A Linear-Programming–Driven Two-Level Factorial Design for Cost-Efficient Alternative Fuel Experiments in a Simulated Cement Calciner

Abstract

The cement industry is among the most energy-intensive sectors and a major contributor to global CO₂ emissions. Although increasing alternative fuel (AF) utilization in calciner operation can reduce coal consumption, laboratory-scale screening of multiple AFs is costly. This study proposes a mathematical framework that embeds a two-level full factorial design within a Linear Programming (LP) model to generate an economically optimized experimental plan under energy constraints. For a given number of AF factors 𝐾, the model (i) assigns Low–High usage levels to each AF, (ii) constructs the complete 2^𝐾 factorial design, (iii) computes the Mixed Coal (MC) required in each treatment to satisfy the target NCV_as-received, and (iv) minimizes the total cost of executing the full factorial design. The LP formulation incorporates decision variables for AF and MC quantities, subject to limits on total AF mass, minimum Low–High separation, and separate line calciner energy requirements. A five-AF case study demonstrates that the optimized 32-run design satisfies all constraints while achieving approximately 41–42% coal substitution relative to pure-coal operation at the same NCV_{as- received}. The results confirm that the proposed framework provides a general, cost-aware planning tool for factorial mixture experiments and is readily extendable to other energy and engineering systems.