The Analytic Hierarchy Process and Linear Programming in Human Resource Allocation 

Abstract

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.

Integrated strategic planning and multi-criteria decision-making framework with its application to agricultural water management

“…The weights of the criteria are determined by the hierarchical analysis method once the hierarchical structure is defined, which involves constructing a pairwise comparison matrix to determine the weights. The comparison matrix’s values are determined using Saaty’s table 55 , and the weights of the criteria are calculated based on the geometric mean values. The next step applies the fuzzy TOPSIS algorithm to evaluate the management alternatives in each of the irrigation management zones of the Sefidroud irrigation and drainage network.…”

Integration of Functional Resonance Analysis with Multicriteria Analysis for Sociotechnical Systems Risk Management

“…AHP aims to select one alternative from a given set of alternatives (Saaty, 1980). Moreover, it has been applied to rank multiple decision criteria in a desirability order based on a rational framework of quantitative comparisons (Saaty, 1980).…”

“…AHP aims to select one alternative from a given set of alternatives (Saaty, 1980). Moreover, it has been applied to rank multiple decision criteria in a desirability order based on a rational framework of quantitative comparisons (Saaty, 1980). Many distinct sectors, including safety management and risk assessment have applied this method to quantify qualitative data (Caputo, Pelagagge, & Salini, 2013).…”

Combining multi-criteria decision analysis with GIS approaches for decentralized organic wastes composting plants site selection in Tiassalé, Southern Côte d’Ivoire

“…Factors, criteria and sub-criteria weighting. Factors, criteria and sub-criteria were weighted using AHP method (Saaty, 1980), which is based on the pair-wise comparison of the importance of the different elements. The first step of this weighting process was the structurization of the factors, criteria and sub-criteria hierarchically.…”

“…In the third step, the expert judgements (scores) for each matrix were imported into Expert Choice software, and the final weight of each factor, criterion and sub-criteria as well as the consistency ratio (CR) of the different matrices were Table 1. Scale for pair-wise comparisons (Saaty, 1980).…”