Online makeup stores are an emergent market phenomenon, representing an adaptation to the digital age of the traditional brick-and-mortar beauty store concept. They offer a convenient platform for consumers to purchase a wide range of makeup products from various brands and have them delivered to their doorsteps. However, their operation is significantly different from a traditional retail store, and involves a complex interplay of various business techniques and technological advancements.

In essence, an online makeup store is an e-commerce platform specialized in selling beauty products. This concept was pioneered by the likes of Sephora and Ulta Beauty in the late 1990s, as the internet began to shape consumer behavior. Since then, the industry has grown exponentially, with a plethora of both multinational corporations and local businesses vying for a share of the online market.

The operation of online makeup stores is primarily based on two functional areas: the business-to-consumer (B2C) model and the supply chain management (SCM). The former deals with the business's direct interaction with consumers and the latter manages the movement of goods from manufacturers to consumers.

The B2C model of online makeup stores is anchored on the principles of customer-centric marketing, powered by advanced data analytics. Websites and mobile applications of these stores are designed in a way that offers a personalized shopping experience to consumers. Machine learning algorithms, an application of artificial intelligence, are utilized to analyze consumer behavior and preferences. These algorithms track the browsing and purchasing habits of customers, creating a feedback loop that allows the store to recommend products that align with the customer's preferences, thereby enhancing customer engagement and boosting sales.

Supply chain management, on the other hand, is the backbone of the operational efficiency of online makeup stores. It involves the coordination of several entities, including manufacturers, wholesalers, logistics providers, and the store itself. The efficiency of the supply chain directly impacts the store's ability to maintain an inventory that meets consumer demand and deliver products promptly. Moreover, a technologically-enabled supply chain, driven by tools like Enterprise Resource Planning (ERP) and digital tracking systems, allows for real-time monitoring and optimization of operations.

However, the operations of online makeup stores are not without challenges. One of the significant challenges is the inability for customers to physically test products before purchase, leading to reliance on product reviews and ratings. Technology has been employed to combat this issue, with Augmented Reality (AR) being the most notable innovation. Brands like L'Oreal and Sephora have launched AR apps that allow customers to virtually "try on" makeup products.

Additionally, online makeup stores must navigate the complexities of international trade laws if they operate across borders. The global nature of e-commerce means these businesses may have to comply with different regulatory standards in different countries, adding another layer of complexity to operations.

Moreover, the broad nature of the online marketplace means these stores must constantly innovate to stay ahead of competitors. This includes staying at the forefront of technological advancements, providing excellent customer service, and consistently offering a wide range of high-quality products.

In conclusion, online makeup stores represent a digital evolution of the traditional beauty retail concept. They operate by combining advanced technologies with well-established business practices, offering a convenient platform for consumers to purchase makeup products. However, their operations are complex and require a constant balancing act between customer satisfaction, technological innovation, and legislative compliance. Nevertheless, as digital consumerism continues to rise, the future of online makeup stores appears promising.