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Math-based Decision Making in Logistics and Operations
Where we are?The group Introduction Description Results Conclusion
UPM
Math-based Decision Making in Logistics and Operations
MbD
MLO
Grupo Inv INGOR
Grupo Inv OS
UD
Org
aniza
ción
de
la P
rodu
cció
n
UD
Adm
inist
raci
ón E
mpr
esas
UD
Eco
nom
ía
UD
Pro
yect
os
UD
Est
adísti
ca
Dep. Ingeniería de Organización, Adm.
de Empresas y Estadística
ETSII UPM
Lab IOL
Math-based Decision Making in Logistic and Operations
UPM
The group Introduction Description Results Conclusion
The team
• Miguel Ortega Mier• Álvaro García Sánchez• Javier Diego• Daniel Herrero• Natalia Ibáñez• Raúl Pulido • Jing Shao• Tamara Borreguero
• Others.
UPM
The group Introduction Description Results Conclusion
Techniques and technologies
Optimization
Modeling
Solver
Simulation Other
Programming and other
specific software
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The group Introduction Description Results Conclusion
6
The inventory routing problem for the Mixed Car Model
Assembly Line
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The group Introduction Description Results Conclusion
7
Relevance
• A high inventory level in the assembly line is a big cost contributor. Some of the car manufacturer’s objectives are keeping low stock levels, performing the replenishment of the production line, and providing the required components at the right time (Monden, 1983).
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The group Introduction Description Results Conclusion
8
Abstract
• A car assembly line usually produces hundreds of cars every day; each workstation in the assembly line needs car components to perform their task.
• The replenishment of the components is a critical issue for the proper operation of the assembly line. In a multi-model assembly line, this task becomes more complicated than in a single model assembly line. A lack of inventory could cause some problems in the production line; excess inventory could also create it.
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The group Introduction Description Results Conclusion
9
Problem description
• In this problem, the assembly line already exists and the production plan, for the planning period, is already known.
• Each model has a set of characteristics, such as types of wheels and tires, radio, sunroof, car seat, and so on. In every workstation, a kit of components is installed; these components can have different trim levels.
• It is assumed that each component needed for the planning horizon is available in a single warehouse from where all the routes depart.
UPM
The group Introduction Description Results Conclusion
10
Problem description
• The early arrival of the component causes space problems with the buffers of the production lines.
• The late arrival causes several problems in the production line. • Dispatch only with a just-in-time policy increases the
transportation cost and the green impact of the production line. It is necessary to select the route and the amount of required components to get the lower cost.
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The group Introduction Description Results Conclusion
11
Problem description
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The group Introduction Description Results Conclusion
12
MIP
• A MIP has been developed.– Transportation Cost– Transportation Vehicle Used Cost– Holding Cos– Violation Cost
• There is a conflict of interest among the objectives.• Right now it is being presented in the CIO 2013 by one of the
authors.
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The group Introduction Description Results Conclusion
min.
13
Two types of Ants• Total Production Rule
Violations• Sequence(i)• Class (i)
• Visited Stations• Total Cost• Vehicle (k)
• Tour (n)• Tour Length• Time Visited (n)
Sequencing
Routing
UPM
The group Introduction Description Results Conclusion
Initial Data• Number of Cars• Number of Car
Classes• Number of Stations• Capacity of Stations• Requirements per
Station by each class• Distance• Number of Vehicles
14
Pheromones & Heuristic info structure
• Pheromone 1 (number of vehicles, number of vehicles)– MAX-MIN approach. – The best ant of the cycle deposit pheromone at the end.– Represent the learnt of desirability of scheduling Cj after Ci.
• Pheromone 2 (number of classes, number of classes)– Initialize in the lower bound– Each time no more cars can be scheduled without violation some
pheromones are added.– Represent the difficult to sequence this class without violating rules.
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The group Introduction Description Results Conclusion
15
Pheromones & Heuristic info structure 2
• Pheromone 3 (number of stations, number of stations)– The best ant of the cycle deposit pheromone at the end.– Represents the learnt of desirability of visiting Sj after Si.
• Dynamic Heuristic info(number of stations, number of stations)– Different options using the stock at determinate time, Traveling time,
distance, and so on.
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The group Introduction Description Results Conclusion
16
Simplified Algorithm
• Pheromones trails are initialized.• For the maximum iteration allowed to do – The sequence ants construct a sequence. – Calculate the demand over the time. – Each route ant constructs a full route. – Each route ant construct a full route using one less
vehicle.– Evaluate the solution using the global function. – Update the pheromone trails with their respective
pheromone and rules.
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The group Introduction Description Results Conclusion
17
Probability
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The group Introduction Description Results Conclusion
18
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Consumed S1 S2 S3 S4 S5
0/0 0/0 0/0 0/0 0/0
Sj
Si
Sj
Si
19
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
RANDOM
Consumed S1 S2 S3 S4 S5
0/1 0/0 0/0 0/0 0/0
20
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
0/1 0/0 0/0 0/0 0/0
21
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
0/2 1/0 0/0 0/0 0/0
22
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
1/2 1/1 0/1 0/0 0/0
23
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
1/3 1/2 1/1 1/0 0/0
24
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .2 .2 .2 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
1/3 1/2 1/1 1/0 0/0
25
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
1/3 1/2 1/1 1/0 0/0
26
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
2/3 1/3 2/1 1/1 0/1
27
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .2 .2
T1
Stock S1 S2 S3 S4 S5
4 4 4 4 4
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
2/4 1/4 3/1 1/3 1/1
28
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
3/4 2/4 4/1 2/3 1/2
29
C 1 2 3 4 5 6 7 81 .8 .8 .8 .8 .8 .8 .82 .8 .8 .8 .8 .8 .8 .83 .8 .8 .8 .8 .8 .8 .84 .8 .8 .8 .8 .8 .8 .85 .8 .8 .8 .8 .8 .8 .86 .8 .8 .8 .8 .8 .8 .87 .8 .8 .8 .8 .8 .8 .88 .8 .8 .8 .8 .8 .8 .8
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
3/4 2/4 4/1 2/3 1/2
30
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .7 .72 .7 .7 .7 .7 .7 .7 .73 .7 .7 .7 .7 .7 .7 .74 .7 .7 .7 .7 .7 .7 .75 .7 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .7 .7 .77 .7 .7 .7 .7 .7 .7 .78 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .4 .2 .3 .2
Y .2 .3 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .3 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Other Ant
31
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .7 .72 .7 .7 .7 .7 .7 .7 .73 .7 .7 .7 .7 .7 .7 .74 .7 .7 .7 .7 .7 .7 .75 .7 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .7 .7 .77 .7 .7 .7 .7 .7 .7 .78 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .3 .2 .3 .2
Y .2 .3 .2 .2
Bk .3 .3 .3 .2
Bl .2 .2 .3 .3
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
We keep doing for the total number of ants
32
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .7 .72 .7 .7 .7 .7 .7 .7 .73 .7 .7 .7 .7 .7 .7 .74 .7 .7 .7 .7 .7 .7 .75 .7 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .7 .7 .77 .7 .7 .7 .7 .7 .7 .78 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
For the best antEvaporate T1
33
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Best Ant
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
34
Iterate
35
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH
WH
WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
36
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3 S4S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2
WH
WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
37
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2
WH S4
WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
38
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WH
S3S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2
WH S4
WH S1
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
39
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WH
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2 S3
WH S4
WH S1
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
40
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WH
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2 S3
WH S4 S5
WH S1
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
41
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2 S3 WH
WH S4 S5 WH
WH S1 WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Routing
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
42
Iterate
43
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH
WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
One vehicle less
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
44
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2 S3 S5 WH
WH S4 S1 WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
One vehicle less
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
45
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WH
S 0 1 2 3 4 5
0 .5 .5 .5 .5 .5 .5
1 .5 .5 .5 .5 .5 .5
2 .5 .5 .5 .5 .5 .5
3 .5 .5 .5 .5 .5 .5
4 .5 .5 .5 .5 .5 .5
5 .5 .5 .5 .5 .5 .5
T3
T2
WH S2 S3 S5 S1 S4
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
One vehicle less
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
46
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .3 .3 .3 .3 .3 .3
1 .3 .3 .3 .3 .3 .3
2 .3 .3 .3 .3 .3 .3
3 .3 .3 .3 .3 .3 .3
4 .3 .3 .3 .3 .3 .3
5 .3 .3 .3 .3 .3 .3
T3
T2
Cl R Y Bk Bl
R .2 .2 .2 .2
Y .2 .2 .2 .2
Bk .5 .3 .3 .2
Bl .2 .2 .2 .2
WH S2 S3 S5 WH
WH S4 S1 WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Update the best ant
47
C 1 2 3 4 5 6 7 81 .7 .7 .7 .7 .7 .9 .72 .7 .7 .9 .7 .7 .7 .73 .7 .7 .7 .7 .9 .7 .74 .7 .7 .9 .7 .7 .7 .75 .9 .7 .7 .7 .7 .7 .76 .7 .7 .7 .7 .9 .7 .77 .7 .7 .7 .7 .7 .7 .98 .7 .7 .7 .7 .7 .7 .7
WHS1S3
S2S4
S5
S 0 1 2 3 4 5
0 .3 .3 .5 .3 .5 .3
1 .5 .3 .3 .3 .3 .3
2 .3 .3 .3 .5 .3 .3
3 .3 .3 .3 .3 .3 .5
4 .3 .5 .3 .3 .3 .3
5 .5 .3 .3 .3 .3 .3
T3
T2
WH S2 S3 S5 WH
WH S4 S1 WH
T1
Sj
Si
Sj
Si
Consumed S1 S2 S3 S4 S5
4/4 2/5 4/2 2/3 1/2
Update the best ant
Cl R Y Bk Bl
R .2 .2 .3 .2
Y .2 .2 .2 .2
Bk .3 .3 .4 .2
Bl .2 .2 .2 .2
48
Iterate
49
Repeat the entire process
50
We keep working
• Which heuristic information is better for the problem. Time to be out stock, time to arrive, distance, and so on.
• Type of filling, series or parallel
• Other updates of pheromones
UPM
The group Introduction Description Results Conclusion
51
Results of MIP
WH S1 S2 S3 S4 S5
Vehicle 1 11 8 5
Vehicle 2 14 4 7 10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
M3 M4 M5 M5 M4 M5 M5 M1 M5 M5 M3 M4 M2 M5 M5
M2 M5 M4 M3 M5 M5 M4 M5 M4 M5 M4 M5 M5 M4 M4
The group Introduction Description Results Conclusion
52
Results of ACO
• The ACO was tuned using the instance small instance where an exact solution can be found by the MIP algorithm.
• The ACO algorithm finds solutions with the gap of 5% in less than 1 minute, when the MIP algorithm takes more than one hour.
• As bigger instance was not possible to solve by exact algorithm and no public instance for the entire problem was founded to compare with the optimal.
• We use the car sequencing instances reported by [Regin, 1997], then we create the replenishment data, such as capacity, vehicle number, and so on.
The group Introduction Description Results Conclusion
53
Practical conclusions• In this work, the car sequencing, the inventory and the routing problem
have been solved jointly. The routing model should consider more factors than just the transportation cost. The main factor in the delivery of material should not only be the decrease of the transportation costs but also the decrease of the holding cost of the components.
• The cost of the space is an amplifier of the savings of the model. The replenishment is made before the inventory level reaches the safety stock. Following the Lean idea, it is possible to decrease the safety stock until it reaches zero safety stock, always keeping in mind the risk of any delay with the consequence of the stoppage of the assembly line.
UPM
The group Introduction Description Results Conclusion
54
Thank you!
UPM
The group Introduction Description Results Conclusion
