"A matheuristic for order picking problems in e-commerce warehouses"
Mustapha Haouassi, Yannick Kergosien, Jorge E. Mendoza and Louis-Martin Rousseau

Fast delivery is one of the most popular services in e-commerce retail. It consists in shipping the items ordered on-line in short times (1h, 2h, or same day). The customer orders thus come with due dates, and respecting this latter is pivotal to ensure a high service quality. We focus through this work on the order picking process. In a nutshell, order picking consists in regrouping orders into batches, assigning batches to order pickers, sequencing the batches assigned to each order picker, and designing the picking tours of each order picker to retrieve the assigned items. To deal with the time-critical orders, the e-commerce retailers often arrange their warehouses using a mixed-shelves storage policy, leading unit loads of an item to be scattered in the warehouse. We thus assume a mixed-shelves storage warehouse in our problem definition. Furthermore, we allow, unlike what is classically assumed in the picking literature, the items of a customer order to be assigned to different order pickers (splitting the customer order). Thus, the objective of the problem is to design the picking tours of order pickers to retrieve all ordered items and minimize the total tardiness of the customer orders. Therefore, we propose a 2-stages matheuristic. In the first stage, the algorithm iterates a set of predefined procedures that construct a pool of promising picking tours. After $N$ iterations, the first stage stops, and the second stage takes place. In this stage, we propose two mixed-integer programming (mip) formulations (time-based formulation and position-based formulation) to solve the set covering problem over the pool of picking tours designed in the first stage. The experiments are still in progress and will be presented in the talk.