This study develops and estimates a mathematical model of the procurement function in selected Nigerian pharmaceutical companies over the period 2015–2025. Procurement performance is operationalised through optimal order quantity (EOQ), while the explanatory variables comprise raw material price volatility, exchange-rate fluctuations, supplier integration, and information technology (IT) adoption. Data were obtained from the audited annual reports of Fidson Healthcare Plc, May & Baker Nigeria Plc, and Neimeth International Pharmaceuticals Plc, supplemented by macroeconomic information from the Central Bank of Nigeria statistical publications and relevant industry sources. The study adopts an ex-post facto research design and employs panel-data techniques. Panel unit-root testing was conducted to examine the stationarity properties of the variables, while the Hausman specification test was used to guide the choice between fixed-effects and random-effects estimation. The reported results indicate that raw material price volatility and exchange-rate movements have positive and statistically significant relationships with optimal order quantity, whereas supplier integration and IT adoption have positive but statistically insignificant relationships. The paper also derives the derivative properties of the EOQ model and of the specified linear panel model. These derivations show that the reported linear coefficients are constant marginal associations rather than elasticities, and that log-linear, interaction, dynamic, panel-ARDL and structural EOQ extensions are required to examine elasticities, changing marginal effects and long-run relationships. The findings suggest that procurement decisions in the Nigerian pharmaceutical sector are strongly associated with macroeconomic volatility, particularly exchange-rate movements and changes in raw material prices. The study recommends integrated mathematical procurement models, improved forecasting, strategic supplier integration, procurement digitalisation, exchange-rate risk management, and diversification of raw-material sourcing. The additional mathematical material is a theoretical clarification and extension; it does not constitute new empirical evidence.