Allocating the fixed cost as a complementary input in two-stage system: a DEA approach

¹ School of Management, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
² School of Business Administration, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, P.R. China
³ School of Economics and Management, Beijing University of Technology, Beijing 100124, P.R. China

^* Corresponding author: lionli@ustc.edu.cn

Received: 13 September 2023
Accepted: 2 April 2024

Abstract

The existing research on fixed cost allocation (FCA) in two-stage system data envelopment analysis (DEA) models typically regards the fixed cost as an additional input for each decision-making unit (DMU). However, these models overlook the prevalent real-world scenario where fixed costs act as complementary inputs in production processes. This study proposes a general two-stage network DEA model that incorporates the fixed cost as a complementary input to optimize the allocation scheme. First, we construct a functional relationship between the efficiency scores of DMUs and their allocated fixed costs using a modified super-efficiency DEA model, which effectively classifies DMUs and solves infeasible solutions within the variable returns to scale (VRS) framework. Then, we propose a fair and unique allocation model based on fairness and efficiency maximization principles. Specifically, we allocate fixed costs based on the operational scale for inelastic DMUs while equitably increasing the efficiency scores for elastic DMUs. Finally, a numerical example and an empirical study on subsidy allocation among 30 provinces demonstrate the rationality and acceptability of our approach.