Robust omnichannel retail operations with the implementation ofship-from-store

In this paper, we consider an omnichannel retailer (o-tailer) selling multiple products througha capacitated retail network over a multi-period horizon, where each inventory facility isequipped with a certain ability to fulfill the orders regardless of the channel. We studyomnichannel retail operations with the implementation of ship-from-store to minimize the o-tailer's expected total cost. At the start of each period, the o-tailer determines how much toreplenish each product for each distribution center (DC), and how to allocate its inventoryfrom DCs to different stores. At the end of each period, the o-tailer decides from whichDCs and/or stores to fulfill the realized online demands. We formulate the problem as amulti-period stochastic optimization model and adopt a robust two-phase approach (RTA) tosolve it. Phase 1 determines the binary replenishment decisions using a target-oriented robustoptimization approach, whereas Phase 2 uses a linear decision rule to adaptively determinethe replenishment, allocation, and fulfillment quantities. Numerical experiments suggest thatthe RTA outperforms existing approaches and can efficiently produce good-quality and robustsolutions for realistic problem instances. A further sensitivity analysis explores the impactsof various system parameters on the RTA's performance and the benefits of omnichannel fulfilment.