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Example of Aggregate Production Plan

Purchasing cost = $100 per work-force Quarter Sales ForeRetiring cost = $500 per work-force Spring 80,000Inventory carrying cost = $0.50 per kg Summer 50,000Production per resource unit = 1,000 kg per quarter Fall 120,000

Beginning resource = 100 work-force Winter 150,000

1. Chase Demand Strategy

Spring 80,000 80,000 80 0 20Summer 50,000 50,000 50 0 30Fall 120,000 120,000 120 70 0Winter 150,000 150,000 150 30 0

Total 400,000 400,000 100 50

Cost $10,000 $25,000

Total Cost

2. Level Production Strategy

Spring 80,000 100,000 20,000Summer 50,000 100,000 70,000

Fall 120,000 100,000 50,000Winter 150,000 100,000 0Total 400,000 400,000 140,000

Total Cost $70,000.00

3. Mixed Strategy (1)

Spring 80,000 90,000 0 10,000 90 0Summer 50,000 80,000 10,000 40,000 80 0Fall 120,000 110,000 40,000 30,000 110 30Winter 150,000 120,000 30,000 0 120 10

Total 400,000 400,000 80,000 40

Cost $40,000.00 $4,000

Total Cost

Quarter

Quarter

Sales

Forecast

Production

Plan

Beginning

Inventory

$54,000.00

Ending

Inventory

WF

Needed

WF

Obtained

WF Needed WF Obtained

WF

Retired

$35,000

Quarter

Sales

Forecast

Production

Plan Inventory

Sales

Forcast

Production

Plan

8/2/2019 APP Example

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cast (kg)

101000

20$10,000

WF

Retired

8/2/2019 APP Example

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Example of Aggregate Production Plan

Purchasing cost = $100 per work-force Quarter Sales Forecast (kg)Retiring cost = $500 per work-force Spring 80,000Inventory carrying cost = $0.50 per kg Summer 50,000Production per resource unit = 1,000 kg per quarter Fall 120,000

Beginning resource = 100 work-force Winter 150,000Beginning inventory = 0 kgMinimum production = 50,000 kg

1. Mixed Strategy (Optimization)

Spring 80,000 80,000 0 0 80 0 20Summer 50,000 80,000 0 30,000 79.99998 0 1.575E-05Fall 120,000 90,000 30,000 0 90.00002 10.00003 0

Winter 150,000 150,000 0 0 150 59.99998 0

Total 400,000 400,000 30,000 70.00002 20.000016Cost $14,999.99 $7,000 $10,000Total Cost

WF

Needed

WF

Obtained

WF

Retired

$32,000.00

Quarter

Sales

Forecast

Production

Plan

Beginning

Inventory

Ending

Inventory

8/2/2019 APP Example

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Microsoft Excel 12.0 Answer ReportWorksheet: [APP Example.xls]Optimization 1Report Created: 3/7/2009 8:27:57 AM

Target Cell (Min)

Cell Name Original Value Final Value

$F$21 Total Cost Ending Inventory $177,000.00 $32,000.00

Adjustable Cells

Cell Name Original Value Final Value

$D$15 Spring Production Plan 80,000 80,000$D$16 Summer Production Plan 50,000 80,000$D$17 Fall Production Plan 220,000 90,000$D$18 Winter Production Plan 50,000 150,000

Constraints

Cell Name Cell Value Formula Status Slack$D$19 Total Production Plan 400,000 $D$19=400000 Not Binding 0$F$19 Total Ending Inventory 30,000 $F$19>=0 Not Binding 30,000$F$15 Spring Ending Inventory 0 $F$15>=0 Binding 0$F$16 Summer Ending Inventory 30,000 $F$16>=0 Not Binding 30,000$F$17 Fall Ending Inventory 0 $F$17>=0 Binding 0$F$18 Winter Ending Inventory 0 $F$18>=0 Binding 0$D$17 Fall Production Plan 90,000 $D$17>=$D$9 Not Binding 40,000$D$15 Spring Production Plan 80,000 $D$15>=$D$9 Not Binding 30,000$D$16 Summer Production Plan 80,000 $D$16>=$D$9 Not Binding 30,000$D$18 Winter Production Plan 150,000 $D$18>=$D$9 Not Binding 100,000

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Microsoft Excel 12.0 Sensitivity ReportWorksheet: [APP Example.xls]Optimization 1Report Created: 3/7/2009 8:27:57 AM

Adjustable Cells

Final Reduced

Cell Name Value Gradient$D$15 Spring Production Plan 80,000 0$D$16 Summer Production Plan 80,000 0$D$17 Fall Production Plan 90,000 0$D$18 Winter Production Plan 150,000 0

Constraints

Final LagrangeCell Name Value Multiplier

$D$19 Total Production Plan 400,000 1$F$19 Total Ending Inventory 30,000 0$F$15 Spring Ending Inventory 0 1$F$16 Summer Ending Inventory 30,000 0$F$17 Fall Ending Inventory 0 1$F$18 Winter Ending Inventory 0 0

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Example of Aggregate Production Plan

Purchasing cost = $100 per work-force Quarter Sales Forecast (kg)Retiring cost = $500 per work-force Spring 80,000Inventory carrying cost = $0.50 per kg Summer 50,000Production per resource unit = 1,000 kg per quarter Fall 120,000

Beginning resource = 100 work-force Winter 150,000Beginning inventory = 10,000 kgMinimum production = 50,000 kg

1. Mixed Strategy (Optimization)

Spring 80,000 70,000 10,000 0 70 0 30Summer 50,000 70,000 0 20,000 69.99996 0 4.164E-05Fall 120,000 100,000 20,000 0 100 30.00008 0

Winter 150,000 160,000 0 10,000 160 59.99996 0

Total 400,000 400,000 30,000 90.00004 30.000042Cost $14,999.98 $9,000 $15,000Total Cost

WF

Obtained

WF

Retired

$39,000.00

Quarter

Sales

Forecast

Production

Plan

Beginning

Inventory

Ending

Inventory

WF

Needed

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Microsoft Excel 12.0 Answer ReportWorksheet: [APP Example.xls]Optimization 2Report Created: 3/7/2009 8:29:18 AM

Target Cell (Min)

Cell Name Original Value Final Value

$F$21 Total Cost Ending Inventory $106,000.00 $39,000.00

Adjustable Cells

Cell Name Original Value Final Value

$D$15 Spring Production Plan 70,000 70,000$D$16 Summer Production Plan 120,000 70,000$D$17 Fall Production Plan 50,000 100,000$D$18 Winter Production Plan 160,000 160,000

Constraints

Cell Name Cell Value Formula Status Slack$D$19 Total Production Plan 400,000 $D$19=400000 Not Binding 0$F$19 Total Ending Inventory 30,000 $F$19>=0 Not Binding 30,000$F$15 Spring Ending Inventory 0 $F$15>=0 Binding 0$F$16 Summer Ending Inventory 20,000 $F$16>=0 Not Binding 20,000$F$17 Fall Ending Inventory 0 $F$17>=0 Binding 0$F$18 Winter Ending Inventory 10,000 $F$18>=0 Not Binding 10,000$D$17 Fall Production Plan 100,000 $D$17>=$D$9 Not Binding 50,000$D$15 Spring Production Plan 70,000 $D$15>=$D$9 Not Binding 20,000$D$16 Summer Production Plan 70,000 $D$16>=$D$9 Not Binding 20,000$D$18 Winter Production Plan 160,000 $D$18>=$D$9 Not Binding 110,000

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Microsoft Excel 12.0 Sensitivity ReportWorksheet: [APP Example.xls]Optimization 2Report Created: 3/7/2009 8:29:18 AM

Adjustable Cells

Final Reduced

Cell Name Value Gradient$D$15 Spring Production Plan 70,000 0$D$16 Summer Production Plan 70,000 0$D$17 Fall Production Plan 100,000 0$D$18 Winter Production Plan 160,000 0

Constraints

Final LagrangeCell Name Value Multiplier

$D$19 Total Production Plan 400,000 1$F$19 Total Ending Inventory 30,000 0$F$15 Spring Ending Inventory 0 1$F$16 Summer Ending Inventory 20,000 0$F$17 Fall Ending Inventory 0 1$F$18 Winter Ending Inventory 10,000 0

8/2/2019 APP Example

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Example of Aggregate Production Plan

Purchasing cost = $100 per work-force Quarter Sales Forecast (kg)Retiring cost = $500 per work-force Spring 80,000Inventory carrying cost = $0.50 per kg Summer 50,000Production per resource unit = 1,000 kg per quarter Fall 120,000

Beginning resource = 100 work-force Winter 150,000Beginning inventory = - kgMinimum production = 80,000 kg

1. Mixed Strategy (Optimization)

Spring 80,000 80,000 0 0 80 0 20Summer 50,000 80,000 0 30,000 80 0 0Fall 120,000 90,000 30,000 0 90 10 0

Winter 150,000 150,000 0 0 150 60 0

Total 400,000 400,000 30,000 70 20Cost $15,000.00 $7,000 $10,000Total Cost

WF

Obtained

WF

Retired

$32,000.00

Quarter

Sales

Forecast

Production

Plan

Beginning

Inventory

Ending

Inventory

WF

Needed

8/2/2019 APP Example

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Example of Aggregate Production Plan

Purchasing cost = $100 per work-force Quarter Sales Forecast (kg)Retiring cost = $500 per work-force Spring 80,000Inventory carrying cost = $0.50 per kg Summer 50,000Production per resource unit = 1,000 kg per quarter Fall 120,000

Beginning resource = 50 work-force Winter 150,000Beginning inventory = 0 kgMinimum production = 50,000 kg

1. Mixed Strategy (Optimization)

Spring 80,000 80,000 0 0 80 30 0Summer 50,000 80,000 0 30,000 79.99996 0 4.414E-05Fall 120,000 90,000 30,000 0 90.00004 10.00009 0

Winter 150,000 150,000 0 0 150 59.99996 0

Total 400,000 400,000 30,000 100 4.414E-05Cost $14,999.98 $10,000 $0Total Cost

WF

Obtained

WF

Retired

$25,000.00

Quarter

Sales

Forecast

Production

Plan

Beginning

Inventory

Ending

Inventory

WF

Needed