Project  Introduction

The public bicycle scheme "Loris Bikes" was launched in 2010 in the City of Istanbul. There are currently 4800 bicycles available at 350 docking stations distributed across central parts of Istanbul. These bicycles are means of short-distance transport both for regular and casual users, with around 24,000 bicycle hires per day.

Bicycles are available at docking stations and also have to be returned at a docking station.  A common source of customer dissatisfaction is shortage of both available bicycles and also of available empty slots in certain areas and certain hours. For example, in the vicinity of train stations there might be insufficient number of bicycles in the morning peak hours, whereas in the evening peak hours, all docking stations might be completely full.

An alternative of constructing  new docking stations and purchasing new bicycles is to enhance the usage of current resources by transporting bicycles from crowded docking stations to other parts of the city where more bikes are demanded. These operations can be easily carried out overnight. However, it is necessary to transport bikes continuously during the day, since in certain zones, the demand for bicycles and empty slots change significantly  depending on the time of the day.  There is a certain number of lorries available for bicycle transportation. Currently, the itineraries are manually created by personnel of the operating company.

The Non-motorised Transportation  Advisory Committee of the City of Istanbul (NMTACoCoL) launched a project for improving the quality of service of the "Loris bikes" scheme. As part of this project, you are commissioned to study how the routing of the lorries could be improved by applying analytical methods. Your task is to develop and solve a mathematical programming model and report back with an analysis of your findings.

Due to the complexity and large scale of the problem, your task is to study a simplified version. In particular, you only have to design the routing for the morning peak hours.  The problem and deliverables are described in detail in the following sections.

Problem description

To simplify the model, the area of operation is partitioned into 18 zones, each containing approximately

19 docking stations.  Rather than analysing capacities of individual docking stations and scheduling lorries between them, the model should consider the capacities and demands of each zone as a whole.

The study has to focus on the morning peak hours (7am-10am).  For this period, we have data available for the following quantities in each of the zones.

• The total number of slots available in the zone.

• The total number of bicycles in the zone at the beginning of the period.

• The expected number of customers willing to travel from the zone during the entire period.

• The expected number of customers willing to travel to the zone during the entire period.