Consider a supply chain that consists of one vendor and multiple retailers. We assume that the vendor procures product from an external source and sells it with the same wholesale price to the retailers. Demands in retailers’market are decreasing function of the price and vendor makes use a vendor managed inventory strategy. In this paper we propose model of supply chain in centralized and decentralized state. Supply chain performance in centralized state can be analyzed by mathematic optimization model while for analyzing supply chain performance in decentralized state use Stackelberg game. Finally, numerical analyses about the proposed models are done and performance of supply chain in centralized and decentralized state is compared.

In recent researches, vendor managed inventory (VMI) policy is rarely considered in the case ofdeteriorating items. This study considers the supply chain partner’s collaboration via a VMI system and provides an EOQ model for a two-level supply chain (single supplier-single retailer) with stockdependent demand and constant deterioration and backlogging rates, to examine the inventory management proceedings for VMI and non-VMI supply chains. The equations are simplified using a new approach in modeling. A comparison between the costs of two mentioned cases is done. The results of analytical examination of inventory costs with and without VMI show that VMI system in our proposed model always has the ability to reduce total costs of the supply chain and is always better than the traditional one. Some numerical examples and sensitivity analysis are also given to illustrate the application of the proposed model.

vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. Previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. This paper presents a bi-objective mathematical model for single manufacture multi-retailer with multi-product in order to maximize their benefits. It is assumed that demand is a decreasing and convex function of the retail price. In this paper, common replenishment cycle is considered for the manufacturer and its retailers. Then, the proposed model converts to the single-objective optimization problem using a weighted sum method. A genetic algorithm (GA) is applied to solve it and response surface methodology is employed to tune the GA parameters. Finally, several numerical examples are investigated to demonstrate the applicability of the proposed model and solution approach.

In this research, an integrated inventory problem is formulated for a single-vendor multiple-retailer supply chain that works according to the vendor managed inventory policy. The model is derived based on the economic order quantity in which shortages with penalty costs at the retailers` level is permitted. As predicting customer demand is the most important problem in inventory systems and there are difficulties to estimate it, a probabilistic demand is considered to model the problem. In addition, all retailers are assumed to share a unique number of replenishments where their demands during lead-time follow a uniform distribution. Moreover, there is a vendor-related budget constraint dedicated to each retailer. The aim is to determine the near optimal or optimal order quantity of the retailers, the order points, and the number of replenishments so that the total inventory cost of the system is minimized. The proposed model is an integer nonlinear programming problem (NILP); hence, a meta-heuristic namely genetic algorithm (GA) is employed to solve it. As there is no benchmark available in the literature to validate the results obtained, another meta-heuristic called firefly algorithm (FA) is used for validation and verification. To achieve better solutions, the parameters of both meta-heuristics are calibrated using the Taguchi method. Several numerical examples are solved at the end to demonstrate the applicability of the proposed methodology and to compare the performance of the solution approaches.

In this study, a two-echelon single-vendor supply chain is selected to do a costbased comparison between short-term performances of a vendor managed inventory (VMI) and a Retailer managed inventory (RMI). While the inventory costs include ordering and storing expenses, the rate of consumption and the price of goods are constant, the rate of production and pace of transportation are in nite and shortage is not allowed. This paper, after a comprehensive literature review, is followed by three cases of single retailer, n-retailer and two-retailer chains. Unlike the second case, in the rst case, VMI shows an absolute superiority to RMI, and this is the reason for devising the third case in which a deeper analysis, including a typical performance assessment system for two-retailer chains is undertaken. The third case reveals that, although VMI is not always the better choice, under most conditions, it can be chosen as the better approach.