اثرات تقاضای ناصاف و محدودیت حجم حمل و نقل: پاسخی به مقاله "نگاهی دوباره به یکپارچه سازی زنجیره تامین در مدیریت موجودی فروشنده "

This paper responds to a comment by Wang et al. [3] regarding the disagreement between Yao et al. [4] and van der Vlist et al. [2] on the impact of vender-managed-inventory (VMI). We explore the factors which affect the shipment size from the vendor to the buyer and identify the conditions where the shipment size will increase/decrease under VMI. A numerical example also shows when and how the inventory shifts between the supplier and the buyer.

Wang et al. [3] try to resolve a disagreement between Yao et al. [4] and van der Vlist et al. [2] regarding the impact of vendor-managed-inventory (VMI) on a supply chain. Yao et al. [4] use a two-tier EOQ model to investigate the costs and order behaviours of the supply chain members in both VMI and non-VMI scenarios. They find some interesting analytical results and identify the distribution of the VMI benefit between the supplier and the buyer. van der Vlist et al. [2] argue that Yao et al. overstate the inventory needed at the supplier, and extend Yao et al.'s model to incorporate shipping costs. The findings in Yao et al. [4] and van der Vlist et al. [2] are different in many ways. For example, Yao et al. assert that the buyer's order size shall decrease under VMI, but van der Vlist et al. have an opposite result. In their response [5], Yao et al. argue that van der Vlist et al. [2] make problematic assumptions on the shipping costs. Wang et al. [3] also support Yao et al.'s original results by studying a special case. It is interesting to note that, while the arguments of Yao et al. [5] and Wang et al. [3] focus on the validity of van der Vlist et al.'s cost assumptions, some of the results in van der Vlist et al. do not rely on these assumptions. To clarify the causes of the disagreement, we relax all the extra assumptions in van der Vlist et al. [2], let the delivery cost be zero and revisit the original paper of Yao et al. [4]. In this note we discuss two important factors on the benefit of VMI: The lumpy demand at the suppliers and the shipment size constraint. Both are neglected in all these papers. Our study clearly shows how these two factors affect the optimal order quantities, and provides intuitive insights for the implementation of VMI.

In this paper, we have shown that the original models in Yao et al. [4] are problematic in two ways: First, the supplier in their models adopts an order pattern which causes excessive inventory all the time. The amount of excessive inventory is proportional to the buyer's order size q. Second, while the lumpy demand at the supplier is modeled in the VMI case, it is overlooked in the non-VMI case. van der Vlist et al. [2] identify the first drawback, but fail to find the second one. In addition, van der Vlist et al. do not provide clear answers to the situation where the shipment size constraint Q ≥ q is concerned. While Yao et al. [5] and Wang et al. [3] focus their responses on the validity of van der Vlist et al.'s cost assumptions, we find that these assumptions are not required for a different result from Yao et al.'s [4]. We then revisit the original paper of Yao et al. [4] to identify the dynamics of the order behaviour when VMI is implemented. By showing the conditions where qVMI⁎ > qNV⁎ or qVMI⁎ ≤ qNV⁎, we resolve the disagreement between Yao et al. [4] and van der Vlist et al. [2] without extra assumptions and special cases. We also provide an intuitive view of the cost functions so that most optimal quantities can be derived from the properties of the EOQ model (e.g., convexity), without going through the first and second order conditions.