A multi-objective optimization approach for the blending problem in the tea industry

The blending problem is one of the oldest and well-known optimization problems. It is generally formulated as a linear program and has been applied in many industries. However, the blending problem encountered in the tea industry requires a lot more than a straight forward linear programming formulation. Indeed, the classical blending model would almost always be infeasible for the blending problem in the tea industry. This is because it is often not possible to match the characteristics of the blends as desired, which prompts the decision makers to search for solutions that are the closest possible to the targeted ones. In this paper, we develop and solve a multi-objective optimization model for the tea blending problem, wherein we minimise the total cost of the raw materials to be used, as well as the violations of the desired characteristic scores of the final blends. We also present a parametric model that is used as benchmark to compare the multi-objective optimization model. Both models are able to provide the decision maker with the flexibility to express their preferences in terms of determining acceptable solutions that will allow them to maintain the high quality of their brands. We employ Monte Carlo simulation approaches to solve both models and also provide the decision maker with an extra tool to analyse the existing trade-off between the violation of the characteristic scores and the total cost of raw materials. The models and solution approach have been tested with real data from a UK-based tea company who brought the problem to us in the first place. The results show that the proposed multi-objective optimization model dominates the parametric model and can usefully serve as decision support tools to select the best solution option from a set of acceptable ones. In fact, a decision support tool based on this research has now replaced their existing decision tool and with this new tool, they are able to save tens of thousands of pounds every week as well as significantly improving the quality of their tea blend.