The Value of Preemptive Pick-Up Services in Dynamic Vehicle Routing for Last-Mile Delivery: Space-Time Network-Based Formulation and Solution Algorithms

Table 1

Comparison of key elements in DVRPTW.

Objective	Service principles	Decision variables	Main constraints	Solution algorithm	Publication
Minimizing the long-run average cost per requested job	Non-preemptive	Time-dependent truck loading state	TW	Reoptimization policy	Yang et al. [13]
Minimizing total travel time	Non-preemptive	Vehicle route	TW; CP	Ant colony system	Montemanni et al. [12]
Minimizing the expected total travel time plus lateness	Non-preemptive	Vehicle-customer type assignment	TW	Parallel tabu search	Ichoua, et al. [15]
Minimizing total distance	Non-preemptive	Vehicle route	TW	Dynamic column generation	Chen and xu [11]
Minimizing total expected cost	Non-preemptive	Customer state	TW; CP; SD	Adaptive variable neighborhood search	Pillac et al. [16]
Maximizing total expected rewards	Preemptive (depot return for delivery requests)	Customer state	TW	Approximate dynamic programming	Ulmer et al. [17]
Maximizing the difference between service utility and operating cost	Preemptive (delivery process interruption for pick-up requests)	Space-time route (with customer return)	STW; SDC	Augmented Lagrangian relaxation method	This paper

Constraints. TW: time window constraint; CP: capacity constraint; SD: side constraint; STW: space-time window constraint; SDC: service duration constraint.