Case Problem At Capital State University Game Day Magazine

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Capital State University (CSU) is evaluating its process for ordering football game-day magazines to improve accuracy and reduce costs. The university has been ordering a fixed quantity of magazines prior to each football season based on past season data, but often faces excess inventory or shortages. The current process involves estimating orders based on previous season data and a general estimate of game popularity, which has led to mismatches between supply and demand. The data available includes multiple variables such as past sales, game characteristics, opponent rankings, attendance figures, and weather conditions over nine seasons. The contract terms specify costs for ordering, selling, and returning unsold magazines, creating incentives to optimize order quantities. The goal is to develop a forecasting model to accurately predict demand, create a simulation for total sales, and determine an optimal order quantity that minimizes costs related to understocking and overstocking, considering batch ordering constraints.

Paper For Above instruction

The challenge faced by Capital State University (CSU) in managing its football magazines exemplifies a common issue in supply chain and inventory management: accurately forecasting demand for seasonal and event-specific products. The core objective is to determine the optimal order quantity for season-specific generic magazines, which can later be customized with game-specific inserts, thereby minimizing costs related to excess inventory and stockouts. This analysis proceeds through several stages: evaluating relevant variables for demand forecasting, constructing a regression model for demand prediction, developing a simulation to forecast total sales, and finally employing this predictive framework to recommend optimal ordering quantities, all within the constraints imposed by the contractual and logistical environment.

Variable Selection and Data Analysis

In building a reliable forecast model, it is crucial to identify which variables contain predictive information about magazine sales. The dataset includes numerous variables such as game attendance, opponent ranking, weather conditions, and historical sales figures. For example, variables like past sales, game attendance, and opponent strength are likely to have high predictive power because they directly influence demand. Conversely, variables such as preseason rank or whether the game is Homecoming may have less direct influence or be redundant when combined with other variables, and thus could be considered for exclusion to simplify the model.

Furthermore, outliers or anomalous observations, such as the Week 1 game of Year 8 characterized by special uniforms and unusually high attendance, should be scrutinized. Such outliers may distort the model if included indiscriminately. Therefore, it would be prudent to perform residual diagnostics, identify influential points via Cook’s distance or leverage measures, and consider excluding extreme outliers to improve model reliability.

Regression Model Development

Using the available data, a multiple linear regression model can be constructed where the dependent variable is the average number of magazines sold per game. Independent variables should include those with potential predictive power: historical sales, total attendance, opponent strength, weather conditions, and game-specific factors such as Homecoming or conference status. Interaction terms and nonlinear transformations (e.g., quadratic terms for attendance) could enhance model accuracy.

Preliminary analysis indicates that attendance is a key driver of sales, with higher attendance correlating to increased demand. Similarly, opponent ranking and weather conditions influence demand unpredictably; for instance, adverse weather may reduce sales. The model should include residual diagnostics to assess fit, heteroscedasticity, and normality of residuals. Techniques such as cross-validation or out-of-sample testing will provide estimates of predictive accuracy.

Forecasting and Simulation

Once the regression model is validated, it can generate demand forecasts for each of the seven home games in Year 10. These predictions serve as inputs for a simulation model that accounts for variability and uncertainty inherent in demand forecasts. The simulation involves generating multiple demand scenarios for each game based on the estimated distribution of residuals from the regression model, thereby producing a distribution of possible sales outcomes.

The total forecasted sales amount is obtained by summing the predicted sales across all games and scenarios. Because the magazine orders are batch-ordered in multiples of 500, it is necessary to determine the optimal order quantity that minimizes the expected total costs. Depending on the demand distribution, the order quantity can be adjusted above or below the forecasted mean, using techniques from inventory theory such as the Newsvendor model.

Cost Analysis and Optimal Order Quantity

The contractual costs include ordering at $14 per magazine, selling at $25 each, with a $2.50 selling fee and a buy-back price of $11.50 for unsold magazines. Ordering exactly the forecasted demand minimizes expected costs in the classic Newsvendor framework. However, due to variability, Kris might consider ordering more or less, balancing expected lost sales and excess inventory costs.

If Kris orders 21,500 magazines in July, the expected costs of lost sales (unmet demand) can be estimated from the demand distribution relative to this quantity. Similarly, unsold magazines incur a cost reflected by the buy-back price minus the order cost, adjusted by the expected surplus. Using the demand forecast distribution, the order quantity that minimizes expected total costs can be identified—this is often the critical ratio point where the marginal cost of overstocking equals the marginal cost of understocking.

Given batch constraints (ordering in multiples of 500), the optimal order quantity might be a rounded value close to the optimal point, considering practical procurement limitations. Simulation can assist in estimating the expected costs at different order quantities, allowing Kris to select a batch size that minimizes the combined expected costs of lost sales and excess inventory.

Insights and Managerial Implications

The regression analysis reveals that variables such as attendance, opponent strength, and weather are significant predictors of demand. The model's residual diagnostics inform how well the model fits and whether further refinement is needed. The simulation approach demonstrates the potential variability in demand, emphasizing the advantage of flexible ordering strategies that incorporate uncertainty.

Furthermore, the analysis suggests that ordering exactly the forecasted mean demand is not always optimal; instead, adjusting order quantities based on the estimated demand distribution—especially considering batch constraints—can yield cost savings. Implementing a data-driven, probabilistic approach allows CSU to better match supply with demand, reducing waste and stockouts, ultimately leading to more efficient use of resources and improved financial outcomes.

In conclusion, applying regression modeling and simulation methodologies enables CSU to enhance its demand forecasting and ordering processes. These tools provide a framework for making informed managerial decisions, balancing costs, and increasing operational efficiency in managing game-day magazine inventories.

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