non-linear programming

Linguistic variables (LVs) provide a reliable expression of cognitive information. By inheriting the advantages of LVs, we can express uncertain and incomplete cognitive information in multiple attribute decision-making (MADM), and they do so better than existing methods.  In the decision-making process, we can consider decision experts’ (DEs’) bounded rationality, such as cognition toward loss caused by the DEs’ cognitive limitations during the decision process. Therefore, it is necessary to propose a novel cognitive decision approach to handle MADM problems in which the cognitive information is expressed by LVs. In this paper, we employ LVs to represent uncertain and hesitant cognitive information. Then, we propose a mathematical programming approach to solve the MADM problems where attributes or cognitive preferences are not independent.  Moreover, the validity and superiority of the presented approach are verified by dealing with a practical problem.

This paper studies a name-your-own-price (NYOP) mechanism in which the retailer allows buyers to participate in the pricing process by submitting bids. Buyers can place both joint and individual bids to purchase products either as a bundle or individually. The retailer utilizes NYOP and posted-price channels simultaneously. The focus of this paper is to assess the impact of adding the postedprice channel and bundling option on buyer behavior and retailer profit. The paper develops a two-stage model where the first stage involves the buyer’s decision on participating in NYOP. Moreover, buyers can choose between bidding for a bundle or a single item. Decisions in the second stage depend on the outcome of the first stage. Four distinct purchasing scenarios are formulated to outline the potential ways that buyers can use to purchase products. Furthermore, the buyers’ learning effect on their bidding strategy is considered. A dynamic programming approach with backward induction is employed to solve the problem. Moreover, the concavity analysis is used to obtain the solution of each nonlinear subproblem. Then, a solution algorithm based on mathematical analysis is proposed. Results reveal that the frictional costs of the first period have a greater impact on the buyer utility than those of the second period. Moreover, applying the NYOP alongside the posted-price can enhance the retailer’s profit. In particular, the retailer can use the NYOP and bundling mechanisms as encouraging tools to attract buyers and increase his profit. Thus, NYOP is a very effective instrument for market penetration.

The Analytic Hierarchy Process (AHP) which was developed by Saaty is a decision analysis tool. It has been applied to many different decision fields. Acquiring Pairwise Comparison Matrices (PCM) is the main step in AHP and also is frequently used in other multi-criteria decision-making methods. In a real problem when the number of alternatives/criteria to be compared is increased, the number of Pairwise Comparisons (PC) often becomes overwhelming. Since the Decision Maker’s (DM) performance in representing the relative preferences tends to deteriorate in such cases, it is preferred to gather fewer data from each individual DM in the form of pairwise comparisons. Missing values in Pairwise Comparison Matrices (PCM) in AHP is a spreading problem in areas dealing with great or dynamic data. The aim of this paper is to present an efficient mathematical programming model for estimating preference vector of pairwise comparison matrices with missing entries.

The purpose of this study is to provide a proper method for evaluating performance of teachers, which leads to authorities awareness about the quality and quantity of activities that are acceptable to the organization; also creating the grounds for empowering human resources, reduction of dissatisfaction, and complaints. This can result in eliminating discrimination or unfair judgments and therefore reduction of tensions, and conflicts between managers and employees. The Analytic Hierarchy Process (AHP) which was developed by Saaty is a decision analysis tool. It has been applied to many different decision fields. In this paper, we use AHP as a performance assessment tool to inquire diverse assessments in the organization about the performance of each employee. Since the number of the items to be compared in AHP is increased, the number of pairwise comparisons that each assessor answer, are increased drastically. So, we develop a method called EVMP to elicit the preference vector of pairwise comparison matrices with missing entries. The newly developed method is tested in a school; the generated results have been proved by experts.