The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

Abstract

For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.

Novel Solution Method for Inventory Models with Stochastic Demand and Defective Units

“…ere are thirty-five papers that had cited Wu and Ouyang [21] in their references. We list them in the following: Mostard et al [22], Wu et al [5], Ho [23], Annadurai and Uthayakumar [24], Tung et al [25], Çapar et al [26], Drezner et al [27], Lin et al [28], Wang [29], Zheng and Liu [30], Gholami-Qadikolaei et al [31], Ma and Qiu [32], Ouyang et al [33], Lin [34][35][36][37], Parvathi et al [37], Lin [38], Jindal and Solanki [39], Lin [40], Lin et al [41], Vishkaei et al [42], Wang et al [43], Madhusoodhanan et al [44,45], Chang et al [46], Jindal and Solanki [47], Madhusoodhanan et al [48], Chang et al [49], Sarkar and Mahapatra [50], Chuang et al [51], Hu et al [52], Maleki Vishkaei et al [53], Noh et al [54], and Singha et al [55]. Most of them only mentioned Wu and Ouyang [21] in their introduction but did not offer further study for Wu and Ouyang [21].…”