Optimizing cost policies in an industrial setting using duality theory: a case study of brewery production company

The concept of duality is applied to achieve optimal revenue generation in a production. It provides optimal cost policies for selling available raw materials when production is not feasible. In this work, the duality theorem is applied to the primal linear programming (LP) model of a brewery production company by Ekwonwune and Edebatu (2016) to achieve an optimal cost policy that satisfies the strong duality theorem. The dual LP model of the brewery production problem is formulated which is aimed at minimizing costs of raw material sales when production is not feasible. The optimal cost obtained provides maximum revenue plans for the brewery as well as minimized cost of purchase for the buyer. Data used in the illustration of the dual LP model is secondary data which includes profit of cartons of drinks, quantity of raw materials used in the production of some selected drinks in a brewery and available quantity of raw materials in the production run. From the analysis of the dual LP model formulated, the optimal amount obtained from sales of raw materials is 43,196. This optimal sales amount corresponds to the optimal profit solution of the primal model when production holds which is also 43,196. This result therefore upholds the strong duality theorem.