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