Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics

In this paper, we analyze the route efficiency effects that emerge from combining realistically constrained first-mile pickup and last-mile delivery operations into joint vehicle routes. Specifically, we examine (i) the individual effect of discrete, non-overlapping time window constraints; (ii) the individual effect of vehicle capacity constraints; and (iii) the joint impact of both constraint types on local route efficiency gains due to the integration of pickup and delivery operations. Extending the existent literature on continuum approximation of route distances, we propose closed-form adjustment factors which accurately capture these non-trivial route efficiency effects. To derive the adjustment factors, we conduct extensive numerical experiments and apply a novel hybrid data analysis approach which combines exploratory data analysis with symbolic regression. Our analysis suggests that these real-world constraints affect the optimal stop sequence and diminish or even eliminate the expected efficiency gains from integrating first- and last-mile operations. The proposed adjustment factors are particularly relevant for the optimal strategic design and operational planning of modern, industrial-scale distribution networks in light of growing and increasingly fragmented e-commerce volumes and a high cost pressure on the logistics industry. They help researchers and practitioners to efficiently quantify the expected benefits from integrating pickup and delivery operations, and to assess under which circumstances such an integration is (not) desirable.