Simultaneous determination of manufacturer's process mean and production run length, and retailer's order quantity

Abstract

In Chen and Liu's optimum profit model with a traditional production system, they did not consider the effect of product quality on the customer's demand order quantity, and also ignored the used cost of customers for product. In fact, the customer's demand quantity is always seriously related to product quality. Hence, in the present paper, we modify Chen and Liu's model to address the determination of the optimal process parameters by employing the idea of quality loss and single sampling rectifying inspection plan. Assuming that the quality characteristic of the product is normally distributed, Taguchi's symmetric quadratic quality loss function is applied in evaluating the product quality. Three decision variables, i.e., the mean of the process characteristic, the production run length of the product and the retailer's order quantity, are jointly determined in our modified model to maximize the expected total profit of society, which includes both the manufacturer and the retailer. A heuristic solution procedure is developed for this optimization problem, and a numerical example is provided for illustration. From the numerical results, it can be seen that both the sale price per unit and the intercept of the mean demand of the customer are two major (or significant) parameters in the model and should be more accurately estimated in practice. Finally, the quality investment policy is provided to compare its effect on the optimum profit model with quality improvement.