Joint determination of process mean, price differentiation, and production decisions with demand leakage: A multi-objective approach

The selection of an optimal process mean is an important problem in production planning and quality control research. Most of the literature in this area has focused on the single objective problem of maximizing the profit for a fixed exogenous price. However, it is known that considering multiple objectives (such as gross income from sales, profit, and expected product uniformity) while allowing process mean, production and pricing to vary can significantly improve the profitability and performance of a firm. This article addresses this multi-objective problem while allowing the firm to sell two classes of products at differentiated prices based on their quality characteristics. These products are sold at differentiated prices depending upon their quality characteristics into primary and secondary markets at full and discounted prices respectively. Any nonconforming items are reworked at an additional cost. Due to customers heterogeneity, the firm experiences demand leakage between the two market segments. The proposed joint decision control for the firm includes the joint determination of full and discounted prices, the process mean selection, and the production quantities for each of the two product classes along with expected reworked items. A mathematical formulation of the objectives is first provided and then the multi-objective problem is transformed into a goal-programming problem. A solution procedure is developed using simulation-based optimization to identify Pareto-optimal solutions. Some important characteristics of the solution procedure are discussed and the performance of the approach is corroborated through detailed numerical experiments.