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Original Articles

A financing perspective on DEA-based resource allocation and the aggregate profit inefficiency decomposition

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Pages 320-341 | Received 31 Jan 2019, Accepted 10 Sep 2019, Published online: 30 Oct 2019
 

Abstract

Identifying the sources of profit inefficiency is of great importance to practitioners and academics. In this paper, we tend to uncover profit drivers from the perspective of resource allocation. Specifically, we focus particularly on the DEA-based resource allocation approach with a possible financing strategy, which is significantly different from prior studies in the sense that it not only offers a flexible way to tackle the infeasibility problem associated with the potential conflicting constraints, but also provides a relatively more profitable allocation plan by taking a possible debt into account. First, we consider the situation in which each of DMUs allocates their resources independently, and develop a corresponding decentralised resource allocation DEA model concerning a possible financing strategy. In particular, a novel concept of profit to financing is defined to establish the linkage between potential profit gain and possible financing strategy. Second, we propose a centralised resource allocation DEA model to solve the problem in which all DMUs are controlled by a central authority, and provide a novel aggregate profit inefficiency decomposition method to uncover sources of the aggregate (or industry) profit inefficiency. Finally, an example of 20 fast-food restaurants is applied to illustrate the effectiveness of our proposed method.

Acknowledgements

The authors thank the editor, associate editor, and two anonymous reviewers whose comments led to significant improvements in the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 Of course, we should here assume that the DMUs have the capacity to secure the funds in need. Furthermore, even the financing choice might be avoided for some specific purposes (e.g., capacity utilization consideration which may not allow such a financing strategy), our model can naturally reduce to its corresponding conventional resource allocation model without considering such a possible financing strategy. In other words, the conventional resource allocation approach can be regarded as a special case of our proposed approach.

2 Note that, our proposed decomposition method differs from Peyrache’s (Citation2015) approach in three ways. First, Peyrache’s (Citation2015) approach is based on the radial efficiency measures, whereas our proposed approach is based on non-radial measures that enable us to account for potential slacks. Second, our proposed approach is from the standpoint of profit-maximization, while Peyrache’s (Citation2015) approach aims to maximize the radial output-oriented technical efficiencies of firms. Third and most important, Peyrache (Citation2015) decomposes industry inefficiency by identifying the reallocation inefficiency arising from sub-optimal configuration of the industry, firm inefficiency arising from a failure to determine the optimal input quantities, and firm inefficiency because of lacking of best performers. In our decomposition method, however, we consider a potential profit inefficiency arising from a failure to choose the optimal allocation strategy (e.g., fail to choose a financing strategy). To our knowledge, this has not been considered in the prior studies.

3 Specifically, the advantages of introducing a possible debt are twofold: on one hand, it guarantees a feasible solution when the budget is inadequate to cover the costs of reaching the given output targets; on the other hand, it generally provides a more profitable allocation plan for the unit with high productivity.

4 The DMU is not necessary projected onto the efficient frontier, that is, the DMU can either be efficient or not.

5 In doing so, on one hand, it may help to tackle with the understaffed situation for some specific branches (i.e., encounter with the peak demand incident); on the other hand, it also facilitates coordinating personnel assignment across different branches.

6 Thanks for one of the reviewers’ comment, we here need to clarify that, in most cases, the decentralized units would have the same risk rating as the centralized group if the units belong to the same organization. Under this circumstance, the financing costs should be equal to that of the centralized group. However, if the individual units are not fully supervised by the centralized authority (e.g., the individual unit has a certain autonomy that can decide on their own financing activities), then the centralized group and the individual DMUs just behave as large and small firms. As such, according to Hennessy and Whited (Citation2007), their external financing costs are typically different, and large firms often behave as if they face small indirect cost of external financing, and small firms behave as if they face large indirect costs of external financing. Hence, we assume ϑα which enables us to include both the scenarios.

7 The cost of the shop size can be interpreted as the rental per 100 square meters.

8 Similar practice can be seen from Lozano (Citation2014).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant No. 71671095.

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