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The Analytic Hierarchy Process (AIM) provides a way to rank the alternatives of a problem by deriving ratio scales to represent these ranks. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities. across different criteria and satisfies given constraints. This leads one to consider the interface between the AHP and the combinatorial approach inherent in Linear Programming (LP). The priorities of the alternatives often serve as coefficients of the objective function of an LP problem. The constraints are determined from existing measurements such as the range of the number of employees needed and the salaries requited for various jobs. It is shown how the absolute measurement mode of the AHP is used to prioritize organizational positions and applicants for these positions and determine the positions to be filled along with the applicants to fill them. A more general concern is how to obtain the coefficients of the constraints themselves as priorities and " how to establish numerical bounds on the constraints. This paper is concerned with examples of an objective function whose coefficients are derived through the AHP and whose constraints involve tangible coefficients. Brief discussion of optimization where the coefficients of an entire LP problem are determined by the AHP and whose variables are tangibles is also given with a simple example.

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Why is group decision making so important today?  In our increasingly complex environment, decision making becomes more and more challenging for leaders and practitioners.  Working in groups appears to be the norm because the alignment of visions and actions are critical for an organization. A leader or a group facilitator needs a supporting system to make collective thinking effective. The book, Group Decision Making: Drawing out and Reconciling Differences, written by Thomas Saaty and myself shows that the AHP is the scientific approach for supporting group processes in the current and future complex environment (Saaty & Peniwati, 2008). https://doi.org/10.13033/ijahp.v9i3.533