Abstract
This paper is a response to two papers. We improve the lengthy proof for the first paper by an elegant verification. For the second paper, we point out the three-sequence approach will result in different convergent rates such that when the other two sequences are converged, the ordering quantity sequence may still not converge to the optimal solution. We construct a novel iterative method to simplify the previous approach proposed by the three-sequence approach for the optimal solution. By the same numerical examples of three published papers, we demonstrate that we can control our findings to converge more accurately than previous results. Moreover, we show that there are three distinct features of our proposed approach. (i) It converges to the desired solution within the preassigned threshold value. (ii) We estimate the convergent ratio. (iii) We find the dominant factors for our proposed convergent sequence.
Highlights
For the past several decades, many important and interesting inventory models had been developed by researchers
Huang [3], Ouyang et al [4], and Wu et al [5] worked on inventory systems with the imperfect quality of goods or stochastic property of lead time
There is a trend to improve previously published papers, for example, Deng [14], Deng et al [15, 16], Lan et al [17], Chang et al [18], Jung et al [19], and Tang et al [20], that had provided useful analytical works to revise some questionable results in previous papers. We will follow this trend to examine inventory models with stochastic demand, crashable lead time, and defective items that were developed by Wu and Ouyang [21], but they did not show the uniqueness of the optimal solution for their minimum cost problem. ere are thirty-five papers that had cited Wu and Ouyang [21] in their references
Summary
For the past several decades, many important and interesting inventory models had been developed by researchers. There is a trend to improve previously published papers, for example, Deng [14], Deng et al [15, 16], Lan et al [17], Chang et al [18], Jung et al [19], and Tang et al [20], that had provided useful analytical works to revise some questionable results in previous papers We will follow this trend to examine inventory models with stochastic demand, crashable lead time, and defective items that were developed by Wu and Ouyang [21], but they did not show the uniqueness of the optimal solution for their minimum cost problem.
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