Optimal Lot Sizing, Pricing and Process Reliability Investment Model for an Imperfect Production System with Customer Return

This study aims at examining both internal and external effects of an imperfect-quality production system along with a pricing decision in practice. The problem investigated involves a production system that follows a non-deteriorating stable process, generating binomial yields, thereby passing defective items to customers and negatively affecting demand along with a firm’s pricing decision. Then customers return those defectives for exchange or refund, and the firm disposes them through rework, salvage, or scrap. For this previously unexplored problem of practical significance, we develop a nonlinear profit-maximization model of jointly determining production lot size, rework frequency, defective proportion and selling price. In solution, due to the mathematical complexity of the model in finding optimal closed-form solutions, we first reduce the objective function using differential calculus and then develop a nonlinear programming model to obtain global optimal solutions. We present a numerical example and conduct extensive sensitivity analyses to illustrate critical behaviors of model variables, in order to provide important managerial insights into practice in making comprehensive marketing and production decisions.