Coordinated procurement/inspection and production model under inspection errors

In this study, we investigate integrating the acquisition of input materials, material inspection and production planning, where type I and type II inspection errors are allowed, and the unit acquisition cost is dependent on the average quality level. This study aims to find an optimal purchase lot size (or here, equivalently, the fixed production rate multiplied by the production run time), input quality level and the associated inspection policy that minimize the total cost per item including the order cost, materials purchase cost, setup cost, inventory holding cost, and the quality-related cost. Furthermore, the boundaries, conditions and properties for the optimal production run time are obtained under an optimal inspection policy when the input material quality level is fixed. These findings will facilitate the establishing of an efficient algorithm for an optimal solution. The study demonstrates that a partial inspection approach could dominate over both the commonly used policies of full or no inspection, which is different from a previous report where the optimal inspection policy is either full or no inspection. A numerical example is performed to evaluate the impact of the two types of inspection errors and the process deterioration because of a nonconforming process input on the optimal solution, where a Weibull shift distribution is used to simulate the process failure time. Finally, conclusions are addressed.