The max-reward and min-penalty frontier: A benchmark for research of supply and demand mismatches

The traditional production-oriented frontier in data envelopment analysis is defective in dealing with supply and demand mismatches, where the emphasis is placed on mismatches between input and supply as well as output and demand, instead of simply how input is used to produce output. Previous techniques to evaluate demand effectiveness and supply-demand effectiveness limited the value ranges of penalty parameters and thus failed to consider some extreme situations. To fill this gap, we abandon the traditional concept of frontier and map production units into a new type of frontier. Supply and demand mismatches can increase production costs but can also bring extra revenues in some situations; these outcomes are called penalty and reward, respectively. We map the production possibility set onto a dataset of input and output penalties, namely, the reward/penalty possibility set. A new frontier, called the max-reward and min-penalty frontier, is provided as the benchmark to evaluate decision-making units' performance in supply management and demand fulfilment and accordingly define reward-penalty effectiveness. Much further research can be done based on this new frontier.