A dynamic DEA model to measure the learning rates of efficient frontier and DMUs: An application to oil and gas wells drilling. (June 2020) - Nedaei, Hessam; Jalali Naini, Seyed Gholamreza; Makui, Ahmad
Highlights: Proposing a new DEA model to calculate the efficiency of periods based on frontiers of every other period. Measuring the learning rates of DMUs. Measuring the learning rate of efficient frontier utilizing crowding distance formula. Validating the proposed model by a numerical example. Investigating the first application of dynamic DEA in oil and gas wells drilling performance analysis. Abstract: Dynamic data envelopment analysis (dynamic DEA) measures the relative efficiency of a set of decision-making units (DMUs) in multiple time periods. Efficiency improvement through time could be measured by learning curve concept, which provides a mathematical representation of the learning process when a task repetition occurs. It is insightful to measure the learning rates of DMUs individually as well as the whole efficient frontier. However, there is no method to provide the efficiency data required for calculating such learning rates in dynamic systems. In order to measure the learning rates of both efficient frontier and DMUs in a single DEA optimization run for each DMU, this paper proposes a new dynamic DEA model that calculates the efficiency of each period based on the frontier of every other period. To clarify the modeling approach, a multi-period non-dynamic model is presented before constructing the final dynamic model in primal and dual forms. The capabilities of the proposed model are then explored by a case study of 20 wells in the South Pars gas field, which is the first application of dynamic DEA in the oil and gas wells drilling performance analysis.