Tien-Yu Lin
2009 Journal of the Operations Research Society of Japan  
Recently, one of the most interesting topics in supply chain management (SCM) is the integrated vendor-buyer production-inventory problem, in which the critical issue is to determine economic lot size per shipment and deliveries. Most researches on this issue assume that products are screened and the process is perfect; however, screening errors (including type-I and type-II) may occur with imperfect quality in practice. In this paper we consider a simple single-vendor single-buyer supply chain
more » ... -buyer supply chain system in which products are received with defective quality, and 100% screening process is performed with possible inspection errors. The objective of this paper is to determine the optimal number of shipments as well as the size of each shipment in order to minimize the joint annual cost incurred by both vendor and buyer. We develop a cost model for the supply chain system and propose a solution procedure to find the optimal solution. A numerical example is given to illustrate the application of the model. Besides, based on the numerical example, a sensitivity analysis is also made to investigate the effects of five important parameters (the inspection rate, the annual demand, the defective rate, Type I error, and Type II error) on the optimal solution. and batches. In the same time, Ertogral et al. [8] analyzed the lot-sizing problem under equal-sized shipment policy, in which they incorporated transportation cost explicitly into the model. Based on the model of equal-size sub-batches shipments to buyer, Goyal [11] proposed the use of unequal-sized sub-batches in which he suggested that the ith shipment size to buyer within a production batch should be adjusted accordingly. Hill [14] extended this idea and proposed general shipment sizes that were increased by a general fixed factor, ranging from 1 to the ratio between the production rate and demand rate. Viswanathan [27] showed that neither the policy with equal-sized sub-batches nor the policy with unequal-sized subbatches dominated each other. Bogaschewsky et al. [2] presented a model for a multi stage production/inventory system in which a uniform lot size is produce through all stages and partial lot size may be transported to the next stages upon completion. Recently, Hoque and Goyal [17] developed an alternative generalized model in which equal and unequal batch shipments of a lot from the vendor to the buyer is considered. However, many researchers pointed out that the issue of defective items or imperfect quality was of practical importance. Porteus [23] incorporated the effect of imperfect items into the basic EOQ model, in which he developed a simple model to illustrate the relationship between quality and lot size. Rosenblatt and Lee [24] assumed the defective items could be reworked at a cost, and they found that defective items motivated smaller lot size. Later, Schwaller [26] assumed that defective items were present in incoming lots so that inspection costs should be incurred due to such items. Cheng [6] developed an EOQ model with demand-dependent unit production cost and imperfect production processes; in his work, he formulated the inventory decision problem as a geometric programming model. Zhang and Gerchak [29] also integrated lot sizing and inspection policy in an EOQ model, in which they assumed that a random proportion of items were defective. Later Yang and Wee [28] employed an integrated approach to determine economic ordering policy of deteriorated item. Under the assumption that defective items could be sold as a single batch by the end of 100% screening process, Salameh and Jaber [25] developed an EOQbased model for items received with imperfect quality; in their work, they found that the economic lot size increased as the average percentage of defective items increased. Goyal and Cardenas-Baeeon [12] developed a simple method to determine the economic production quantity for items with imperfect quality. Recently Huang [19] incorporated the integrated method and the process unreliability into the production-inventory model. Based on the work of Huang [19] , Chung [7] developed a necessary and sufficient condition for the existence of the optimal solution to complete and improve the solution procedure of Huang's work. Papachristors and Konstantaras [22] further discussed the issue of non-shortages in inventory models with imperfect quality. More recently, Hsu et al. [18] developed a deteriorating inventory replenishment model and presented an algorithm to derive both vendor's managing cost and buyer's optimal replenishment cycle, shortage period, as well as order quantity; in which they demonstrated that buyer's profit was highly influenced by vendor's lead time. Chen and Kang [5] developed the integrated vendor-buyer cooperative inventory models with the permissible delay in payments to determine the optimal replenishment time interval and replenishment frequency. More recently, Maddah and Jaber [20] rectified a flaw in an economic order quantity (EOQ) model with unreliable supply, characterized by a random fraction of imperfect quality items and a screening process, developed by Salameh and Jaber [25] . In their work, several batches of imperfect quality items to be consolidated and shipped in one lot are also discussed. Although the production-inventory model has received considerable attention, most re-
doi:10.15807/jorsj.52.307 fatcat:476fii6yyzge3exkllw62stthm