In the movie rental industry, inventory value depreciates at an exceptionally rapid pace, creating a unique and punishing economic environment for retailers. Unlike traditional retail sectors where products retain value over months or years, a new release DVD or digital copy loses the vast majority of its rental demand within weeks of its street date. This compressed lifecycle creates a high-stakes operational dilemma: excess stock of "yesterday's release" sitting on shelves past its prime demand window immediately triggers capital loss through writedowns and mounting carrying costs, while stockouts during the opening weekend cause permanent and unrecoverable revenue loss as customers turn to competitors or alternative entertainment options. This paper systematically analyzes how the disciplines of time-series forecasting and inventory economics intersect to solve this fundamental allocation problem, proposing a data-driven framework for navigating the narrow profitability window of new release titles. The research introduces a novel application of a mixed-effects time-series model specifically designed for the movie rental context. Unlike conventional forecasting approaches that treat all titles uniformly, our model distinguishes between the universal decay pattern common to all rentals—the fixed effect—and title-specific deviations driven by unique characteristics—the random effects. Crucially, the model incorporates a comprehensive set of external regressors to measure their quantitative effect on rental velocity throughout a title's lifecycle. These regressors include pre-release box office performance (opening weekend gross and total gross), critical reception metrics (Rotten Tomatoes Tomatometer scores and audience scores), audience engagement indicators (IMDB user ratings and social media buzz), and industry recognition events (major award season nominations such as Oscars or Golden Globes). By dynamically integrating these external signals, the model can anticipate whether a critically acclaimed independent film will demonstrate stronger long-tail demand than a big-budget blockbuster that peaks and declines rapidly. Our optimization technique employs a sophisticated cost-function approach that asymmetrically weights forecast errors based on their timing and financial impact. Rather than minimizing standard error metrics equally across all periods, the model assigns differential penalties that reflect the real-world economics of movie rental: stockouts are penalized more heavily during week one when rental velocity and customer expectations are at their peak, while overstocking is penalized more heavily during week four when inventory has substantially depreciated and carrying costs accumulate. This asymmetric weighting ensures that inventory decisions are economically rational rather than statistically convenient, aligning operational execution with profit maximization objectives. The results chart a viable path toward "precision retailing" in the entertainment software sector. By implementing our integrated forecasting and optimization framework, retailers can achieve a 12% reduction in total inventory carrying costs through more accurate alignment of supply with the rapidly decaying demand curve. Simultaneously, the model's focus on preventing early-period stockouts contributes to measurable improvements in customer retention rates, as subscribers experience consistently better availability of high-demand new releases during their critical opening windows. These findings demonstrate that the intersection of advanced time-series methods and inventory economics offers a powerful solution to the acute allocation problem inherent in short-life-cycle products, with implications extending beyond movie rental to any industry facing rapid demand decay and asymmetric error costs.
Demand Forecasting, Inventory Management, Time-Series Analysis, Movie Rental Economics, Short-Life-Cycle Products.
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