Fixed Cost Allocation Based on the Utility: A DEA Common-Weight Approach

Abstract

In management decisions, situations frequently occur when the decision makers need to allocate some amount of fixed cost among a group of decision-making units (DMUs). In this paper, we propose an approach for allocating fixed cost among a group of DMUs based on the utility and data envelopment analysis (DEA) common-weight evaluation framework. First, we give the definition of utility of a DMU to a set of fixed cost allocation and common weights' selection result. Then, an approach, which contains a max-min model and an algorithm, is given for fixed cost allocation and common weights reselection of the DMUs. Specifically, the max-min model aims to generate for the DMUs the fixed cost allocation and common weights selection result that maximizes the minimum utility among all the DMUs. In addition, the algorithm is given to solve the max-min model linearly. Compared with the other fixed cost allocation approaches, our proposed approach not only has the ability to maximize the utilities of all the DMUs and guarantee the Pareto optimality of the utilities but also ensures the uniqueness of the fixed cost allocation and common-weight selection result. Finally, the proposed approach is applied for a real case study of allocating advertising expenditure among dealers of a car manufacturer. INDEX TERMS Fixed cost allocation, data envelopment analysis, utility, common-weight evaluation.

Balanced performance assessment under uncertainty: an integrated CSW-DEA and balanced scorecard (BSC)

“…Research on the issue of common-weights has attracted many attentions in the recent years; thus, various models have been presented with different approaches in this regard. Among the most recent studies, Chu and Jiang (2019) proposed a method for allocating fixed cost among a group of DMUs based on the utility and common-weight DEA evaluation framework and applied the proposed method, which contains a max-min model and an algorithm, for allocating advertising expenditure among the dealers of a car manufacturer. Mavi et al (2019) proposed a new approach to find common set of weights (CSW) in a twostage network DEA model in cases with undesirable inputs, intermediary products, and outputs.…”

Fixed cost allocation based on the principle of efficiency invariance in two-stage systems

“…Considering the game relations in the allocation process, Li, Li, Emrouznejad, Liang, and Xie (2019) proposed a cooperative game allocation approach for cost allocation. To guarantee the uniqueness of the allocation result, Chu and Jiang (2019) defined the concept of utility of each DMU and obtained the cost allocation result by maximizing the minimum utility.…”