Sequencing and routing in a large warehouse with high degree of product rotation

Abstract

The paper deals with a sequencing and routing problem originated by a real-world application context. The problem consists in defining the best sequence of locations to visit within a warehouse for the storage and/or retrieval of a given set of items during a specified time horizon, where the storage/retrieval location of an item is given. Picking and put-away of items are simultaneously addressed, by also considering some specific requirements given by the layout design and operating policies which are typical in the kind of warehouses under study. Specifically, the considered sequencing policy prescribes that storage locations must be replenished or emptied one at a time by following a specified order of precedence. Moreover, two fleet of vehicles are used to perform retrieving and storing operations, whose routing is restricted to disjoint areas of the warehouse. We model the problem as a constrained multicommodity flow problem on a space-time network, and we propose two Mixed-Integer Linear Programming formulations, whose primary goal is to minimize the time traveled by the vehicles during the time horizon. Since large-size realistic instances are hardly solvable within the time limit commonly imposed in the considered application context, a matheuristic approach based on a time horizon decomposition is proposed. Finally, we provide an extensive experimental analysis aiming at identifying suitable parameter settings for the proposed approach, and testing the matheuristic on particularly hard realistic scenarios. The computational experiments show the efficacy and the efficiency of the proposed approach.

The Green Sequencing and Routing Problem

“…iii) safety requirements for workers. We refer to [6] for a more detailed and comprehensive description of the features above. Here we consider the case where a subset of the vehicles of type F2 are electric and equipped with a lithium-ion battery.…”

“…Thus, besides planning the routing of the vehicles in order to move inbound items (from the input points towards the preassigned storage locations) and outbound items (from storage locations towards the collection area), battery charging operations need to be scheduled as well. As in [6], the primary aim is to minimize the travel time of all the vehicles within the warehouse.…”

“…Several parameters are introduced to describe the features of vehicles and incoming and outgoing commodities. We refer to [6] for a complete description. We introduce here only those related to the energy consumption model for the battery.…”

“…For the sake of brevity, we do not report the above mentioned constraints, which can be found in [6]. On the other hand, we present below those constraints which regulate the energy behavior of the electric vehicles, since they are peculiar to the Green SRP.…”

“…Recently, [6] addressed a SRP related to a large production site of an Italian company. The SRP is characterized by some specific requirements, originated by the layout design of the warehouse, and also by the particular kind of products stocked, i.e., tissue products for sanitary and domestic use.…”