Fixed cost allocation with data envelopment analysis based on lexicographical allocation

Fixed cost allocation (FCA) refers to the reasonable allocation of the costs of shared platforms or resources within an organisation to all relevant decision-making units (DMUs). A natural question is how to determine an equitable and unique FCA scheme. In reality, the lack of a powerful central decision-maker drives each rational DMU to pursue the lowest possible cost for itself. However, if all DMUs pursue individual cost minimisation, fixed costs are not fully allocated. This article develops a novel lexicographic FCA (LEX-FCA) model. Within the LEX-FCA framework, the costs of all DMUs are determined in lexicographical allocation for each possible sequence, but subject to the constraint that the costs of all determined DMUs cannot be changed. The cost assigned to each DMU is defined as the average lexicographic cost, computed by averaging lexicographic costs across all possible sequences. Furthermore, an algorithm based on a tree-search enumeration procedure is developed to compute the final FCA scheme efficiently. The proposed LEX-FCA method is illustrated through a numerical example and applied to a real-world case involving the allocation of a collaborative pollution control fixed cost among nine provinces in the Yellow River Basin of China, demonstrating its practical effectiveness.