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Process Selection and Facility Layout

Process Selection and Facility Layout. Learning Objectives Explain the strategic importance of process selection. Explain the influence that process

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Page 1: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Process Selection and

Facility Layout

Page 2: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Learning ObjectivesLearning Objectives

Explain the strategic importance of process selection.

Explain the influence that process selection has on an organization.

Describe the basic processing types. Discuss automated approaches to

processing.

Page 3: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Learning ObjectivesLearning Objectives

List some reasons for redesign of layouts. Describe the basic layout types. List the main advantages and

disadvantages of product layouts and process layouts.

Solve simple line-balancing problems.

Page 4: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Process selection Deciding on the way production of

goods or services will be organized Major implications

Capacity planning Layout of facilities Equipment Design of work systems

IntroductionIntroduction

Page 5: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Forecasting

Product andService Design

TechnologicalChange

CapacityPlanning

ProcessSelection

Facilities andEquipment

Layout

WorkDesign

Process Selection and Process Selection and System DesignSystem Design

Page 6: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

• Key aspects of process strategy– Capital intensive (mix of equipment/labor)

– Process flexibility

– Design

– Volume

– Technology

Process StrategyProcess Strategy

Page 7: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Kinds of TechnologyKinds of Technology

Operations management is primarily concerned with three kinds of technology: Product and service technology Process technology Information technology

All three have a major impact on: Costs Productivity Competitiveness

Page 8: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Technology Competitive Technology Competitive AdvantageAdvantage

Innovations in Products and services

Cell phonesPDAsWireless computing

Processing technology Increasing productivity Increasing qualityLowering costs

Page 9: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Variety How much

Flexibility What degree

Volume Expected output

Job Shop

Batch

Repetitive

Continuous

Process SelectionProcess Selection

Page 10: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Job shop Small scale

Batch Moderate volume

Repetitive/assembly line High volumes of standardized goods or

services

Continuous Very high volumes of non-discrete goods

Process TypesProcess Types

Page 11: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Process Type

Job Shop Appliance repairEmergency

room

Ineffective

Batch Commercialbaking

ClassroomLecture

Repetitive Automotiveassembly

Automaticcarwash

Continuous(flow)

Ineffective Steel ProductionWater purification

Product and Service Product and Service ProcessesProcesses

Low Volume High Volume

Page 12: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Dimension Job shop Batch Repetitive Continuous

Job variety Very High Moderate Low Very low

Process flexibility

Very High Moderate Low Very low

Unit cost Very High Moderate Low Very low

Volume of output

Very low Low High Very High

Product – Process MatrixProduct – Process Matrix

Other issues; schedulingwork-in-process inventorylabor skill

Page 13: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Process and Product ProfilingProcess and Product Profiling Process selection can involve substantial

investment in Equipment Layout of facilities

Product profiling: Linking key product or service requirements to process capabilities

Key dimensions Range of products or services Expected order sizes Pricing strategies Expected schedule changes Order winning requirements

Page 14: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Automation: Machinery that has sensing and control devices that enables it to operate Fixed automation Programmable automation

AutomationAutomation

Page 15: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

• Computer-aided design and manufacturing systems (CAD/CAM)

• Numerically controlled (NC) machines

• Robot

• Manufacturing cell

• Flexible manufacturing systems(FMS)

• Computer-integrated manufacturing (CIM)

AutomationAutomation

Page 16: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Layout: the configuration of departments, work centers, and equipment, with particular emphasis on movement of work (customers

or materials) through the system

Product layouts

Process layouts

Fixed-Position layout

Combination layouts

Facilities LayoutFacilities Layout

Page 17: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Objective of Layout DesignObjective of Layout Design

1. Facilitate attainment of product quality2. Use workers and space efficiently3. Avoid bottlenecks4. Minimize unnecessary material handling

costs5. Eliminate unnecessary movement of

workers or materials6. Minimize production time or customer

service time7. Design for safety

Page 18: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Requires substantial investments of money and effort

Involves long-term commitments Has significant impact on cost and

efficiency of short-term operations

Importance of Layout Importance of Layout DecisionsDecisions

Page 19: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Inefficient operations

For Example:

High CostBottlenecks

Changes in the designof products or services

The introduction of newproducts or services

Accidents

Safety hazards

The Need for Layout DesignThe Need for Layout Design

Page 20: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Changes inenvironmentalor other legalrequirements

Changes in volume ofoutput or mix of

products

Changes in methodsand equipment

Morale problems

The Need for Layout Design The Need for Layout Design (Cont’d)(Cont’d)

Page 21: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Product layouts

Process layouts

Fixed-Position layout

Combination layouts

Basic Layout TypesBasic Layout Types

Page 22: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Product layout Layout that uses standardized processing

operations to achieve smooth, rapid, high-volume flow

Process layout Layout that can handle varied processing

requirements Fixed Position layout

Layout in which the product or project remains stationary, and workers, materials, and equipment are moved as needed

Basic Layout TypesBasic Layout Types

Page 23: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Raw materialsor customer

Finished item

Station 2

Station 2

Station 3

Station 3

Station 4

Station 4

Material and/or labor

Station 1

Material and/or labor

Material and/or labor

Material and/or labor

Used for Repetitive or Continuous Processing

Product LayoutProduct Layout

Page 24: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

High rate of output Low unit cost Labor specialization Low material handling cost High utilization of labor and equipment Established routing and scheduling Routine accounting, purchasing and

inventory control

Advantages of Product LayoutAdvantages of Product Layout

Page 25: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Creates dull, repetitive jobs Poorly skilled workers may not maintain

equipment or quality of output Fairly inflexible to changes in volume Highly susceptible to shutdowns Needs preventive maintenance Individual incentive plans are

impractical

Disadvantages of Product LayoutDisadvantages of Product Layout

Page 26: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

1 2 3 4

5

6

78910

In

Out

Workers

A U-Shaped Production LineA U-Shaped Production Line

Ease to cross-travel of workers and vehicles More compact More communication between workers

Page 27: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Work Station 1

Work Station 2

Work Station 3

Product Layout(sequential)

Used for Repetitive Processingor Continuous Processes

Product LayoutProduct Layout

Page 28: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Dept. A

Dept. B Dept. D

Dept. C

Dept. F

Dept. E

Used for Intermittent processingJob Shop or Batch Processes

Process Layout(functional)

Process LayoutProcess Layout

Page 29: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Can handle a variety of processing requirements

Not particularly vulnerable to equipment failures

Equipment used is less costly Possible to use individual incentive

plans

Advantages of Process LayoutsAdvantages of Process Layouts

Page 30: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

In-process inventory costs can be high Challenging routing and scheduling Equipment utilization rates are low Material handling slow and inefficient Complexities often reduce span of supervision Special attention for each product or customer Accounting and purchasing are more involved

Disadvantages of Process Disadvantages of Process LayoutsLayouts

Page 31: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Fixed Position LayoutsFixed Position Layouts

Fixed Position Layout: Layout in which the product or project remains stationary, and workers, materials, and equipment are moved as needed.

Nature of the product dictates this type of layout Weight Size Bulk

Large construction projects

Page 32: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Cellular Production Layout in which machines are grouped into

a cell that can process items that have similar processing requirements

Group Technology The grouping into part families of items with

similar design or manufacturing characteristics

Cellular LayoutsCellular Layouts

Page 33: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Dimension Functional CellularNumber of moves between departments

many few

Travel distances longer shorter

Travel paths variable fixed

Job waiting times greater shorter

Throughput time higher lower

Amount of work in process

higher lower

Supervision difficulty higher lower

Scheduling complexity higher lower

Equipment utilization lower higher

Functional vs. Cellular LayoutsFunctional vs. Cellular Layouts

Page 34: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Warehouse and storage layouts Retail layouts Office layouts

Service LayoutsService Layouts

Page 35: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Line Balancing is the process of assigning tasks to workstations in such a way that the workstations have approximately equal time requirements.

Design Product Layouts: Line Design Product Layouts: Line BalancingBalancing

Page 36: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Cycle time is the maximum time allowed at each workstation tocomplete its set of tasks on a unit.

Cycle TimeCycle Time

Page 37: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

D

OT = timecycle = CT

rateoutput Desired= D

dayper timeoperating OT

CT

OT = rateOutput

D

OT = timecycle = CT

rateoutput Desired= D

dayper timeoperating OT

CT

OT = rateOutput

Determine Maximum OutputDetermine Maximum Output

Page 38: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

task timeof sum = t

CT

t)( =N

Determine the Minimum Number Determine the Minimum Number

of Workstations Requiredof Workstations Required

Page 39: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Precedence diagram: Tool used in line balancing to display elemental tasks and sequence requirements

A Simple Precedence Diagrama b

c d e

0.1 min.

0.7 min.

1.0 min.

0.5 min. 0.2 min.

Precedence DiagramPrecedence Diagram

Page 40: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Arrange tasks shown in Figure 6.10 into three workstations. Use a cycle time of 1.0 minute Assign tasks in order of the most number of

followers

Example 1: Assembly Line Example 1: Assembly Line BalancingBalancing

Page 41: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Workstation

TimeRemaining Eligible

AssignTask

RevisedTime Remaining

StationIdle Time

1 1.0

0.9

0.2

a, c

c

none

a

c

-

0.9

0.2

0.2

2 1.0 b b 0.0 0.0

3 1.0

0.5

0.3

d

e

-

d

e

-

0.5

0.3 0.3

0.5

Example 1 SolutionExample 1 Solution

Page 42: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Percent idle time = Idle time per cycle

(N)(CT)

Efficiency = 100 – Percent idle time

Calculate Percent Idle TimeCalculate Percent Idle Time

Page 43: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Assign tasks in order of most following tasks. Count the number of tasks that follow

Assign tasks in order of greatest positional weight.

Positional weight is the sum of each task’s time and the times of all following tasks.

Some Heuristic (intuitive) Rules:

Line Balancing RulesLine Balancing Rules

Page 44: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Example 2Example 2Plan to produce 400 units in 1 day (8 hours)

Immediate Task time Task follower (min)a b 0.2b e 0.2c d 0.8d f 0.6e f 0.3f g 1.0g h 0.4h end 0.3

c d

a b e

f g h

0.2 0.2 0.3

0.8 0.6

1.0 0.4 0.3

Page 45: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Station 1 Station 2 Station 3 Station 4

a b ef

d

g h

c

Solution to Example 2Solution to Example 2

Page 46: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

1 min.2 min.1 min.1 min. 30/hr. 30/hr. 30/hr. 30/hr.

Bottleneck

Bottleneck WorkstationBottleneck Workstation

Page 47: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Parallel WorkstationsParallel Workstations

1 min.

2 min.

1 min.1 min. 60/hr.

30/hr. 30/hr.

60/hr.

2 min.

30/hr.30/hr.

Parallel Workstations

Page 48: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Copier ExampleCopier Example

This means that This means that tasks B and E tasks B and E cannot be done cannot be done until task A has until task A has been completedbeen completed

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666

Page 49: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Copier ExampleCopier Example

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666 I

GF

C

D

H

B

E

A

10

1112

5

4 3

711 3

Figure 9.13

Page 50: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

I

GF

C

D

H

B

E

A

10

1112

5

4 3

711 3

Figure 9.13

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666

Copier ExampleCopier Example480 available

mins per day40 units required

Cycle time =

Production time available per day

Units required per day

= 480 / 40= 12 minutes per unit

Minimum number of

workstations=

∑ Time for task i

Cycle time

n

i = 1

= 66 / 12= 5.5 or 6 stations

Page 51: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

I

GF

C

D

H

B

E

A

10

1112

5

4 3

711 3

Figure 9.13

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666

Copier ExampleCopier Example480 available

mins per day40 units required

Cycle time = 12 mins

Minimum workstations = 5.5 or 6

Line-Balancing Heuristics

1. Longest task time Choose the available task with the longest task time

2. Most following tasks Choose the available task with the largest number of following tasks

3. Ranked positional weight

Choose the available task for which the sum of following task times is the longest

4. Shortest task time Choose the available task with the shortest task time

5. Least number of following tasks

Choose the available task with the least number of following tasks

Table 9.4

Page 52: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

480 available mins per day

40 units required

Cycle time = 12 mins

Minimum workstations = 5.5 or 6

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666

Copier ExampleCopier Example

I

GF

H

C

D

10 11

12

5

4

3 7

11

3B

E

A

Station 1

Station 2

Station 3

Station 5

Station 4

Station 6

Figure 9.14

Page 53: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

PerformancePerformance Task Must FollowTask Must FollowTimeTime Task ListedTask Listed

TaskTask (minutes)(minutes) BelowBelow

AA 1010 ——BB 1111 AACC 55 BBDD 44 BBEE 1212 AAFF 33 C, DC, DGG 77 FFHH 1111 EEII 33 G, HG, H

Total time Total time 6666

Copier ExampleCopier Example480 available

mins per day40 units required

Cycle time = 12 mins

Minimum workstations = 5.5 or 6

Efficiency =∑ Task times

(actual number of workstations) x (largest cycle time)

= 66 minutes / (6 stations) x (12 minutes)

= 91.7%

Page 54: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Example 1Example 1PerformancePerformance Task Must FollowTask Must Follow

TimeTime Task ListedTask ListedTaskTask (minutes)(minutes) BelowBelow

11 0.200.20 --22 0.400.40 --33 0.700.70 1144 0.100.10 1,21,255 0.300.30 2266 0.110.11 3377 0.320.32 3388 0.600.60 3,43,499 0.270.27 6,7,86,7,8

1010 0.380.38 5,85,8

1111 0.500.50 9,109,10

1212 0.120.12 1111

Total time 4 min.Total time 4 min.

Balance by Balance by

1 Longest task time 1 Longest task time methodmethod

2 RPW method2 RPW method

Page 55: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Example 2Example 2PerformancePerformance Task Must FollowTask Must Follow

TimeTime Task ListedTask ListedTaskTask (minutes)(minutes) BelowBelow

11 0.50.5 --22 0.30.3 1133 0.80.8 1144 0.20.2 2255 0.10.1 2266 0.60.6 3377 0.40.4 4,54,588 0.50.5 3,53,599 0.30.3 7,87,8

1010 0.60.6 6,96,9

Total time 4.3 min.Total time 4.3 min.

Balance by Balance by

1 Longest task time 1 Longest task time methodmethod

2 RPW method2 RPW method

Page 56: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Information Requirements:

1. List of departments

2. Projection of work flows

3. Distance between locations

4. Amount of money to be invested

5. List of special considerations

6. Location of key utilities

Designing Process LayoutsDesigning Process Layouts

Page 57: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

1 3 2

30

170 100

A B C

Example 3: Interdepartmental Work Example 3: Interdepartmental Work FlowsFlows

for Assigned Departmentsfor Assigned Departments

Page 58: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Gearcutting

Mill Drill

Lathes

Grind

Heattreat

Assembly

111

333

222

444

222111444

111 3331111 2222

222

3333

111

444111

333333333

44444

3333

3322

222

Functional LayoutFunctional Layout

Page 59: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

1111 -1111

2222 - 2222

Ass

emb

ly

3333 - 3333

4444 - 4444

Lathe

Lathe

Mill

Mill

Mill

Mill

Drill

Drill

Drill

Heat treat

Heat treat

Heat treat

Gear cut

Gear cut

Grind

Grind

Cellular Manufacturing LayoutCellular Manufacturing Layout

Page 60: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Used to obtain optimal solutions to problems that involve restrictions or limitations, such as: Materials Budgets Labor Machine time

Linear ProgrammingLinear Programming

Page 61: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Objective Function: mathematical statement of profit or cost for a given solution

Decision variables: amounts of either inputs or outputs

Feasible solution space: the set of all feasible combinations of decision variables as defined by the constraints

Constraints: limitations that restrict the available alternatives

Parameters: numerical values

Linear Programming ModelLinear Programming Model

Page 62: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

1.Set up objective function and constraints in mathematical format

2.Plot the constraints

3.Identify the feasible solution space

4.Plot the objective function

5.Determine the optimum solution

Graphical Linear ProgrammingGraphical Linear Programming

Graphical method for finding optimal solutions to two-variable problems

Page 63: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Objective - profitMaximize Z=60X1 + 50X2

Subject toAssembly 4X1 + 10X2 <= 100 hours

Inspection 2X1 + 1X2 <= 22 hours

Storage 3X1 + 3X2 <= 39 cubic feet

X1, X2 >= 0

Linear Programming ExampleLinear Programming Example

Page 64: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Assembly Constraint4X1 +10X2 = 100

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Pro

du

ct X

2

Linear Programming ExampleLinear Programming Example

Page 65: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Linear Programming ExampleLinear Programming Example

Add Inspection Constraint2X1 + 1X2 = 22

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Pro

du

ct X

2

Page 66: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Add Storage Constraint3X1 + 3X2 = 39

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Pro

du

ct X

2

AssemblyStorage

Inspection

Feasible solution space

Linear Programming ExampleLinear Programming Example

Page 67: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Add Profit Lines

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Pro

du

ct X

2

Z=300

Z=900

Z=600

Linear Programming ExampleLinear Programming Example

Page 68: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

The intersection of inspection and storage Solve two equations in two unknowns

2X1 + 1X2 = 223X1 + 3X2 = 39

X1 = 9X2 = 4Z = $740

SolutionSolution

Page 69: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Solutions and Corner PointsSolutions and Corner Points

Feasible solution space is usually a polygon Solution will be at one of the corner points

Enumeration approach: Substituting the coordinates of each corner point into the objective function to determine which corner point is optimal.

Page 70: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

Simplex: a linear-programming algorithm that can solve problems having more than two decision variables

Simplex MethodSimplex Method

Page 71: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

MS Excel Worksheet for MS Excel Worksheet for Microcomputer ProblemMicrocomputer Problem

Page 72: Process Selection and Facility Layout. Learning Objectives  Explain the strategic importance of process selection.  Explain the influence that process

MS Excel Worksheet SolutionMS Excel Worksheet Solution