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In this research , we consider a two-echelon system including one supplier , one vendor and some buyers. Every buyer has a distinct and uniform demand . The policy for ordering is (r,q) and shortage is not permitted. Buyers have no dependence on each other and every buyer orders it's demand from the vendor by itself . Hence, the vendor will be faced with discrete and different demands. Considering these assumptions, we use vendor management inventory and determine the order quantities for buyers and vendor in order to minimize the total cost of system  

In this study vendor-managed inventory policy in supply chains is investigated and a formulation is developed to optimize replenishments from vendor to retailer and also price for negotiator customers. As a result, we consider a two echelon supply chain containing a vendor and a retailer managed according to VMI policy. The goal is to find the optimal replenishment from vendor to retailer at the beginning of the month and by using dynamic programming approach to maximize the supply chain profit. Demand is nondeterministic and it is supposed Poisson distribution with unknown parameter. We will consider Gamma distribution for this parameter which its parameters are learning in dynamic... 

Inventory problems are studied for a long time and many authors have investigated models with shortage phenomenon. To reduce inventory holding cost or decaying items we can have a shortage period in witch a part of demand is backordered; Although we pay fines to pending costumers, as shortage period is extended a larger portion of them will refuse to wait until replenishment. So, calculating an optimal duration for on hand inventory and shortage period with respect to inventory costs has became an interesting research field. However, related studies are rarely appeared in supply chain researches, where an integrated inventory model for a supplier and a retailer is proposed; especially when a... 

This research deals with a supply chain consisting of one vendor and several retailers. Every retailer orders a fixed discrete quantity in fixed discrete time intervals. Order quantity and order cycle of each retailer could be different from the others. The vendor orders the required quantity to a supplier to fulfill the received demands. Also the vendor orders a discrete quantity, which will be immediately received at the vendor’s warehouse. In this supply chain system, the lead-time is assumed to be zero and shortage is allowed for vendor. The aim is to find minimum vendor’s inventory cost. We proposed a backward Dynamic Programming algorithm for the model. The algorithm creates vendor’s... 

Although inventory control under discrete demand in dynamic quantities and time intervals are very common in reality, existing literature has largely ignored them. In this thesis, we investigate the inventory control decisions in a two echelon supply chain. The vendor supplies a product to several retailers, buying discrete quantities in pre-determined time intervals. The order quantity and order cycles for each retailer can be different from others. We have developed a new efficient algorithm to find the optimal ordering policy involves the scheduling and the order quantity of vendor to his supplier to minimize his cost function in infinite time horizon. Moreover, we have designed a revenue... 

The endeavors towards achieving a sustainable management of supply chains have brought about new cardinal logistic aims in addition to the common cost minimization objective. Traditional and sometimes disoriented constraints and assumptions such as demand certainty, infinite shelf life of products and so forth have resulted in a noticeable number of improper decisions made by supply chains’ members. Furthermore, intensified environmental concerns, consumers’ awareness of health problems, growth of demand for high quality products, scarcity of natural resources, etc. have brought many challenges and complexities to inventory management and routing problems. Due to supply chain managers’ and... 

This thesis introduces a inventory-routing problem under a vendor managed inventory strategy in a two-echelon supply chain. The VMI Routing problem in this study consists of multiple suppliers, multiple retailers and a single item. The suppliers plan inventory replenishments for retailers based on deterministic demand over multiple planning period. Also they allow stock-outs at retailers, which are considered lostsales. Transshipments are allowed, neither between suppliers nor between customers. Retailers can be supplied just by one assigned supplier. Model also considers some constraints on time and capacity. A mixed integer programming formulation is presented to describe the model. We... 

In recent years, numerous companies in various industries apply supply-chain management to improve their market competitiveness. Advances in information technology bring new approaches for managing supply chain activities. Consequently, emphasis on supply-chain coordination has increased in recent years. Vendor managed inventory (VMI) is an important coordination initiative. In VMI, the vendor assumes responsibility for managing inventories at retailers using advanced online messaging and data-retrieval systems. In this dissertation we investigate the effect of VMI on supply chain performance under make-to-order and make-to-stock environment. By using renewal reward theorem, we derive the... 

This study proposes a deep reinforcement learning approach to solve a perishable inventory allocation problem in a two-echelon supply chain. The inventory allocation problem is studied considering the stochastic nature of demand and supply. The examined supply chain includes two retailers and one distribution center (DC) under a vendor-managed inventory (VMI) system. This research aims to minimize the wastages and shortages occurring at the retailer's sites in the examined supply chain. With regard to continuous action space in the considered inventory allocation problem, the Advantage Actor-Critic algorithm is implemented to solve the problem. Numerical experiments are implemented on...