Math Programming

Conceptof

Optimization (L.O. a )

Linear Programming

Managerial Value

of Information(L.O. d)

Theory(L.O. b)

ExampleApplications

(L.O. c)

SensitivityAnalysis

(L.O. b, d)

ModelingSkills

(L.O. c)

SchedulingResource

Allocation

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 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 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.

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

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.

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

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

3 Steps of Linear Programming Model Formulation

Spreadsheet Based Algebraic

Model Solution Graphical Analysis Simplex Method (LINDO, CPLEX, etc.) Excel Solver

Sensitivity Analysis

More Practice…. A purchasing application

DuPont make or buy problem

TJ Nut Inc. product mix problem