This paper considers the integrated Order picking (joint Order batching and picker routing) and delivery problem in a manual picker-to-parts and multi-block 3D warehouse with considering overbooking and delivery-delay allowed strategies. Received Orders by the customers are grouped into the batches, assigned to the pickers with horizontal and vertical velocities to compute the travel time, picked up from the shelves of the warehouse, and delivered to customers’ community. The warehouse’s policy is to accept Orders for a certain number of unavailable products in addition to the available products. Thus, the concept of the overbooking strategy for supplying unavailable products and the delivery postponed strategy for delayed delivery is applied. Hence, this study introduces a novel mathematical model to deal with such a system, where the objective aims to minimize the cost of the completion time of all batches, the purchasing of the unavailable products and the return time of all vehicles to the depot. To solve this model, four new heuristic algorithms are devised, a broad range of numerical experiments is investigated to illustrate the validity and applicability of the proposed model and solution approaches.