5.3. Solution accuracy and efficiency
The optimal decision model presented in this paper does not take the rejection cost into account. To illustrate this simplification is appropriate, the paper assesses the resulted cost deviations at four levels of rejection cost (in dollars per lot): 10, 50, 100, and 500. The setting of this comparative study is the same as that in Section 5.1. Results are summarized in Table 4. For example, if the rejection cost is 10 dollars per lot and it is not modeled by the sample size decision, this simplification reduces the expected NC cost by 0.006 percent, increases the expected rejection cost by 0.726 percent, and increases the total cost by 0.004 percent. When the rejection cost is increased by 10 times, to 100 dollars per lot, the expected total cost is increased by only 0.296 percent. However, the impact becomes less trivial when the reject cost is increased to 500 dollars per lot. At this level of rejection cost, excluding the consideration of it increases the expected total cost by 2.769 percent. This comparison confirms the fact that the rejection cost is less sensitive to sample size decisions than other cost components for incoming inspections, particularly, when the reject cost is low.
To demonstrate that selecting the starting point and narrowing the boundary for the BNB procedure help reduce the solution time, the paper examines the reduction in solution time for ten cases. These ten cases have different levels of inspection resource, ranging from 320 to 3200 minutes and with an increment of 320 minutes per case. The amount of inspection resource has a direct impact on both the sparsity of the optimal solution to the problem (P) and the sample sizes, thus impacting the solution time. The average solution time for each case is based on five replications. Fig. 5 shows the average solution time and its 95 percent confidence interval for each case, both before and after applying the technique for reducing solution time. The proposed approach works consistently for the ten cases examined, and the average reductions range from 48.3 to 90.2 percent.