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

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.