In today's fiercely competitive retail landscape, implementing effective pricing strategies is critical not only for boosting sales but also for securing a larger market share and ensuring long-term business sustainability. The ability to capture a greater share of the market directly influences a retailer's positioning and competitive edge, making pricing decisions pivotal. This paper introduces a hybrid optimization model that strategically combines Everyday Low Pricing (EDLP) and High-Low Pricing (HL) strategies, designed to address the intricacies of dynamic retail markets. The model is initially formulated as a nonlinear optimization problem aimed at maximizing sales to increase market share, all while maintaining profitability within a predefined threshold to ensure the retailer does not incur losses. To enhance the model's practical applicability, particularly in small-scale scenarios, the nonlinear problem is transformed into a Mixed-Integer Programming (MIP) model, facilitating its solvability. However, as retail applications scale up, the computational complexity becomes more challenging, necessitating the use of the Grey Wolf Optimization (GWO) algorithm. The GWO algorithm effectively balances computational efficiency with solution quality, making it a robust approach for large-scale problems. A significant contribution of this research is the linearization of the model under conditions where the products designated for High-Low pricing (referred to as 'Golden' products) are predetermined by the retailer. This linearization simplifies the computational process, enabling the model to scale and be applied in large retail settings. Developed in collaboration with a major Iranian supermarket chain, the model leverages real-world data to optimize discount levels and timing across various product categories. Extensive numerical experiments demonstrate the model's effectiveness in increasing sales, thereby contributing to a larger market share while ensuring that profitability remains within acceptable bounds. By providing actionable insights and strategic recommendations, this research offers a practical, scalable solution for optimizing retail pricing strategies in a data-driven and competitive environment, ultimately supporting retailers in their quest to dominate the market.

An examination of two areas of promotion and assortment planning in an environment is attempted in this paper. Sales promotion is a marketing strategy used by retailers to increase sales and profits by retaining customers and preventing them from switching to their competitors. Various products are available on the market that can substitute each other, so the best product assortment must be determined as well. In order to model the above subject, a nonlinear integer programming problem is proposed. Model solution involves rephrasing the problem as mixed integer linear programming. Small- and medium-sized problems can therefore be solved using MIP solver software. Firefly algorithms are designed to solve large-scale problems. According to the numerical results, determining the best product assortment for stores must also be done simultaneously with finding the optimal promotion. As a matter of fact, the promotion of the products significantly affects the assortment scenarios for the stores. Consequently, the selection of the promotional discount may result in large profit losses if the assortment planning is not taken into consideration. In order to assess the importance and sensitivity of the model parameters, a sensitivity analysis is conducted. The sensitivity analysis demonstrates that the model is able to respond to changes in market demand and competition, and provides an effective tool for chain stores to optimize their promotion and assortment strategies. To further validate the effectiveness of the model, a case study is conducted in Tehran, Iran. The results of the case study demonstrate the ability of the model to effectively optimize promotion and assortment strategies in real-world settings. Overall, the proposed model provides a valuable tool for chain stores to optimize their promotion and assortment strategies, and improve their market competitiveness.