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Background: Supply chain companies have merits and demerits regarding operational and economic transactional policies. The effectiveness of supply chain companies corresponds to a cumulative score on a multi-criteria and perspectives-based evaluation. In this paper, we analyse the performances and challenges of several celebrated e-commerce companies to perceive their overall impression of supply chain management. Method: A mathematical model is framed as a multi-criteria decision-making (MCDM) problem with challenges as criteria and companies as alternatives. The criteria importance through inter-criteria correlation (CRITIC) method is used in this paper to adjust weights representing the available data. The ranking of e-commerce companies is evaluated using multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method. Results: This model investigates the most dependent criteria and sub-criteria for the adaptation challenges of supply chain companies (SCCs). Furthermore, the SCCs are prioritized based on various conflicting criteria. Conclusion: Various challenges of SCCs, like logistics constraints, disruptions in supply chains, issues with technology, ethical sourcing and inconsistency between the products’ availability and the pace of consumption, are considered and analysed. We amassed the difficulties as criteria and sub-criteria in a numerical process using the MCDM approach. Additionally, the sensitivity and comparative of several optimal phenomena are analysed based on distinctive combinations of challenges in the ranking arena.

Background: Neutrosophic logic explicitly quantifies indeterminacy while also maintaining the independence of truth, indeterminacy, and falsity membership functions. This characteristic assumes an imperative part in circumstances, where dealing with contradictory or insufficient data is a necessity. The exploration of differential equations within the context of uncertainty has emerged as an evolving area of research. Methods: the solvability conditions for the first-order linear neutrosophic differential equation are proposed in this study. This study also demonstrates both the existence and uniqueness of a solution to the neutrosophic differential equation, followed by a concise expression of the solution using generalized neutrosophic derivative. As an application of the first-order neutrosophic differential equation, we discussed an economic lot sizing model in a neutrosophic environment. Results: This study finds the conditions for the existing solution of a first-order neutrosophic differential equation. Through the numerical simulation, this study also finds that the neutrosophic differential equation approach is much better for handling uncertainty involved in inventory control problems. Conclusions: This article serves as an introductory exploration of differential equation principles and their application within a neutrosophic environment. This approach can be used in any operation research or decision-making scenarios to remove uncertainty and attain better outcomes.

Background: What are the cumulative influences of pricing, promotions of commodities, order size-based discount opportunities, and alternative warehousing scenarios on effective decision-making concerning inventory management? It is observed that the prices and promotion of products influence the demand rate. The shortage can be partially backlogged, and the backlogging rate depends on the waiting time. Also, discount and trade credit facilities may be available when purchasing items. This paper describes a novel inventory control model regarding optimal warehousing decision-making scenarios. Methods: This paper includes the facts in its hypothesis and examines the overall impact of the mentioned issues on profitability. The inventory carrying scheme associated with the proposed model consists of both rented and owned warehouse facilities in which the cost increases linearly with time. The numerical and visual simulation succeeds the mathematical approach to analyze the proposed inventory model in Mathematica software. Results: The results show that a price hike enhances profit despite the negative impact on demand creation. Also, promotion frequency favors profitability, suppressing the corresponding costs. Another managerial intuition is revealed through the numerical result that the stock should be held in a rented warehouse when deterioration in the owned warehouse increases, despite the cost of a rented warehouse. Conclusions: Besides several mentioned management insights, this study includes several existing models as particular cases and tackles challenges in the analytical optimization approach. This study leads toward the consequences of future research scopes with industry-based raw data.