Network Flow Programming Syllabus - Network Flow Programming Class
 Required Texts Operations Research Models and Methods, Paul A. Jensen and Jonathan F. Bard, John Wiley Inc., 2003 Network Flow Programming by Paul A. Jensen, Printed by the University Coop Custom Publishing, Summer 2002 Computer Programs Access to Microsoft Excel version 97 or later for Windows or Mac OS. Syllabus Situations arising from the fields of transportation, water resources, manufacturing and many others give rise to network flow models. A flow network is a collection of nodes and arcs. Each arc passes from one node to another and carries a commodity called flow. A requirement is that flow be conserved at each node. The optimization problem is to find the flow in each arc that minimizes the total cost of the flow in the network. This course has three aspects: modeling real problems as networks, the theory associated with network optimization, and algorithms implementing the theory. The course covers the broad range of network flow problems, but stresses the pure and generalized, single commodity, minimum cost network flow problem. Exams There are three exams including the final exam. All exams have equal weight in the exam average. Class Contribution Each student should prepare a web site or give a verbal presentation of some topic of interest to this class.

Schedule

The references to MMOR are from Models and Methods of Operations Research. The references to the Lecture Notes are to notes supplied by Paul Jensen. The leaf images are linked to pages in this site or to pdf files for supplements.

 Lect Date Topic Read MMOR Lecture Notes HW Link Network Flow Programming Models 1 Introduction and Network Models 5.1 1-5 Terminology 2 Modeling Examples 5.2 6-12 Distribution Example Special Cases Other Examples 3 Optimization Add-ins for Excel General Discussion of Add-ins Math Programming Add-in Network Models Transportation Model Network Solver Add-in Excel Files (Network Models) Excel Demo (Math Programming) 4 Nonlinear Costs/Economic Model 13-18 HW 1 5 Side Constraints 19-22 6 Integer Variables 23-29 HW 2 7 Distance Problems 31-33 8 Nonlinear Problems HW 3 9 Modeling Exercises 10 Modeling Exercises 11 Exam Solution Methods for Specialized Problems 12 The Transportation Problem 6.1 34-36 Teach Transportation Add-in Transportation Demo 13 MST and SPT Algorithms 6.2 37-48 MST and SPT Demonstrations 14 Maximum Flow Problem 6.3 49-57 HW 4 15 Primal and Dual Problems 58-62 Primal Simplex Methods for Network Problems 16 LP and Network Flows 63-68 HW 5 17 Basic Solutions for the Pure Problem 6.4 69-72 18 The Primal Simplex for the Pure Problem 73-78 HW 6 19 Simplex for Upper Bounded Problems 79-86 Teach Networks Add-in Network Simplex Demo 20 The Shortest Path and Maximum Flow Problems 87-88 HW 7 21 Computational Implementation 89-94 22 Review 23 Exam The Generalized Ñetwork Problem 24 The Basis for the Generalized Problem C.1 95-96 HW 8 25 Finding the Primal and Dual Solutions C.2 97-100 26 Finding the arcs to enter and Leave the Basis C.3 101-109 HW 9 27 Networks with Upper Bounds 138-140 110-122 Teach Network Add-in for Generalized Problems 28 Review HW 10 29 Review Final Exam

Operations Research Models and Methods
Internet
by Paul A. Jensen