Matheuristic approaches to the green sequencing and routing problem

The paper addresses the green sequencing and routing problem, which consists in determining the best sequence of locations to visit within a warehouse for storing and/or retrieval operations, using a fleet composed of both electric vehicles, e.g., equipped with a lithium-ion battery, and conventional vehicles, i.e., with an internal combustion engine. We present a Mixed-Integer Linear Programming formulation to the problem and propose two matheuristics based on suitable decompositions of the mathematical formulation. The two matheuristics have been tested on a pool of small-medium size instances and their performance has been compared to the one of a third matheuristic, previously proposed for the case of conventional vehicles only and here suitable extended to deal with the green aspects of the problem. The performed analysis allowed one to identify the most promising matheuristic in terms of some standard computational indicators, i.e., computing time and percentage optimality gap, as well as in terms of some qualitative aspects of the solutions agreed with a reference company. Such a most promising algorithm has then been further tested to gather some technical insights on what makes the problem hard to solve, as well as to outline some managerial insights. Moreover, its performance has been tested on a pool of real instances comprising ordinary days (with a usual amount of operations to perform) and extremely busy days, showing its efficacy and efficiency also in the considered real application context.