a mathematical method for managing inventories in a dual channel supply chain

the advent of e-commerce has prompted many manufacturers to redesign their traditional channel structure by engaging in direct sales. in this paper, we present a dual channel inventory model based on queuing theory in a manufacturer-retailer supply chain, consisting of a traditional retail channel and a direct channel which stocks are kept in both upper and lower echelon. the system receives stochastic demand from the both channel which each channel has an independent demand arrival rate. a lost-sales model which no backorder is allowed is supposed. the replenishment lead times are assumed independent exponential random variables for both warehouse and the retail store. under the replenishment inventory policy, the inventory position is kept constant at a base-stock level. to analyze the chain performance, an objective function included holding and lost sales costs is defined. at the end, a proposed algorithm named, best neighborhood (bn) is used to find a good solution for inventory and the results are compared with simulated annealing (sa) solutions.