A dynamic multi-stage data envelopment analysis model with application to energy consumption in the cotton industry

- We propose a multi-stage DEA model to evaluate energy consumption efficiencies in farming.
- The farms which consume resources to produce cotton are considered decision making units.
- Inputs not consumed during a planning period are carried over to the next planning period.
- We determine the overall efficiency of the farms with dynamic inputs.
- We also calculate the efficiency score of each farm in each planning period.

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of homogenous decision making units (DMUs) with multiple inputs and outputs. In this paper, we present a dynamic multi-stage DEA (DMS-DEA) approach to evaluate the efficiency of cotton production energy consumption. In the proposed model, the farms which consume resources (i.e., fertilizers, seeds, and pesticides) to produce cotton are assumed to be the DMUs. Inputs not consumed during a planning period are carried over to the next period in the planning horizon. Initially, a DMS-DEA model is used to determine the overall efficiency of the DMUs with dynamic inputs. Next, the efficiency score of each DMU is calculated for each time period in the planning horizon. We demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms with a real-life case study of energy consumption in the cotton industry.