Economic production lot sizing under imperfect quality, on-line inspection, and inspection errors: Full vs. sampling inspection

Abstract

A manufacturer’s choice between full inspection and sampling inspection can significantly impact economic production lot sizing decision for items with imperfect quality and inspection errors. This can further change depending on whether the manufacturer opts for on-line or off-line inspection. The present literature does not consider on-line inspection in the context of acceptance sampling for economic production lot sizing decision problem. In this paper, we develop an on-line sampling inspection model and argue that the choice between full inspection and sampling inspection usually depends on the threshold level of unit inspection cost. Our paper leads to several significant findings. Firstly, we establish that such an on-line sampling inspection scheme can lead to significant savings in inventory holding costs and lead to higher optimal expected profit. Secondly, we establish the intuitively anticipated result that for high unit inspection costs, on-line sampling leads to a higher optimal expected profit than a full inspection. Contrary to the common intuition, we also show that, even when inspection costs are low, sampling inspection could still be more profitable than full inspection in many situations. Finally, we establish that on-line sampling inspection provides a higher optimal expected profit than the usually preferred off-line sampling inspection. We also discuss the impact of relaxing some of the standard assumptions. In addition to our theoretical findings, through a detailed numerical analysis, we present the impact of changes in various parameters, particularly true defective fraction, proportion of inspection errors, sample size, rework effectiveness, and unit inspection cost on the choices between full versus sampling inspection.