Cognitive task allocation employs task analysis to identify the performance and operational requirements of task functions; and demand/resource matching to match the identified requirements and the human and computer resources available for implementation. The current methodologies of cognitive task allocation are either too aggregate to provide adequate resolution of performance requirements or domain-specific and thus of limited applicability. The paper introduces a formal, quantitative, and domain-independent model of cognitive task allocation aimed at reducing the limitations inherent in the currently practiced methodologies. Demand/resource matching is modeled as an Analytic Hierarchy Process. The Analytic Hierarchy Process of Demand/Resource Matching is defined as a mapping process along a four-level Analytic Hierarchy. By means of the Analytic Hierarchy Process, a task function (Level 1 of the Analytic Hierarchy) is analyzed into its cognitive processes (Level 2); performance criteria are set for each cognitive process (Level 3) by means of which the capacities of the human, computer, or interactive human/computer controller (Level 4) are evaluated and compared. The Analytic Hierarchy Process then integrates judgements of human and computer abilities and limitations into a weighted average indicating the relative capacity of human and computer to perform this function. This assessment of relative merit of performance can hence be integrated with work design, economic, and other contextual factors towards the final allocation design. The Analytic Hierarchy Process was applied and evaluated in the design of task allocation in production planing and control of a flexible manufacturing system by comparing the allocation designs of two groups of subjects. One group was supported by the decision model, the other received no decision support. The observed differences between the two groups indicated that the decision model can effectively support detailed task analysis and an adequate resolution of performance requirements; the identification of the design, trade-offs between human allocation and automation; and provide the computational resources to reduce decision bias.