VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) has been developed and applied for over twenty-five years, gaining recognition as a prominent multi-criteria decision-making (MCDM) method. Over this period, numerous studies have explored its applications, conducted comparative analyses, integrated it with other methods, and proposed various modifications to enhance its performance. This paper aims to delve into the fundamental principles and objectives of VIKOR, which aim to maximize group utility and minimize individual regret simultaneously. However, this study identifies a significant limitation in the VIKOR methodology: its process amplifies the weight of individual regret, and the calculated index values further magnify this effect. This phenomenon not only affects the decision-making balance but also leads to the critical issue of ranking reversal, which undermines the reliability of the results. To address these shortcomings, this paper introduces an enhanced version of VIKOR that mitigates the impact of individual regret while preserving the method’s original objectives. This paper validates the effectiveness of the proposed enhanced VIKOR method using various MCDM approaches, including (1) ten different versions of VIKOR and (2) eleven commonly used MCDM methods. Furthermore, this study confirms that the enhanced VIKOR can be effectively applied across various existing VIKOR versions, broadening its adaptability. A sensitivity analysis is additionally performed by adjusting the criteria weights using the ordered weighted averaging method. An illustrative case study involving the selection of a manufacturing process validates the proposed model. The results show that the proposed model is robust and capable of producing more reliable outcomes. It also demonstrates its practicality and effectiveness in real-world decision-making scenarios.

In this paper, we develop an economic order quantity (EOQ) model for fixed shelf-life items and a non-increasing demand. The objective of this model is to maximize the total profit. We find the criterion to decide (i) the interior maximum solution or (ii) the boundary maximum solution. Eight numerical examples are given to illustrate all possible scenarios of this generalized model. Our results identify a scenario for which the maximum profit is always negative. This is highly relevant for firms in the public sector operating at a financial loss.

Uncertainty exists in reality decision-making problems. Therefore, fuzzy theories, fuzzy intervals, intuitionistic fuzzy, and Z-numbers have been proposed and successfully applied to multi-criteria decision-making (MCDM). However, since the information presented in the Z-numbers method is the subjective opinion of the decision-maker, the problem of overestimating or underestimating the reliability of the information may occur in both individual and group decision-making. The Extended Z-numbers (Z^E-numbers) method was proposed in 2021 to solve this problem; hence, the decision-making process no longer relies on subjective opinions only but seeks external experts related to the problem to further vote on the evaluation value given by the internal decision-maker, in order to modify the information’s reliability, and thus to obtain a more realistic result. This paper combines the Z^E-numbers method with the improved Elimination et Choix Traduisant la Realite II (ELECTRE II) proposed in 2022 and proposes a new MCDM method based on Z^E-numbers, named Z^E-ELECTRE II. The green supplier selection problem was used as an illustrative example. Meanwhile, the close analysis in this paper examines two primary dimensions of variability: (1) simulation of external expert voting situations to analyze the variations in information reliability and decision-making results and to cross-compare them with other MCDM methods; (2) investigation of the impact of internal preferences, as reflected through systematic adjustments to the weights of the evaluation criteria. The results show that uncertainty of information, reliability, and the perspectives of different decision-makers and expert groups can be considered through Z^E-numbers. The proposed Z^E-ELECTRE II is applicable to group decision-making, validates the robustness of the process, and is suitable for dynamic decision-making under varying decision-maker preferences. Furthermore, using the Z^E-numbers along with the MCDM method can obtain more flexibility and more reliable results.

Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.