In this project work, you are expected to provide solutions to a real-life business problem with
randomly generated data. You are free to use any of the methods and/or approaches you discussed
in the class. You may completely or partially formulate some part of the problem as a linear
programming problem, and obtain a solution using an optimization solver package/software or use
heuristic algorithms that you have developed or learned in the class. Note that the overall problem
consists of several subproblems that look alike the standard textbook type problems covered in the
class. In this respect, neither a mathematical programming problem formulation nor an algorithm
from the class notes will not be sufficient to attack this problem. You have to be creative: you may
either expand on/extend the methods/formulations/approaches you have learned from the class or
you may use them in combination to solve the problem in parts and bring these parts together to
solve the complete problem. The project description and the corresponding data file are attached.
Note that there is no standard solution or a solution key to this problem. Your grade will be based on
the use of sophisticated analytical methods, the quality of the solutions and your creativity in
attacking the problem.
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At the end of this project, you should prepare a short formal “typewritten” report of at most 10 pages
(with standard 1.5 line spacing). Your report should clearly discuss your approach and your results
with respect to the particular questions explained in the project description. Along with your project
report, you should also submit the implementation files (programs, coded algorithms, spreadsheet
applications, etc.) of your solution method.

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We consider the bottle delivery service of a waterseller in a particular district of Istanbul with one main
store-depot. Upon the request from the customers, the waterseller delivers the bottles to the customers
with motor-biker-crews driving from the depot. We assume that a customer requests one bottle at a
time, and the biker-crew may serve at most two customers in one round-trip starting from the depot
and ending at the depot as each motorbike has a capacity of 2 bottles. We suppose that the service
region can be represented by a rectangular map with 20 blocks in length and 6 blocks in width. As
demonstrated in Figure, each block consists of 20 buildings: 10 buildings from north to south and 2
buildings from east to west. If we suppose that each building is a customer node, the corresponding
network can be considered as a Manhattan network with 2400 customer nodes. Each building is located
on a square land with 20 meters on each side. Street widths are negligible.
The waterseller accepts order from 8:00 in the morning until 8:00 in the evening (20:00). Each building
may have requested one bottle during a typical day from 08:00 to 20:00. Ideally, a demand request
should be satisfied at most in two hours after the order is received from the customer. A customer is
denoted by vertical and horizontal coordinates. The building at the south-left corner of the strict is
denoted as (1,1) while the building at the north-right corner is denoted as (40,60). The main depot is
located at (31,43). The average speed of the motorbike is 200 meters/minute and the fuel consumption
is directly proportional to the total distance covered. A biker-crew needs 3 minutes to prepare the bike
(i.e. load the bottles onto the bike) if the cabin of the motorbike is empty; once the biker arrives at the
customer location, it takes another 3 minutes to complete the delivery.

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The list of orders on a typical day is given in the spreadsheet in MS430_2012F_Project_Data_500.xlsx.
Figure 1. Service region of the waterseller demonstrated on a representative map
A. Suppose that the list of orders is known beforehand at the beginning of the day; provide a
delivery plan for the waterseller that minimizes the total fuel cost (i.e. distance travelled) given
that 6 bikers are available at any time from the beginning of the day until the end. Suppose that
the last order is accepted at 20:00; yet, the delivery may continue until 21:00. The service time
of 2 hours may be ignored once in a while if it is impossible to satisfy the order in that time
period. What is the total travelled distance at the end of the day? How much (what
percentage) of the customers are serviced within 2 hours of order time, i.e. what is the overall
service level of the waterseller?
Along with this daily plan of deliveries, you should also try to come up with a service rule for the
waterseller: the service rule should explain how customer orders should be combined and how
long should a customer wait before being served. Does your plan completely comply with the
rules you provide? Or, are there any exceptions?
B. Suppose that the orders in the list are known only when they arrive during the day. Construct a
real-time delivery plan for the waterseller. You may use the rules you have designed in part (a)
to do the real-time planning decisions.
How much does the total travelled distance and the overall service level (with respect to 2 hours
of service time) change with real-time planning? Discuss how the quality and effectiveness of
the plan changes from advance planning to real-time planning.

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C. The waterseller plans to buy some vans to use as mobile stations. Throughout the day once a
van is filled up to 20 bottles at a time, it is to be located at a block corner. After a delivery is
completed, a biker-crew will be able to pick up more bottles from the van without having to go
back to the depot-store for the subsequent deliveries. The deliveries can be dispatched to the
bikers instantly with sms messaging. Whenever an order is dispatched to a biker, the crew
checks the motorbike cabin; if he/she does not have extra bottles on his bike, he goes to the
nearest mobile station to pick up more bottles. When the mobile station is empty, one of the
bikers drives the van to the depot-store. The van may be filled up to 20 bottles again, can be
driven to another location. Suppose that the van travels at an average speed of 260
meters/minute and the average fuel consumption rate per km is twice that of a bike.
Based on the planning approaches and results you have obtained in parts A and B, consider the
integration of mobile stations (i.e. vans) into the delivery system of the waterseller. The
waterseller expects to see some significant reduction in daily fuel costs and increase in the
overall service level when the vans are used. They try to determine how many vans would be
sufficient to achieve these goals; what they have in mind is to buy 3, 4 or at most 5 vans. What
is your suggestion? You should redo the delivery plans both for the advance planning approach
(along with delivery rules) and the real-time planning approach considering the use of vans. Try
the options of having 3, 4 or 5 vans, and provide numerical results to show how much savings is
obtained from the fuel/travel costs and how much improvement is obtained in terms of service
level.

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