Proceedings of the 5 th NA International Conference on Industrial Engineering and Operations Management Detroit, Michigan, USA, August 10 - 14, 2020 © IEOM Society International Multilevel Reorder Strategy-based Supply Chain Model Hesamoddin Tahami, Hengameh Fakhravar Engineering Management & Systems Engineering Department Old Dominion University Norfolk, VA 23529, USA htahami@odu.edu, hfakhrav@odu.edu Abstract We investigate the stochastic integrated inventory model wherein the buyer’s lead time demand follows the mixture of normal distributions. Due to the high acquisition cost of land, we assume that buyer’s maximum permissible storage space is limited and therefore adds a space constraint to the respective inventory system. Besides, it is assumed that the manufacturing process is imperfect and produces defective units, and hence each lot received by the buyer contains percentage defectives. The paper also considers controllable lead time components and ordering cost for the system. Based on lead-time components, a multilevel reorder strategy-based supply chain model is developed for the proposed system, and a Lagrange multiplier method is applied to solve the problem to reduce the expected inventory cost of both buyer and vendor. We develop a solution procedure to find the optimal values and show the applicability of the model and solution procedure in numerical examples. Keywords Integrated vendor-buyer model, Imperfect production, Stochastic lead time, Nonlinear constrained optimization, Mixture of normal distributions 1. Introduction The integrated inventory model of both buyer and vendor has been received a lot of attention in the past decade. Researchers have proposed that having better coordination of all parties involved in a supply chain will lead to benefit the entire supply network rather than a single company. (Goyal, 1977) and (Banerjee, 1986) were the first researchers that aim to obtain coordinated inventory replenishment decisions. In the mentioned studies, demand and lead time were assumed to be deterministic. However, demand or lead time across different industries is distributed stochastically, so it is relevant and meaningful to consider uncertainty in integrated inventory models. Also, with the successful Japanese experience of using Just-In-Time (JIT) production, the benefits associated with controlling the lead time can be perceived. These benefits include lower safety stock, improve customer service level, and, thus, increase the competitiveness in the industry. To address this issue, researchers started to extend the previously established models by developing lead time reduction inventory models under various crashing cost functions. (Liao & Shyu, 1991) were the first researchers to introduce variable lead times in the inventory model. In their model, they assumed that to reduce the lead time to a specified minimum duration, lead time could be decomposed into several components with different crashing costs. Since then, many researchers have made significant contributions to controllable lead-time literature. ((Ouyang et al., 2004), (Tahami et al., 2019)). Ordering cost reduction has become an essential aspect of business success and has recently attracted considerable research attention. It can be shown that ordering cost control can affect directly or indirectly the ordering size, service level, and business competitiveness. Integrated vendor-buyer inventory models were typically developed to consider fixed ordering costs. However, in some practical situations, the cost of ordering can be controlled and reduced in various ways. It can be achieved through workforce training, process changes, and special equipment acquisition. (Porteus, 1985) was the first researcher proposed an inventory model considering an investment in reducing set up cost. (Chang et al., 2006) suggested that in addition to controllable lead time, ordering cost could also be considered as a controllable variable. They proposed that the buyer ordering cost could be reduced by the additional crashing cost, which could be defined as a function of lead time length and ordering lot size. Later, other researchers developed setup/order cost reduction inventory models under various assumptions. ((Lou & Wang, 2013), (Tahami et al., 2016)) Assuming that buyer possesses infinite storage capacity is not realistic. In contrast, most probably, the buyer storage capacity is limited. Most previous research on space-constrained inventory problems focused on deterministic demand 1319