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Network Models

Network Models. Tran Van Hoai Faculty of Computer Science & Engineering HCMC University of Technology. Harmful Waste Collection at HCM city. Industrial zone. Industrial zone. Processing Factory. Processing Factory. Industrial zone. Industrial zone. Typical route. Depot. Solution.

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Network Models

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  1. Network Models Tran Van HoaiFaculty of Computer Science & Engineering HCMC University of Technology Tran Van Hoai

  2. Harmful Waste Collection at HCM city Industrial zone Industrial zone Processing Factory Processing Factory Industrial zone Industrial zone Tran Van Hoai

  3. Typical route Depot Tran Van Hoai

  4. Solution HIGHLY COMPLEX PRACTICAL ISSUES Tran Van Hoai

  5. Problem Constraints • Vehicle’s capacity • Customer’s Time Window • Conflict Harmful Waste cannot transport in the same vehicles • Maximum time for a route • … Tran Van Hoai

  6. Objectives • Minimize cost travel • Minimize the number of vehicles • Balance workload among the vehicles • Minimize waiting time needed to serve customers in their required hours • Satisfy service requirements • … Tran Van Hoai

  7. Delivery route without optimization STRATEGY:GO TO THE NEAREST LOCATION FIRST Tran Van Hoai

  8. Delivery route with optimization • Practical problems are much more difficult • Traffic jam (time-dependence) • Delivery time (time-window) • Carrier capacity (space-dependence) • Precedence constraint • … Traffic jam from 6:30am to 9am Delivery time from 9am to 10am Tran Van Hoai

  9. Networks • Network = • A set of nodes • A set of arcs (connecting nodes) • Functions defined on nodes & arcs • Nodes • Microchips, cities, TV stations,… • Arcs • Wires, roads, satellite transmission,… • Functions (defining resource) • Resource: electrical current, delivery trucks, TV program,…) Tran Van Hoai

  10. Classification (1) • Network flow models • Delivery of goods or resource from supply nodes, thru intermediate nodes, to demand nodes • Examples: • Transportation models • Capacitated transshipment models • Assignment models • Shortest path models • Maximum flow models Tran Van Hoai

  11. Classification (2) • Network connectivity models • Link all nodes together • Examples: • Traveling salesman models • Minimal spanning tree models Flow models can be modeled as LP (although they are ILP) Connectivity models cannot modeled as LP Tran Van Hoai

  12. Terminology (1) Decisionvariable FLOW Xij i j CAPACITY Uij i j i j Directed arc Undirected arc Tran Van Hoai

  13. Terminology (2) Path 4 6 1 3 2 7 5 Cycle Tran Van Hoai

  14. Terminology (3) Spanning tree Tree 4 6 1 3 2 7 5 Tran Van Hoai

  15. Transportation model • m sources • Supply resource at source Si • n destinations • Demands for resource at destination Di • Unit shipping cost Cij between i & j GOAL: minimize total shipping cost Tran Van Hoai

  16. Carlton Pharmaceutical transportation network Distributionwarehouses Productionplants 4 35 D1=1100 1 S1=1200 30 40 32 5 D2=400 37 40 2 S2=1000 42 25 6 40 D3=750 15 3 S3=800 20 28 7 D4=750 Tran Van Hoai

  17. Assumptions (simplification) • Constant per item shipping cost • All shipping performed simultaneously (within fixed time frame) • Vaccine only shipped from source to destination Tran Van Hoai

  18. Formulation • Xij: shipment from i (1,…,3) to j (4,…,7) • 12 integer variables • Complexity increases quickly when number sources (destinations) increases Tran Van Hoai

  19. Practical issues • Blocked routes • Xij = 0 means no vaccine assigned to route i to j • Or …. • Minimum/maximum shipments • Lij ≤ Xij ≤ Uij • Production planning can be considered as transportation model Tran Van Hoai

  20. Capacitated transshipment networks Distributionwarehouses Productionplants 4 35 D1=1100 1 S1=1200 30 40 32 5 D2=400 37 40 2 S2=1000 42 25 6 40 D3=750 15 3 S3=800 20 28 7 Intermediate nodes (no supply, no demand) D4=750 Tran Van Hoai

  21. Capacitated transshipment • Constraints: • supply node: net flow out (flow out – flow in) not exceed its supply • intermediate node:net flow out = 0 • demand node: net flow out = - demand GOAL: minimize total shipping cost (capacitated transshipment = general network model) Tran Van Hoai

  22. Depot Max Transshipment nodes Supply nodes Demandnodes S1=10 Alexandria Fall Church D5=12 Fairfax $15 $5 $7 $20 $7 $6 $11 $15 $10 Chevy chase Gerogetown Bethesda S2=17 D6=13 10 8 12 17 7 3 5 6 7 Tran Van Hoai

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