<p>This study formulates a multi-item inventory model for perishable products with a fixed-life time characterized by diverse price-dependent demand structures, in which the selling price influences consumer demand through heterogeneous functional relationships. In parallel, a novel promotional profit component is introduced as an independent revenue-enhancing component, derived from brand collaborations that reward inventory visibility and shelf presence. Given the perishable nature of the products, their maximum shelf life is a critical determinant in inventory planning, as once this threshold is reached, the items become unfit for consumption or reuse. Hence, expiration constraints are explicitly incorporated into the model alongside shortage considerations, where shortages are partially backlogged, while deteriorated items retain a salvage value, enhancing cost efficiency. The model integrates four replenishment policies: individual, joint, a paired policy, and a hybrid coordination approach to assess cost-minimizing strategies. A comparative analysis underscores the dominance of ordering costs in total inventory expenditures. The optimal replenishment policy and order quantity are derived to minimize the total cost per unit of time under partial backlogging conditions. The proposed framework has extensive applicability in industries dealing with perishable goods, such as dairy products, packaged vegetables, and processed meats. Numerical methods are employed to analyze the convexity of the cost function, thereby validating the optimization approach.</p>