A performance measurement framework considering undesirable outputs, exogenous inputs and missing data using additive dea model

Use of performance measurements helps managers decide on how resources and efforts should be allocated to ensure effectiveness and use of performance measurements keeps management focused on the key goals of an organization. Furthermore, organizations use performance measurement for benchmarking efforts which helps them balance their internal problem solving and improvement activities with the realities of their external environment. Studies in performance measurement shared concerns for the development of methods to aid decisions in administrative procedures and practices to ensure efficient delivery of services and increase the productivity of workers in various businesses. From review of different performance measurement methods shortfalls of current measurement methods were identified: it basically revolves around the shortfall of capturing the holistic view of performance and such failure to consider appropriately the existence of undesirable outputs, exogenous variables, missing and interval data in measuring efficiency were also identified. These three factors are important since it does not only characterize the organization but ultimately it has an effect on the evaluation of performance and so much with the organization ranking relative to other organizations. To address this, a performance measurement framework involving the use of an additive Data Envelopment Analysis (DEA) model was developed along with an estimation methodology for missing data. The DEA model was enhanced to be able to accommodate the three factors identified. In particular the objective of the model was to maximize opportunity scores for the organization to increase performance with specific constraints for each input and output concerned, along with the corresponding constraints for undesirable output and exogenous input. To allow for interval and missing data adjustments in the model. Hurwics criterion was incorporated to encompass the optimistic and pessimistic decisions made by the organization. The model was validated through the use of premium excel solver. The inputs used were first screened and adjustments for missing data were done through an interval estimate methodology developed. Behavior of the model was investigated and the effects of the optimistic and pessimistic model, the undesirable output and the exogenous inputs were analyzed. The undesirable outputs have effects on the opportunity scores and it may significantly change the efficiency rankings. As for the exogenous input it was observed that the effect of the exogenous inputs is on how it limits the Decision Making Units (DMUs) in their benchmarking choices. The treatment in exogenous inputs tends for DMUs to benchmark to other DMUs that operate in similar exogenous environment. Further analysis to the model has indicated that exclusion of undesirable output and exogenous input will change ranking scores. The number of allowable missing data is variable depending upon the data set. However for data that has low correlation among and between inputs and outputs, the proportion of allowable number of missing is also lower. For exogenous inputs the number allowable tends to be less than the controllable input and output. Also the resulting optimistic and pessimistic scores tend to be sensitive to the estimated data, a small increase or decrease in the estimates tends to bring changes in the ranking scores of DMUs. For future studies it can be recommended to consider dynamic effects of past or historical data in efficiency evaluation develop a more appropriate estimation methodology for non-linearly related data possibly integrate estimation of missing data into a single DEA model and investigate the effect on the production possibility set when missing data is allowed in the calculation of efficiency or opportunity scores