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IE652 ProductionPlanning and Control

Instructor: Dr. Rıfat Gürcan Özdemir, Assist. Prof.

Teaching Assistant: İlkay Gültaş

http://web.iku.edu.tr/~rgozdemir/index(ie_652).htm

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Course MaterialsText Books1. “Production Planning, Control and Integration”,

D. Sipper and R. Bulfin, McGraw-Hill, 1997.2. “Operations Research in Production Planning, Scheduling,

and Inventory Control”, D.C. Montgomery, L. A. Johnson, John Wiley & Sons, 1974

Software“GAMS LP Solver”

Lecture notes1. “pdf files of Power Point Slides” (will be given via internet)

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Course Topics

PART I – Aggregare production planning

Chapter 1:

Aggregate Production Planning through Spread Sheet Models and Transportation Models

Chapter 2:

Production Planning through Static LinearProgramming Models

Chapter 3:

Aggregate Production Planning throughDynamic Linear Programming Models

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Course TopicsPART II – Inventory management

Chapter 4:

Inventory Management and EOQ ModelsChapter 5:

Quantity Discount and Multi Item InventoryModels

Chapter 6:

Dynamic Lot Sizing TechniquesChapter 7:

Sthocastic Inventory ModelsChapter 8:

Material Requirements Planning (MRP)

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Course Topics

PART III – Job scheduling

Chapter 9:

Scheduling and SequencingChapter 10:

Single Machine SchedulingChapter 11:

Parallel Machine, Flow Shop and Job ShopScheduling

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Grading

� Exams (85% of total grade)�Quizzes (10%)�Midterm I (20%) �Midterm II (20%)�Final (35%)

� Assignments (10% of total grade)� Participation (5% of total grade)

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IE652 - Chapter 1

Aggregate Production Planningthrough Spread Sheet andTransportation Models

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Aggregate Production Planning

� Aggregate production planning is usedto satisfy the intermediate-range demandforecasts.

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Aggregate Production Planning� Step 1. Aggregation: Different products are

aggregated into a common unit.� Step 2. Planning: Demand fluctuations are

absorbed by:� Changing the size of the workforce (hiring & laying

off),� Varying the production rate (introduction of overtime

and/or idle time, relying on outside subcontracting),� Accumulating seasonal inventories,� Resorting to planned backlogs whenever customers

may accept delays in filling their orders,� Shifting the demand to another period.

or a combination of these decisions

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Basic Aggregate ProductionPlanning Strategies

� Since the demand, cost components orcapacities may change over time, theconditions that affect the productionprocesses will be unstable

� Therefore, it is important to prevent underand overloading of fixed resourses and tosmooth aggregate production levels

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11

Holding inventories

time

dem

and

Producion capacity

+inventory

–inventory

+inventory

12

Allowing for backlogging(backordering)

time

dem

and

Producion capacity

–backordering

backordering+

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13

Allowing overtime or subcontracting

time

dem

and

Producion capacity

Overtime and/orsubcontracting

+

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Costs relevant to aggregateproduction planning1. Basic production costs

• Material• Direct labor• Overhead= fixed cost (setup cost) + variable cost

2. Production rate change costs• Hiring personnel• Training personnel• Laying off personnel• Overtime compensations• Subcontracting

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Costs relevant to aggregateproduction planning

3. Inventory related costs

• Inventory holding cost(= cost of capital tied up in inventory + storing +

insurance + taxes + spoilage + obsolescense)

• Shortage cost(very difficult to measure; loss of customer

goodwill and loss of sales revenues resulting

from the shortage situation)

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Planning Strategies

1st Strategy: Changing workforce levels

Compensation of laying off.Laying off personnel in caseof a decrease in demand

Promotion, travelling, interview, training, etc. expenses.

Hiring personnel in case of an increase in demand

Relevant CostsMethod

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Planning Strategies2nd Strategy: Changing production levels

Additional costs of subcontracting

Use subcontracting

Overtime compensationsIntroducing overtime withoutchanging workforce levels

Relevant CostsMethod

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Planning Strategies3rd Strategy: Keeping inventory, and

allowing for backlogging

Inventory holding costsHolding the product in slackperiods

Costs of advertisement, promotion or discountprograms

Shifting demand to slackperiods

Delay in cash flow, loss of customers

Backlogging the product tofollowing periods

Relevant CostsMethod

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Example 3.1� A company is to plan workforce and production levels for

the six-month period January to June.� Forecast demands over the next six months for a

particular line of products are as follows:

15

1400

June

1252226182420Working days

7420200012009006401280Demand

TotalMayAprilMarchFeb.Jan.Month

� Ending inventory in December (current month) is expected to be 500 units, and the firm would like to have600 units on hand at the end of June

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Example 3.1 Continued� There are currently (end of December) 300

workers in the plant� There are only three costs to be considered:

� Cost of hiring workers = CH = $500 /worker� Cost of firing workers = CF = $1000 /worker� Cost of holding inventory = CI = $80/unit/month

� shortages are not permitted, i.e., cumulativeproduction at least as great as cumulativedemand each period

� K = 0.14653 (number of aggregate unitsproduced by one worker in one day

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21Demand of June = 1400 + 600 = 2000

Demand of January = 1280 – 500 = 780

Fixed Workforce Plan (Workforce Level)E=B/DD=C*KCBA

18.316

16.118

12.895

9.085

6.447

2.931

Cumulative

Units/Worker

125

110

88

62

44

20

Cumulative

Working Days

7520

5520

3520

2320

1420

780

Cumulative

Demand

411June

343May

273April

256March

221February

267January

Number of

WorkersMonth

K= 0.14653 (number of aggregate units produced by one worker in one day

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Fixed Workforce Plan

5962Total

7520

5520

3520

2320

1420

780

Cumulative

Net Demand

D

7528

6625

5300

3734

2650

1205

Cumulative

Production

C=B*411

18.316

16.118

12.895

9.085

6.447

2.931

Cumulative

Units/Worker

B

8

1105

1780

1414

1230

425

Ending

Inventory

E = C – D A

June

May

April

March

February

January

Month

12

23

Fixed Workforce Plan

CumulativeDemand

CumulativeProduction

1 2 3 4 5 6

1

2

3

4

5

6

7

8C

umul

ativ

enu

mbe

rof

uni

ts(t

hous

and)

Month

24

Cost of Plan

Hiring Cost = (411 – 300)500 = $55,500

Inventory

Holding Cost = (5962 + 600)80 = $524,960

Total Cost = 55,500 + 524,960 = $580,460

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25Demand of June = 1400 + 600 = 2000

Demand of January = 1280 – 500 = 780

Zero Inventory Plan (Workforce Level)E=B/DD=C*KCBA

2.198

3.224

3.810

2.638

3.517

2.931

Units/Worker

15

22

26

18

24

20

Working Days

2000

2000

1200

900

640

780

Demand

910June

621May

315April

342March

182February

267January

Number of

WorkersMonth

K= 0.14653 (number of aggregate units produced by one worker in one day

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Zero Inventory Plan

7527

5527

3525

2325

1423

783

Units

Produced

D=B*C

910

621

315

342

182

267

Number of

Workers

C

145755Total

27

85

33

Workers

Fired

F=Ct-1-Ct

289

306

160

Workers

Hired

E=Ct-Ct-1

2.198

3.224

3.810

2.638

3.517

2.931

Units/Worker

BA

June

May

April

March

Feb.

Jan.

Month

14

27

Zero Inventory Plan

7520

5520

3520

2320

1420

780

Cumulative

Net Demand

D

7527

5527

3525

2325

1423

783

Units

Produced

B

30Total

7

7

5

5

3

3

Ending

Inventory

E=C-D

7527

5527

3525

2325

1423

783

Cumulative

Production

CA

June

May

April

March

Feb.

Jan.

Month

28

Zero Inventory Plan

Cumulative Demand

Cumulative Production

1 2 3 4 5 6

1

2

3

4

5

6

7

8

Cum

ulat

ive

num

ber

of u

nits

(th

ousa

nd)

Month

15

29

Cost of Plan

Total Cost = $572,900

Inventory

Holding Cost = (30 + 600) 80 = $50,400

Firing Cost = 145 (1000) = $145,000

Hiring Cost = 755 (500) = $377,500

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Mixed Strategy

18.318

16.120

12.896

9.086

6.448

2.931

Cumulative

Number of Units

Produced per Worker

C D = B / CBA

4117520June

3435520May

2733520April

2562320March

2211420February

267780January

Ratio

(rounded up)

Cumulative

Net DemandMonth

Workforce level for the first four months

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31

Mixed Strategy

5.422

3.224

Cumulative

Number of Units

Produced per Worker

C D = B / CBA

7384000June

6212000May

Ratio

(rounded up)

Cumulative

Net DemandMonth

Workforce level for the last two months

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Mixed Strategy

738

738

273

273

273

273

Number of

Workers

B

1622

2379

1040

720

960

800

Monthly

Production

D = B x C

2.198

3.224

3.810

2.638

3.517

2.931

Number of Units

Produced per Worker

CA

June

May

April

March

February

January

Month

17

33

Mixed Strategy

7520

5520

3520

2320

1420

780

Cumulative

Net Demand

D

7521

5899

3520

2480

1760

800

Cumulative

Production

C

1622

2379

1040

720

960

800

Monthly

Production

B

1

379

0

160

340

20

Ending

Inventory

E = D – C A

June

May

April

March

February

January

Month

Σ = 900

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Mixed Strategy

Cumulative Demand

Cumulative Production

1 2 3 4 5 6

1

2

3

4

5

6

7

8

Cum

ulat

ive

num

ber

of u

nits

(th

ousa

nd)

Month

18

35

Mixed Strategy

465

Number of

Hired

C

738

738

273

273

273

273

Number of

Workers

B

27

Number of

Fired

DA

June

May

April

March

February

January

Month

Total = 465 Total = 27

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Mixed Strategy

Total Cost = $379,500

Inventory

Holding Cost = (900 + 600) 80 = $120,000

Firing Cost = 27 (1000) = $27,000

Hiring Cost = 465 (500) = $232,500

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Transportation Model

� Optimal mixed strategy solutions can be found by transportation models

� Costs such as:• cr = regular time production cost

• co = overtime production cost

• cs = subcontract production cost

• c = inventory holding cost

• b = backordering cost

are combined into transportation costs

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Transportation Costs When Backordering is not Allowed

csSubcontract

coOvertime4

crRegular Time

cs+ccsSubcontract

co+ccoOvertime3

cr+ccrRegular Time

cs+2ccs+ccsSubcontract

co+2cco+ccoOvertime2

cr+2ccr+ccrRegular Time

cs+3ccs+2ccs+ccsSubcontract

co+3cco+2cco+ccoOvertime1

cr+3ccr+2ccr+ccrRegular Time

3c2cc0Beginning InventoryProduction Period

4321Demand Period

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Transportation Costs When Backordering is Allowed

cscs+bcs+2bcs+3bSubcontract

coco+bco+2bco+3bOvertime4

crcr+bcr+2bcr+3bRegular Time

cs+ccscs+bcs+2bSubcontract

co+ccoco+bco+2bOvertime3

cr+ccrcr+bcr+2bRegular Time

cs+2ccs+ccscs+bSubcontract

co+2cco+ccoco+bOvertime2

cr+2ccr+ccrcr+bRegular Time

cs+3ccs+2ccs+ccsSubcontract

co+3cco+2cco+ccoOvertime1

cr+3ccr+2ccr+ccrRegular Time

3c2cc0Beginning InventoryProduction Period

4321Demand Period

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Example 3.2

/unit$25cs=Subcontract:

/unit$15co=Over time:

/unit$10cr=Regular time:

/unit/period$5c=Inventory holding:

Costs

Suppose that backordering is not allowed in aggregate planning

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Example 3.2 Continued

5000Subcontract =

500Over time =

1000Regular time =

1000Beginning inventory =

Capacities of production resources (in units)

Forecast demands for 4 succeeding periods:Period 1 2 3 4Demand 1500 2500 3000 2500

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Transportation Costs

25Subcontract

15Overtime4

10Regular Time

3025Subcontract

2015Overtime3

1510Regular Time

353025Subcontract

252015Overtime2

201510Regular Time

40353025Subcontract

30252015Overtime1

25201510Regular Time

151050Beginning InventoryProduction Period

4321Demand Period

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17500

Idle

2500

4

27000300025001500Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

500Overtime2

1000Regular Time

5000Subcontract

500Overtime1

1000Regular Time

1000Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

44

17500

Idle

2500

4

2600030002500500Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

500Overtime2

1000Regular Time

5000Subcontract

500Overtime1

1000Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

23

45

17500

Idle

2500

4

25500300025000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

500Overtime2

1000Regular Time

5000Subcontract

500Overtime1

500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

46

17500

Idle

2500

4

24500300015000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

500Overtime2

01000Regular Time

5000Subcontract

500Overtime1

500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

24

47

17500

Idle

2500

4

24000300010000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

500Overtime1

500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

48

17500

Idle

2500

4

2350030005000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

25

49

17500

Idle

2500

4

23000300000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

1000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

50

17500

Idle

2500

4

22000200000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

26

51

17500

Idle

2500

4

21500150000Demand

5000Subcontract

500Overtime4

1000Regular Time

5000Subcontract

0500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

52

17500

Idle

2500

4

20000000Demand

5000Subcontract

500Overtime4

1000Regular Time

35001500Subcontract

0500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

27

53

17500

Idle

1500

1000

4

19000000Demand

5000Subcontract

500Overtime4

0Regular Time

35001500Subcontract

0500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

54

17500

Idle

1000

500

1000

4

18500000Demand

5000Subcontract

0Overtime4

0Regular Time

35001500Subcontract

0500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

28

55

17500

Idle

0

1000

500

1000

4

17500000Demand

4000Subcontract

0Overtime4

0Regular Time

35001500Subcontract

0500Overtime3

01000Regular Time

5000Subcontract

0500Overtime2

01000Regular Time

5000Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25

56

0

4000

3500

5000

5000

Idle

0

1000

500

1000

4

0000Demand

0Subcontract

0Overtime4

0Regular Time

01500Subcontract

0500Overtime3

01000Regular Time

0Subcontract

0500Overtime2

01000Regular Time

0Subcontract

0500Overtime1

0500500Regular Time

0

1000

Beginning

Inventory

Production

Period

Capacity321Demand Period

10

0 5 10 15

15 20 25

15

25

20 25 30

30 35 40

10 15 20

15

25

20 25

30 35

10 15

15

25

20

30

10

15

25