Joint optimization of inventory replenishment and rationing policies for an omnichannel store with both in-store and online demands

Abstract

Boosted by the COVID-19 pandemic, omnichannel retail has become a popular retail model and is expected to further grow. We study inventory replenishment and rationing of a product in an omnichannel store that fulfils both in-store and online demands. Both demands follow Poisson process. As each in-store demand must be satisfied immediately whereas each online order has a delivery time window, the two demand classes have different behaviors facing stockout: offline demand is lost while online order is backlogged with backorder cost charged only if it is delivered late. The inventory replenishment and rationing between the two demand classes in this omnichannel inventory system are controlled by a continuous review (Q, r) policy and a critical level policy, respectively. The intertwined nature of inventory replenishment and rationing in this system makes its analytical cost evaluation and its joint optimization of the two policies challenging. After deriving an analytical formula for evaluating the expected cost of the system, two heuristic algorithms are proposed to jointly optimize the two policies. Numerical experiments on randomly generated instances demonstrate that the multi-start local search algorithm and the scatter search algorithm can obtain a near-optimal solution quickly with percentage cost gap no larger than 0.81% and 0.18%, respectively, and the critical level policy can yield cost savings up to 10.91% compared to the first-come, first-served policy. Finally, a sensitivity analysis is conducted to evaluate the influences of system parameters on the optimal critical level.