Simulation analysis of initial inventory in BSSs
Authors: Ramirez-Nafarrate Adrian , Moncayo-Martinez Luis Antonio , Munguía-Williams Gerardo Steve 
Published: March 2021

Purpose
This paper aims to propose an alternate, efficient and scalable modeling framework to simulate large-scale bike-sharing systems using discrete-event simulation. This study uses this model to evaluate several initial bike inventory policies inspired by the operation of the bike-sharing system in Mexico City, which is one of the largest around the world. The model captures the heterogeneous demand (in time and space) and this paper analyzes the trade-offs between the performance to take and return bikes. This study also includes a simulation-optimization algorithm to determine the initial inventory and present a method to deal with the bias caused by dynamic rebalancing on observed demand.

Design/methodology/approach
This paper is based on the analysis of an alternate and efficient discrete-event simulation modeling framework. This framework captures the heterogeneity of demand and allows one to experiment with large-scale models. This study uses this model to test several initial bike inventory policies and also combined them with an optimization engine. The results, provide valuable insights not only for the particular system that motivated the study but also for the administrators of any bike-sharing system.

Findings
The findings of this paper include: most of the best policies use a ratio of bikes: docks near to 1:2; however, it is important the way they are initially allocated; a policy that contradicts the demand profile of the stations can lead to poor performance, regardless the quick and dynamic changes of bike locations during the morning period; the proposed simulation-optimization algorithm achieves the best results.

Research limitations/implications
The findings are limited to the initial inventory of the system under study. The model assumes a homogeneous probability distribution function for the travel time. This assumption seems reasonable for the system under study. This paper limits the tested inventory policies to simple practical rules. There might be other sophisticated methods to obtain better solutions, but they might be system-specific.

Practical implications
The insights of this paper are valuable for operators of bike-sharing systems because this study focuses on the analysis of the impact of the initial inventory assuming that dynamic rebalancing may not be existing during the morning peak-time. This paper finds that initial inventory has a great impact on the performance, regardless of how quickly the bikes are dispersed across the system. This study also provides insights into the effect of dynamic rebalancing on observed demand.

Social implications
Increasing knowledge about the operation of the bike-sharing system has a positive effect on society because more cities around the world could consider implementing these systems as a public transportation mode. Furthermore, delivering suggestions on how to increase the user service level could incentivize people to adopt bikes as a mobility option, which would contribute to improve their health and also reduce air pollution caused by motorized vehicles.

Originality/value
This paper considers that the contributions of this work to existing literature are the following: this study proposes a novel efficient and scalable simulation framework to evaluate initial bike inventory policies; the analysis presented in the paper includes an approach to deal with the bias in the observed demand caused by dynamic rebalancing and the analysis includes the value of demand information to determine an effective initial bike inventory policy.