Modeling centralized resources allocation and target setting in imprecise data envelopment analysis

Data Envelopment Analysis (DEA) is a nonparametric mathematical programming methodology for performance measurement of organizational units that can be utilized normatively and proactively in resource allocation and target setting. While previous studies along this line have commonly utilized exact (crisp) data, the prospective and proactive use of DEA in the activity planning frequently involves uncertainty or impreciseness as to the feasible ranges for resources to be allocated and output targets to be established. The current paper proposes an imprecise DEA-based linear programming method with interval inputs and outputs by addressing the gap of missing the imprecise data settings. For this aim, we present common set of weights models to obtain the interval efficiency of Decision-Making Units (DMUs) with interval inputs and outputs. We then propose DEA-based models to allocate imprecise resources and setting imprecise targets to DMUs such that the interval efficiency of all the DMUs improves or at least remains. The proposed model provides reasonable managerial objectives with respect to the efficiency of the subordinate units when the centralized planner implements resource allocation and target setting. We exemplify the applicability and efficacy of the proposed method using a numerical example in the frame of two distinct scenarios.