O perations R esearch Fall Semester 2004

The slides used in presentation of the lectures are available for downloading in .pdf (Portable Document Format) and were produced by Adobe Acrobat. You may read them using an Adobe Acrobat Reader on either Macintosh, PC, or UNIX platform; Acrobat Reader may be freely downloaded from Adobe's web site.

Note: The notation (x).pdf indicates x screens per page, where x might be 1, 2, 4, 8, etc.

• Course organization, introduction to Operations Research, etc. (1).pdf, (4).pdf
• Solving Systems of Linear Equations (1).pdf, (2).pdf or (4).pdf
• Pivot Example (1).pdf, (4).pdf
• Linear Programming: optimization of a linear function of several variables, with the restriction that these variables satisfy certain linear equations or inequalities.
  • Lectures
    • Formulating LP Models (1).pdf, (6).pdf
    • More LP Formulations (1).pdf, (2).pdf, or (8).pdf
    • Using Sets in LINGO (1).pdf, (4).pdf
    • Curve-fitting using LP to minimize mean or max absolute error rather than mean square error (1).pdf, (4).pdf
    • Introduction to the Simplex Method (1).pdf, (2).pdf, or (8).pdf following a path, vertex to vertex
    • The Simplex Method (1).pdf, (2).pdf, or (8).pdf
    • Simplex flowchart (1).pdf, (4).pdf
    • Classifying LP tableaux (1).pdf, (4).pdf
    • Variants of the simplex tableau appearing in textbooks which might cause confusion (1).pdf, (4).pdf
    • Initial BFS (basic feasible solution) for Simplex Method (1).pdf, (2).pdf, or (8).pdf
    • Further Simplex Examples (1).pdf, (2).pdf, or (8).pdf
    • A flowchart summarizing the simplex method (1).pdf or (4).pdf
    • Revised Simplex Method (1).pdf, (2).pdf, or (8).pdf maintains inverse of basis matrix, not full tableau
      • Example #1 (phase II only) (1).pdf or (4).pdf
      • Example #2 (both phases I & II (1).pdf or (4).pdf
      • Efficiency of the Revised Simplex Method (1).pdf, (2).pdf, or (8).pdf
    • Linear Programming Duality Theory (1).pdf, (2).pdf, or (8).pdf
    • Sensitivity Analysis, Part 1 (1).pdf, (2).pdf, or (8).pdf effect of rhs or cost coefficient changes
    • Sensitivity Analysis, Part 2 (1).pdf, (2).pdf, or (8).pdf examples with LINDO
    • Parametric Programming on the Right-hand-side (1).pdf, (2).pdf, or (8).pdf
    • Data Envelopment Analysis (DEA), LP-based technique for evaluating unit efficiencies (1).pdf, (2).pdf, or (8).pdf
  • Examples & Activities
    • Chicken Feed LP model (1).pdf, (4).pdf
    • Walnut Orchard LP model (1).pdf, (4).pdf
    • BISCO LP model (1).pdf
    • Feed & Ship LP model (1).pdf
    • Drinking glasses LP model (1).pdf, (4).pdf
    • Incinerators LP model (1).pdf, (4).pdf
    • Graph of feasible region in 2-D (1).pdf
    • Graph & basic variables (1).pdf
    • PAR golf bag manufacturing (illustrating interpretation of dual variables using parametric analysis) (1).pdf, (4).pdf
    • Assigning students to schools (1).pdf, (4).pdf
    • Gasoline blending (1).pdf, (4).pdf
    • Ankelor (sensitivity analysis exercise) (1).pdf, (4).pdf
    • Short quiz on LP (1).pdf, (2).pdf, or (8).pdf
      
• Transportation & Assignment Problems: special cases of linear programming, which may be solved more efficiently than by using a standard LP solver. They have the very desirable feature that (under certain conditions) the optimal solutions are guaranteed to have only integer values of the variables!
  • Transportation problem (1).pdf, (2).pdf, or (8).pdf
  • Assignment Problem (1).pdf, (2).pdf, or (8).pdf
  • Airline Crew Assignment (1).pdf, (2).pdf, or (8).pdf (example of assignment problem)
    
• Project Scheduling: finding the shortest completion time of a large and complex project requiring the completion of many tasks, some of which require the completion of other tasks before they can be begun.
  • Project Networks (1).pdf, (2).pdf, or (8).pdf activity-on-arrow (AOA) and activity-on-node (AON)
  • Critical Path Method (CPM) (1).pdf, (2).pdf, or (8).pdf assumes task durations to be known with certainty
  • Project Evaluation & Review Technique (PERT) (1).pdf, (2).pdf, or (8).pdf allows random durations
  • "Crashing" a Project (1).pdf, (2).pdf, or (8).pdf allocating additional resources to reduce completion time
    
• Integer Programming Model Formulation: Often, in linear programming problems, it is necessary that some or all of the variables have discrete values in the optimal solution.
  • Introduction (1).pdf, (2).pdf, or (8).pdf
  • ILP Models Part I (1).pdf, (2).pdf, or (8).pdf
  • ILP Models Part II (1).pdf, (2).pdf, or (8).pdf
    
• (Deterministic) Dynamic Programming
  • Index (1).pdf, (2).pdf or (8).pdf
  • Prototype DP Model (1).pdf, (2).pdf or (8).pdf (transitions & payoffs given in tabular form)
  • Knapsack problem (1).pdf, (2).pdf or (8).pdf
  • Deterministic production planning (1).pdf, (2).pdf or (8).pdf
  • Powerplant capacity planning (1).pdf, (2).pdf or (8).pdf
  • Nim "game of matches" (1).pdf, (2).pdf or (8).pdf (remove matches from pile, avoid last match)
  • Deterministic machine replacement (1).pdf or (4).pdf
  • Optimal redundancy to achieve reliability (1).pdf, (2).pdf or (8).pdf
  • Political redistricting (1).pdf, (2).pdf or (8).pdf (assign multiple representatives to districts)

Dennis Bricker
Dept of Mechanical & Industrial Engineering
University of Iowa
Iowa City, Iowa 52242
USA

Last modified: 23 October 2004

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