linear programminglecture 1

1
Math Programming
Concept of Optimization (L.O. a )
Linear Programming
Managerial Value of Information (L.O. d)
Theory (L.O. b)
Example Applications (L.O. c)
Sensitivity Analysis (L.O. b, d)
Modeling Skills (L.O. c)
Scheduling
Resource Allocation
2
Designing a Spreadsheet Model

• Sketch the spreadsheet on paper first
• Organize the spreadsheet into modules group
  similar items together
• Isolate input parameters
• Design for use and communication
• Example KPiller, Inc. Product Mix Problem

3
3 Components for a Spreadsheet Optimization
Problem

• There is one cell which can be identified as the
  Target or Set Cell, the single objective of the
  problem that is to be maximized or minimized.

• There is at least one cell that is limited to
  assume values over specified ranges. These cells
  are referred to as Constraint Cells.

• There is at least one Changing or Variable Cell
  (decision variable). The set of changing cells
  must influence the target cell and all of the
  constraint cells. Formulas should not be entered
  in the changing cells! The changing cells may
  have upper and lower bounds.

4
Linear Programming (LP)

• A mathematical programming problem is one that
  seeks to maximize or minimize an objective
  function subject to constraints.
• If both the objective function and the
  constraints are linear, the problem is referred
  to as a linear programming problem.

5
Linear Programming Applications

• Production Planning
• several products
• multiperiod demand
• limited period resources
• want minimal production costs or maximum
  profitability
• Transportation/Distribution Problems
• different routes
• limited supply at several sources
• demand requirements at various locations
• want minimal transportation costs

6
Linear Programming Applications

• Investment Planning
• several investment alternatives
• risk and capital restrictions
• want maximum expected return
• Labor Scheduling
• full-time and part-time workforce
• multi-period staffing requirements
• workforce staffing restrictions
• want minimum total labor cost

7
3 Steps of Linear Programming

• Model Formulation
• Spreadsheet Based
• Algebraic
• Model Solution
• Graphical Analysis
• Simplex Method (LINDO, CPLEX, etc.)
• Excel Solver
• Sensitivity Analysis

8
More Practice.

• A purchasing application
• DuPont make or buy problem
• TJ Nut Inc. product mix problem