# q2 by shuifanglj

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```									REFUSE AND RECYCLING
COLLECTION IN THE CITY
OF NEW YORK

PRODUCTION SCHEDULING

JORDI REIG
HAOWEI WANG
BRIAN WONG
PROBLEM DEFINITION
Study the refuse collection problem in the city of New York

Given the current resources,
could we improve the situation?

2
PROJECT SCOPE
We will limit our study to the region officially designated as
Manhattan CB#7

• Upper West Side neighborhood
(59th St. to 110th St., Hudson River
to Central Park West)

• Representative zone
• Appropriate dimension for the study

3
SCHEDULING PROBLEM
FORMULATION
Construct a grid of points where recollection trucks have to go at
some point of the schedule.

•   j – Jobs. Every pick up point corresponds to a job

•   sij – Setup time. Distance between pick up points. [time]
and/or [distance]

•   pj – Processing time. Depending on the quantity of waste
in each point. [time]

mTSP – multiple Traveling Salesman Problem

4
DATA &
ASSUMPTIONS (I)

A. Waste generation

i.     Population density per blocks
ii.    Identify commercial zones/streets
iii.   Average waste generation per person over time
iv.    Average waste generation in commercial zones

Assumption
Same amount of waste in
every pick up point

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DATA &
ASSUMPTIONS (II)

B. Pick up points

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DATA &
ASSUMPTIONS (II)
B. Sij matrix

i.     Distance between points
ii.    Velocity of trucks
iii.   Crossings/traffic lights it goes through
iv.    Driving directions of every street and avenue

Assumption
- From a given point, trucks will only be
allowed to move to adjacent points.
All other distances (Sij) are set to ∞
- Traffic light cycles are considered equal for
all streets, and equal for all avenues.

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OBJECTIVE
FUNCTION

More necessary data:

i.     Cost per mile.
ii.    Hourly salary
iii.   Truck garbage capacity
iv.    Maximum hours of operation
(e.g. from 12am to 6am)

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OPTIMIZATION
VARIABLES
On the optimization process of these objective values, two
variables will be considered:

• Frequency (f). e.g. Collect every other day
• Number of vehicles (m)

Using these two variables, the schedule will be virtually
solved as done in only one day:
m = 10 trucks
f = 1 day                        m’ = 10 trucks

m = 10 trucks
f = 2 days                       m’ = 20 trucks
*Machines 1 to m correspond to 1st day, and m+1 to 2m correspond to 2nd day.

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mTSP code
Open Traveling Salesman Problem - Genetic Algorithm
by Joseph Kirk. 23 Aug 2008

Input:
• XY (float) is an Nx2 (or Nx3) matrix of cities
• DMAT (float) is an NxN matrix of point to point distances/costs
• POP_SIZE (scalar integer) is the size of the population (should be
divisible by 4)
• NUM_ITER (scalar integer) is the number of desired iterations for the
algorithm to run
• SHOW_PROG (scalar logical) shows the GA progress if true
• SHOW_RES (scalar logical) shows the GA results if true

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RESULTS
Total Distance = 592407.4800, Iteration = 1
60

50

40

30

20

10

0
-1   0   1   2                        3                        4   5   6   7

12
13
Total Distance = 292707.4000, Iteration = 1
30

25

20

15

10

5

0
-1   0     1        2         3        4        5      6   7

14
Total Distance = 115896.0300, Iteration = 48525
30

25

20

15

10

5

0
-1   0       1        2         3        4        5        6   7

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City Locations                            Distance Matrix
30

20                                        100

10                                        200

0                                         300
-5           0         5            10                 100       200          300

5
Total Distance = 115896.0300              x 10 Best Solution History
30
3

20                                         2

10                                         1

0                                          0
-5           0         5            10         0             2          4
4
x 10

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Total Distance = 20984.6400, Iteration = 62933
10

9

8

7

6

5

4

3

2

1

0
-1   0       1        2        3        4         5       6   7

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City Locations                              Distance Matrix
10

20

40
5
60

80

0                                        100
-5           0         5           10             20      40       60    80      100

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Total Distance = 20984.6400              x 10 Best Solution History
10
8

6
5
4

2

0                                         0
-5           0         5           10         0                5                 10
4
x 10

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NEXT STEPS

• Try to change the initial solution

• Understand how the code finds new possible solutions

• Run simulations for longer time

• Consider other objective functions

• Study optimal schedule considering variables f and m

• Compute trivial solution and compare to results
obtained from simulation

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THANK YOU!

20

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