1. 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

2. National Technical University of Athens Optimization: Fundamental principles 2 harbor cranes / berth 20 containers / crane / hour 15 working hours / day 2 x 20 x 15 = 600 containers / berth / day 3 shipping lines Blue : 3000 containers / ship Red : 3000 containers / ship Green : 1200 containers / ship

3. National Technical University of Athens Conflicting aspects and limitations of optimization Additional energy and maintenance cost C e Fixed operating cost C f Cost due to intensive terminal work C w Port cost Port equipment utilisation factor Cost per loading unit transshipped Port equipment utilisation factor Total cost Port cost Ship cost Number of berths and/or equipment: under consideration

4. National Technical University of Athens 2 harbor cranes Work progress 0% Business rules: Setting FiFo service discipline FiFo priority

5. National Technical University of Athens Business rules: Service discipline favor specific customers 2 harbor cranes Work progress 0% Shipping line Blue has priority Difference form FiFo

6. National Technical University of Athens Business rules: Service discipline improves port productivity Shipping line Green is served first as it has low transshipment volume 2 harbor cranes Work progress 0% Difference form FiFo

7. 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 cranes 2 harbor cranes 0 harbor cranes (1 st phase) 4 harbor cranes (2 nd phase) 4 harbor cranes (1st phase) 2 harbor cranes (2nd phase) Work progress 0% Difference form FiFo Assuming no productivity losses due to multi-crane operations on the same ship

8. 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 a i (i=1,2 …m) n sinks each having demands bj (j=1,2,…n) x ij, number of units of the product transported from source i to destination j, via the route (i,j) at cost c ij per unit Cost relationship is linear ( i.e. the cost of transporting x ij units over route (i,j) is c ij *x ij ) sinks sources 1 2 n 1 2 m Transportation problem Assignment problem The assignment problem represents a special case of the transportation problem, where a i =1,  i  I, where I={1,2,…n} b j =1,  j  J, where J={1,2,…n}

9. 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

10. National Technical University of Athens Solving the typical transportation and assignment problems Minimize the total transport costunder the conditions: where = availabilities and= requirements

11. National Technical University of Athens Methodological approach for solving the transportation problem (two dimension domain)

12. 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 : assumption 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