###### Abstract  
The introduction of automated parcel locker (APL) systems is one possible approach to improve urban logistics (UL) activities. Based on the city of Dortmund as case study, we propose a simulation-optimization approach integrating a system dynamics simulation model (SDSM) with a multi-period capacitated facility location problem (CFLP). We propose this integrated model as a decision support tool for future APL implementations as a last-mile distribution scheme. First, we built a causal-loop and stock-flow diagram to show main components and interdependencies of the APL systems. Then, we formulated a multi-period CFLP model to determine the optimal number of APLs for each period. Finally, we used a Monte Carlo simulation to estimate the costs and reliability level with random demands. We evaluate three e-shopper rate scenarios with the SDSM, and then analyze ten detailed demand configurations based on the results for the middle-size scenario with our CFLP model. After 36 months, the number of APLs increases from 99 to 165 with the growing demand, and stabilizes in all configurations from month 24. A middle-demand configuration, which has total costs of about \(750,000\)e, already locates a suitable number of APLs. If the budget is lower, our approach offers alternatives for decision-makers. hybrid modeling; system dynamics; facility location problems; Monte Carlo simulation; automated parcel lockers; last-mile delivery +
Footnote †: journal: 28 January 2021  
The general overview of experiences with APLs is presented in [1; 4]. APLs have several advantages, such as less traffic in city centers, out-of-hours deliveries, fewer kilometers and stops, and cost reductions for e-retailers and delivery companies [5]. Unattended delivery could reduce the number of failed deliveries [4; 6; 7]. In addition, the use of APLs also offers environmental benefits, such less pollutant emissions [8]. Furthermore, online shoppers are free to choose any pickup time for their parcels, and they can use it as both a delivery and a collection point to return unsatisfactory items. However, APLs have some disadvantages, such as limited payment flexibility in situ, limited storage space, and susceptibility to crime or vandalism [6]. Despite the advantages of the APL concept, from a scientific point of view this strategy has not been discussed sufficiently in the field of LML [9]. Urban parcel deliveries need to be studied in more detail. Most current research shows that the simulation of system dynamics (SD) applied in the LML field [10] is almost completely missing. In the available publications, local visions are adopted without a systemic or holistic perspective. Most of these did not take into account the different viewpoints of stakeholders, processes, interactions, and others [7; 11]. Furthermore, for online buyers, the location of APLs is important to decide on their use [6; 7]. Many studies have focused on analyzing the savings potential of using APLs, but have not addressed network design issues such as their number and review the associated installation costs. In this paper, we focus on a challenging and appropriate approach to analyze a number of APL configurations in an uncertain demand environment. Different methods can be used for decision support in UL [1; 12], such as empirical approaches, statistical analyses, or integrated computer science models and algorithms, to name a few. As for the last category of methods, researchers use simulation and optimization (SO) techniques as separate approaches in the field of operational research to solve complex problems [13]. On the one hand, exploring the behavior of systems and estimating their response to various environmental changes is a main purpose of using simulation [14]. On the other hand, optimization seeks to solve logistic problems, minimize total costs of ownership, or maximize profit. However, in real complex systems there are very specific properties that make it almost impossible to address the complexity of the problem with only one specific approach.