Optimizing omnichannel retailer inventory replenishment using vehicle capacity-sharing with demand uncertainties and service level requirements

• Study vehicle capacity-sharing in omnichannel retail inventory replenishment. • Consider demand uncertainties and service level requirements in the study. • Determine vehicle capacity-sharing rules for omnichannel inventory replenishment. • Construct a mixed-integer linear programming model based on the established rules. • Develop a three-layer solution procedure for the replenishment problem. This study explores an inventory replenishment problem for an omnichannel retailer selling a product with demand uncertainties and service level requirements in different channels through a capacity-sharing strategy. The omnichannel retailer allows customers to order products online and then pick them up in retail stores. The capacity-sharing strategy is considered to reduce travel costs when the omnichannel retailer delivers products in different channels. With the capacity-sharing strategy, some products can be transferred from the online delivery vehicle to the retail store delivery vehicle. The expectation and the bounds on the online route travel cost of the capacity-sharing strategy are determined, based on which the capacity-sharing rules are established. Optimization models and a solution procedure are developed to solve the omnichannel retailer inventory replenishment problem. To ensure adequate performance, service level requirements are considered when making delivery decisions. Numerical experiments using randomly generated and artificial instances are performed to verify the effectiveness and practicality of the proposed optimization models and the solution procedure. The results show that the proposed models and solution procedure can effectively reduce travel costs, and can provide effective schedule and delivery quantity decision support for omnichannel retailers.