Retailing has changed dramatically from single-channel brick-and-mortar stores to multi-channel and omnichannel retailers over the last few decades. Omnichannel retailers employ different strategies to integrate online and offline sales channels as well as order fulfillment processes. Among these strategies, the ship-from-store is the most popular and widely accepted among retailers. It enables retailers to use inventory from store locations to fulfill online demand. An omnichannel retailer with a distribution center and a retail store has to make important, interlinked decisions — (1) how much inventory to keep at the retail store, and (2) where to fulfill the online demand from and how much. In this work, we model the integrated inventory replenishment and online demand allocation decisions for an omnichannel retailer employing the ship-from-store strategy. We analyze this problem for both single-period and multi-period settings. We extend the analytical framework of the single-period problem by providing a finite-horizon Markov decision process (MDP) formulation for the multi-period problem. Our findings suggest that for a single-period setting, decentralized inventory replenishment and demand allocation system maximizes the profit of the omnichannel retailer for low values of the incentive for fulfilling the online demand through store inventory, while for sufficiently high values of the incentive, a pooled system provides the optimal profit. An increment in the discount factor has the same effect on the optimal decisions in a multi-period setting as that of salvage value in a single-period setting for a given value of the incentive for the ship-from-store strategy. We also provide several extensions (such as cross selling, endogenous and correlated demand streams) of our analytical framework for the multi-period problem.