NF2 - Lecture 5 Integration of Network Flow Programming...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 5 Integration of Network Flow Programming Models Topics Min-cost flow problem (general model) Mathematical formulation and problem characteristics Pure vs. generalized networks GAINS 8 ATL 5 NY 6 DAL 4 CHIC 2 AUS 7 LA 3 PHOE 1 (6) (3) (5) (7) (4) (2) (4) (5) (5) (6) (4) (7) (6) (3) [150] [200] [300] [200] [200] [200] (2) (2) (7) [250] [700] [supply / demand] (shipping cost) arc lower bounds = 0 arc upper bounds = 200 Distribution Problem Warehouses store a particular commodity in Phoenix, Austin and Gainesville. Customers - Chicago, LA, Dallas, Atlanta, & New York Supply [ s i ] at each warehouse i Demand [ - d j ] of each customer j Shipping links depicted by arcs, flow on each arc is limited to 200 units. Dallas and Atlanta - transshipment hubs Per unit transportation cost ( c ij ) for each arc Problem: Determine optimal shipping plan that minimizes transportation costs Example : Distribution problem Min-Cost Flow Problem In general: [supply/demand] on nodes (shipping cost per unit) on arcs In example: all arcs have an upper bound of 200 nodes labeled with a number 1,...,8 Must indicate notation that is included in model: ( c ij ) unit flow cost on arc ( i , j ) ( u ij ) capacity (or simple upper bound) on arc ( i , j ) ( g ij ) gain or loss on arc ( i , j ) All 3 could be included: ( c ij , u ij , g ij ) Notation for Min-Cost Flow Problem arc name termination node cost gain origin node lower bound upper bound x ij i j l ij The origin node is the arcs tail The termination node is called the head Supplies are positive and demands are negative External flow balance: total supply = total demand i j u ij c ij g ij external flow s i or - d i Spreadsheet Input Data And here is the solution ... Data Entry Using Jensen Network Solver Network Model Name: Net1 Solver: Excel Solver Ph. 1 Iter. 13 5300 Type: Net Type: Linear Total Iter. 15 17 Change Goal: Min Sens.: Yes Comp. Time 00:06 TRUE Cost: 5300 Side: No Status Optimal TRUE Solve TRUE 100 Vary Arc Data and Flows Node Data and Balance Constraints Num. Name Flow Origin Term. Upper Cost Red. Cost Num. Name Fixed Balance Dual Values Basis 1 Phoe-Chi 200 1 2 200 6-3 1 Phoe 700-11-4 2 Phoe-LA 200 1 3 200 3-7 2 Chi-200-2 6 3 Phoe-Dal 200 1 4 200 3-2 3 LA-200-1 12 4 Phoe-Atl 100 1 5 200 7 4 Dal-300-6-7 5 Dal-LA 4 3 200 5 5 Atl-150-4 8 6 Dal-Chi 4 2 200 4 6 NY-250 27 7 Dal-NY 50 4 6 200 6 7 Aus 200-8-13 8 Dal-Atl 50 4 5 200 2 8 Gain 200...
View Full Document

This note was uploaded on 01/26/2011 for the course IEOR 4004 taught by Professor Sethuraman during the Fall '10 term at Columbia.

Page1 / 25

NF2 - Lecture 5 Integration of Network Flow Programming...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online