Closest target setting with minimum improvement costs considering demand and resource mismatches

Data envelopment analysis models can be used to measure efficiency performance and yield an improvement target for the evaluated decision-making units. However, such models have not considered market factors. Demand fulfillment and resource management also matter in production. Sales losses due to insufficient stock or inventory holding costs happen when the production output of a factory is lower or higher than the market demand. Moreover, the cost of purchasing to cover shortages of a necessary resource or disposing of a surplus resource happens when the resource amount is lower or higher than the level required for production. In this study, we adopt the definition of penalized output used to quantify the mismatch between demand level and actual output, and we propose the concept of penalized input to deal further with mismatches between owned resources and actual input. We then develop an extended closest target setting model with both penalized input and penalized output to find a projection on the demand-truncated frontier with minimum improvement costs. Finally, two simple numerical examples are used to demonstrate the applicability and practicality of the proposed approach.