A linear mathematical optimization model for variable costs calculation in fertilizer production complex

A fertilizer production complex presents a highly intensive industrial process mutually interlinked with raw materials, products, co-products, and by-products. It constantly demands energy improvement and smart utilization of all utilities, especially natural gas. In order to minimize the production costs, it is developed a linear mathematical economic optimization model for maximizing total profit with variable production cost calculation for different fertilizer products. The main objective of the work is model development for precise and rapid calculation of various fertilizers products, co-products and by-products variable costs taking in account all constraints during production process. The model was solved by a set of comprehensive expressions in LINGO software. MS Access was used as a database, while MS Visio was used for the graphical presentation of interlinks between different production units. The model results are compared against real accounting data from the Petrokemija fertilizer production complex. The model shows that the objective function is the most sensitive to the natural gas price. The model is simple and flexible for daily use and presents a powerful tool for making decisions about production outages. The paper significance is attributed to proper tracking and allocation of the variable costs amongst different fertilizer products.