Lecture Operations management: Creating value along the supply chain (Canadian edition) - Chapter 14S

Chapter 14 supplement - Linear programming. This chapter includes contents: Model formulation, graphical solution method, linear programming model solution, solving linear programming problems with excel, sensitivity analysis.

Robert S Russell, Bernard W Taylor III, Ignacio Castillo, Navneet Vidyarthi

CHAPTER 14

SUPPLEMENT

Linear Programming

OPERATIONS

MANAGEMENT: Creating Value

Along the Supply Chain,

Canadian Edition

Lecture Outline

Linear Programming (LP)

representing a firm’s objective and resource

constraints

determines a level of operational activity in order to achieve an objective, subject to restrictions called constraints

Types of LP

Types of LP

Types of LP

LP Model Formulation

— symbols representing levels of activity of an operation

— linear relationship for the objective of an operation

— most frequent business objective is to maximize profit

— most frequent objective of individual operational units (such as a production or packaging department) is to

minimize cost

— linear relationship representing a restriction on decision making

xj = decision variables

bi = constraint levels

cj = objective function coefficients

aij = constraint coefficients

Constraints

Highlands Craft Store

Labor Clay Revenue

Product (hr/unit) (lb/unit) ($/unit)

There are 40 hours of labor and 120 pounds of clay

available each day

Decision variables

x1 = number of bowls to produce

x2 = number of mugs to produce

Resource Requirements

Highlands Craft Store

Graphical Solution Method

plane

where all constraints are satisfied simultaneously

boundary of this space that maximizes (or

minimizes) value of objective function

Graphical Solution Method

4 x1 + 3 x2 120 lb

x1 + 2 x2 40 hr

Area common toboth constraints

Computing Optimal Values

| 20

| 30

| 40

x1

x2

24 8

Extreme Corner Points

x1 = 224 bowls x2 = 8 mugs

|20

|30

|40

Z = $2,100

Z = $24

Z = 6x1 + 3x2

Simplex Method

— Mathematical procedure for solving LP problems

— Follow a set of steps to reach optimal solution

— Slack variables added to ≤ constraints to represent unused resources

Solution Points With Slack Variables

Solution Points With Surplus Variables

Solving LP Problems with Excel

Click on “Data”

to invoke “Solver”

Solving LP Problems with Excel

After all parameters and constraintshave been input, click on “Solve”

LP Solution

Sensitivity Range for Labor Hours

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