Optimum profit model under the single variable sampling plan with consumer’s quality protection

Abstract

A variables sampling plan is an acceptance sampling technique, where the process/ quality characteristics are measured in a continuous scale, and usually requires a smaller sample size than an attributes sampling plan. In the rectifying sampling plan, 100% inspection is performed to find the defectives in the rejected lot and then to replace those non-conforming items by conforming ones, which is able to provide the assurance of product quality level. In the present study, a newsvendor problem (pure procurement system) with application of a rectifying sampling plan under the constraint of the specified consumer’s risk is formulated to maximize the expected total profit, including both the producer and the retailer. The retailer’s order quantity and producer’s process mean, and the parameters of sampling plan are decision variables in our model and are jointly determined by maximizing the expected total profit. The solution procedure of this model is proposed and a numerical example is given. Based on the sensitivity analysis, it is obvious that producer’s processing cost and retailer’s selling price significantly affect the expected profit. Particularly, a lower processing cost always leads to a larger sample size, a larger order quantity and a higher expected profit. In addition, a lower retailer’s selling price generally results in a lower expected profit.