Arc routing based compact formulations for picker routing in single and two block parallel aisle warehouses

Order picking is the most expensive and labor-intensive warehouse activity. The objective of the order picking problem (OPP) is to collect the items on the pick list in a sequence that minimizes the total travel time. While the literature has generally modeled the OPP as a special case of the traveling salesman problem, this paper presents arc routing-based binary integer programming formulations for the OPP in single- and two-block parallel-aisle warehouses, by taking into account the special properties of the graph corresponding to both warehouse layouts. These formulations depend on replacing the subtour elimination constraints with a much smaller number of disconnectivity elimination constraints, which significantly reduces the integrality gap. Our computational experiments show that the proposed formulation solves large instances within significantly short computing times when compared with its counterparts in the literature for single- and two-block parallel-aisle warehouses. The efficiency of these formulations implies that not only can they be used to solve the OPP in a timely manner, but they can also be incorporated into integrated models that consider multiple warehouse decision problems at the operational level. More importantly, when compared to other state-of-the-art formulations, the extensibility of our proposed model makes it an ideal candidate for further research in this field.