining a sequence of targets in DEA

Data Envelopment Analysis (DEA) can be used for assessing the relative efficiency of a number of operating units, finding, for each inefficient unit, a target operating point lying on the efficient frontier. Most DEA models project an inefficient unit onto a most distant target, which makes its attainment more difficult. In this paper, we advocate determining a sequence of targets, each one within an appropriate, short distance of the preceding. The proposed Constant Returns to Scale approach has two interesting features: (a) the sequence of targets ends in the efficient frontier and (b) the final, efficient target is generally closer to the original unit than the one-step projection is.

Coordinated scheduling of production and delivery from multiple plants and with time windows using genetic algorithms

This paper deals with the problem of selecting and scheduling a set of orders to be manufactured and immediately delivered to the customer site. We provide m plants for production and V vehicles for distribution. Furthermore, another constraints to be considered are the limited production capacity at plants and time windows within which orders must be served. A genetic algorithm to solve the problem is developed and tested empirically with randomly generated problems. In order to benchmark the GA, a graph-based exact method is proposed. However, such exact method is not efficient and, therefore, can only be used for small problems. Results attest that our GA produces good-quality solutions.

DEA-based pre-merger planning tool

Data envelopment analysis (DEA) can be used as a pre-merger planning tool to estimate expected cost and profit efficiency gains. Specifically, in this paper, two alternative DEA models are presented, one to minimize post-merger input cost and the other to maximize post-merger profit. The first model assumes that input prices are known, whereas the second assumes that output prices are known. As both models explicitly consider the possibility of closing existing units, they are especially apt for in-market horizontal mergers, in which considerable overlap may exist among the branches of the merging firms. Indicative efficiency ratios are proposed based on the results of the models. The proposed approach is, in addition, rather flexible, allowing the optional inclusion of a variety of features and constraints, such as incompatibility among units, employment guarantees, etc.