An approach to Optimization and Business rules context
description
Transcript of An approach to Optimization and Business rules context
National Technical University of Athens
An approach to Optimization and Business rules context
Contents
1. Optimization: Fundamental principles (maritime terminal example)
2. Examples of Business rule effects
3. Mathematical solutions (transportation and assignment problem)
4. Adopting the transportation / assignment solutions for the F-MAN
asset management allocation problem
National Technical University of Athens
Optimization: Fundamental principles
2 harbor cranes / berth20 containers / crane / hour
15 working hours / day2 x 20 x 15 = 600 containers / berth / day
3 shipping linesBlue : 3000 containers / shipRed : 3000 containers / shipGreen: 1200 containers / ship
National Technical University of Athens
Conflicting aspects and limitations of optimization
Additional energy and maintenance cost Ce
Fixed operating cost Cf
Cost due to intensive terminal work Cw
Port cost
Port equipment utilisation factor
Cost per loading unit transshipped
Cost per loading unit transshipped
Port equipment utilisation factor
Total cost
Port cost
Ship cost
Number of berths and/or equipment: under consideration
Number of berths and/or equipment: under consideration
National Technical University of Athens
2 harbor cranes
2 harbor cranes
2 harbor cranes
Work progress 0%
Work progress 0%
Business rules: Setting FiFo service discipline
FiFo priorityFiFo priority
Shipping line
Ve
ss
el
Nu
mb
er
Be
rth
N
um
be
r
Wa
itin
g
tim
e * Service Time Total
Time (days)
Red 1 1 0 3000/600 = 5 5
Blue 1 2 0 >> 5
Red 2 3 0 >> 5
Red 3 1 5 5 10
Blue 1 3 5 5 10
Green 2 1 5 1200/600=2 7
Average dwell time: Shipping line Blue 7,507,006,67
Average dwell time for all shipping lines 7,00
* (starting from the moment of snapshot)
GreenRed
National Technical University of Athens
Business rules: Service discipline favor specific customers
2 harbor cranes
2 harbor cranes
2 harbor cranes
Work progress 0%
Work progress 0%
Shipping line Blue has priority Shipping line Blue has priority
-33%
0%
25%
0%
Difference form FiFo
Shipping line
Ve
ss
el
Nu
mb
er
Be
rth
N
um
be
r
Wa
itin
g
tim
e * Service Time Total
Time (days)
Red 1 1 0 3000/600 = 5 5Blue 1 2 0 5 5Blue 1 3 0 5 5Red 2 3 5 5 10Red 3 1 5 5 10Green 2 1 5 1200/600 = 2 7
Average dwell time: Shipping line Blue 5,007,008,33
Average dwell time for all shipping lines 7,00
GreenRed
* (starting from the moment of snapshot)
National Technical University of Athens
Business rules: Service discipline improves port productivity
Shipping line Green is served first as it has low transshipment volume Shipping line Green is served first as it has low transshipment volume
2 harbor cranes
2 harbor cranes
2 harbor cranes
Work progress 0%
Work progress 0%
0%
-71%
10%
-7%
Difference form FiFo
Shipping line
Ve
ss
el
Nu
mb
er
Be
rth
Nu
mb
er
Wa
itin
g
tim
e * Service Time Total
Time (days)
Red 1 1 0 3000/600 = 5 5
Blue 1 2 0 >> 5
Green 2 3 0 1200/600=2 2
Red 3 1 2 5 7
Blue 1 3 5 5 10
Red 2 1 5 5 10
7,502,007,336,50
* (starting from the moment of snapshot)
GreenRed
Average dwell time: Shipping line Blue
Average dwell time for all shipping lines
National Technical University of Athens
Business rules: Service discipline favor specific customers while as secondary effect port productivity is improved
Shipping line Blue has priority. The norm foresees 4 harbor cranesShipping line Blue has priority. The norm foresees 4 harbor cranes
2 harbor cranes
0 harbor cranes (1st phase)
4 harbor cranes (2nd phase)
4 harbor cranes (1st phase)
2 harbor cranes (2nd phase)
Work progress 0%
Work progress 0%
Difference form FiFo
Assuming no productivity losses due to multi-crane operations on the same ship
-50%
0%
25%
-6%
Shipping line
Ve
ss
el
Nu
mb
er
Be
rth
Nu
mb
er
Wa
itin
g
tim
e * Service Time Total
Time (days)
Red 1 1 2,5 3000/1200 = 2,5 5
Blue 1 2 0 3000/600=5 5
Blue 1 3 0 3000/1200 = 2,5 2,5
Red 2 1 5 3000/600 =5 10
Red 3 2 5 3000/600 =5 10
Green 2 3 2,5+2,5=5** 1200/600=2 7
3,757,008,336,58
Average dwell time: Shipping line BlueGreen
* (starting from the moment of snapshot)** (2,5 days to enter and 2,5 days without cranes)
Red Average dwell time for all shipping lines
National Technical University of Athens
Typical transportation and assignment problems
sinks
sources
1 2 n
1 2 m
m sources each having a single commodity ai
(i=1,2 …m)n sinks each having demands bj (j=1,2,…n)xij, number of units of the product
transported from source i to destination j, via the route (i,j) at cost cij per unit Cost relationship is linear ( i.e. the cost of transporting xij units over route (i,j) is cij*xij)
sinks
sources
12
n
1 2 m
Transportation problem
Assignment problem
The assignment problem represents a specialcase of the transportation problem, whereai=1, iI, where I={1,2,…n} bj=1, jJ, where J={1,2,…n}
National Technical University of Athens
Various other methodological approaches
A
2 1
1. Pickup and delivery problem with time windows
2. Emergency response Fleets (fire department, ambulance etc)
3. Real time Emergency Vehicle Dispatching and Routing
4. Taxi dispatching
5. Time dependent shortest-path algorithms
Analytical solutions under assumptions
Heuristics
B
National Technical University of Athens
Solving the typical transportation and assignment problems
ij
n
1jij
m
1i
m
1i
i xcSxz
n
jj
m
ii ba
11
m
iia
1
n
jjb
1
Minimize the total transport cost under the conditions:
iinii a....xxx 21
111211 axxx n ....
222221 axxx n .... . . . . . . . . . . . .
mmnmm axxx ....21 , m s u p p l y e q u a t i o n s
jnjjj bxxx ....21
112111 bxxx n ....
222212 bxxx n .... . . . . . . . . . . . .
nmnnn bxxx ....21 , n d e m a n d e q u a t i o n s
0ijx , f o r e a c h ( ), NMji
where = availabilities and = requirements
National Technical University of Athens
Methodological approach for solving the transportation problem (two dimension domain)
Cost function
National Technical University of Athens
Adopting the transportation /assignment solutions for the F-MAN asset management allocation problem
A) Defining the cost function:
(1) Geographical proximity
(2) Railway line length and /or time
(1) Use statistics for the required time and probabilities of non-shown
D) Solving the :
n
jj
m
ii ba
11assumption by BUSINESS RULES!
(3) Trip time statistics
B) Include uncertainties in the decision making
(2) Generalized cost functions (including uncertainties)
C) Adopting time windows by filters