Journal of Production and Industrial Engineering Volume 5, Issue 2, December 2024, pp 48 - 58 https://doi.org/10.26706/jpie.5.2.20240902 48 Journal of Production and Industrial Engineering https://www.rame.org.in/jpie/ Determining the Weights of Integer Linear Programming Model using the Analytic Hierarchical Process (AHP) Ansseif A.latif Ansseif 1,* , Aseel Nasser Sabti 2 , Zaid A.Mohammed 3 1,2,3 College of Administration and Economics, Al-Iraqia University, Baghdad, Iraq. * Correspondence: nsseif.latif@aliraqia.edu.iq Abstract: This research presents a well-studied quantitative method based on Integer Linear Programming (ILP) in order to determine the effect of the available alternatives in the company's products through the relative importance weights of the sample variables and based on the Analytic Hierarchical Process (AHP) without resorting to speculative methods in the process of calculating and weighting the weights of the decision variables. investigated sample. Therefore, we will discuss the application of the (AHP) method through a questionnaire prepared for the purpose of determining the Pairwise Comparisons Matrices and the relative importance of a set of criteria and alternatives in the research sample, and thus using it to feed the mathematical model (ILP) to know the effect of these alternatives on the company's products as well maximize the weighting of the available alternatives to take the optimal decision. Keywords: Analytic Hierarchical Process (AHP); Integer Linear Programming (ILP); Pairwise Comparisons Matrices; Eigenvector. 1. Introduction In view of the dynamism and rapid development that surrounds industrial or service institutions; it has become difficult for that administration to solve the problems it faces by relying on the method of intuition and guesswork. Therefore, these institutions realized the necessity of using models and quantitative methods in the decision-making process, especially that the practical reality required solving problems and achieving several goals at the same time.[1] Therefore, decision makers resorted to using and developing special quantitative methods that address multifactorial decision problems and criteria, meaning that the decision maker has to choose between several alternatives.[2]. There are many applications of Integer Linear Programming (ILP) and analytic hierarchical process in the available literature for example [3] They submitted an approach based on linear programming (LP) that estimates the weights for a pairwise comparison matrix generated within the framework of the analytic hierarchy process and LP models were formulated for many matrices of pair comparisons and the results of LP models were compared with two widely used methods EM and LLS. Through LP models, the same weights were obtained from the two methods.[4] improved a multiple objective mixed integer stochastic programming (SMIP) model for the vendor selection problem (VSP) with stochastic demand under multi- products purchases. [5] He proposed a model of selecting the right vendor from a group of vendors using the Integer Linear Programming (ILP) model for multiple products and this model was resolved as a decision support system according to the visions and plans of a company. [6] Article/ Review – Peer Reviewed Received: 17 Sept 2024 Accepted: 20 Nov 2024 Published: 30 Dec 2024 Copyright: © 2024 RAME Publishers This is an open access article under the CC BY 4.0 International License. https://creativecommons.org/licenses /by/4.0/ Cite this article: Ansseif A.latif Ansseif, Aseel Nasser Sabti, Zaid A.Mohammed, “Determining the Weights of Integer Linear Programming Model using the Analytic Hierarchical Process (AHP)”, Journal of Production and Industrial Engineering, RAME Publishers, vol. 5, issue 2, pp. 48-58, 2024. https://doi.org/10.26706/ijceae.5.2.2 0240902