Multi-Echolon Multiplicative and Additive Data Envelopment Analysis Models

Mithun J. Sharma, Min Eui Jeong, and Song Jin Yu


DEA, Multiechelon, Process cycles, Multiplicative decomposition, Additive decomposition


In this paper we modify the standard DEA model by taking into account the series relationship of the multi-stages/processes within the overall process. Under this framework, the efficiency of the overall process can be decomposed into product of the efficiencies of four process cycles. This paper develops a multiplicative and additive multi-echelon efficiency measurement of supply chain. We first examine closed loop serial supply chain processes where each stage has its own inputs and at the same time uses carryover inputs from the previous stage. This is the case for all the intermediate echelons but not for the polar echelons. For instance, the first echelon that constitute the supplier stage do not have any carryover inputs as it is the polar echelon of the closed loop supply chain. We show that breaking down the production processes of supply networks for evaluation can generate more practical insights in how to improve the supply network performance.

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