Geometric Programming Approach to Cost Optimisation in Nigerian Cement Manufacturing

Cement manufacturing in Nigeria is dominated by a small number of large producers operating rotary kiln facilities in states including Cross River, Ogun, Rivers, and Sokoto, with production costs heavily influenced by energy input, raw material blending, and logistics expenditure. This study applies geometric programming to formulate and solve a cost minimisation problem for the kiln clinker production process at a cement plant in Calabar, Cross River State, South South Nigeria. The objective function minimises total production cost per tonne of cement, expressed as a posynomial function of decision variables including fuel consumption rate, limestone-to-clay ratio, kiln rotational speed, and coolant air volume. Technical constraints from process engineering specifications define the feasible region. The condensation method is applied to transform the geometric programme into a computationally tractable form, and the KKT conditions are derived and solved analytically. The optimal production parameters reduce total cost per tonne by 9.3 percent relative to the current operating point, with fuel consumption optimisation contributing 62 percent of the total saving. The study further demonstrates that geometric programming yields globally optimal solutions due to the convex structure of the problem, unlike gradient-based local search methods. Keywords: geometric programming, cost optimisation, cement manufacturing, Calabar, kiln operations.