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Transcript of IE652 Production Planning and Control - web.iku.edu.trweb.iku.edu.tr/~rgozdemir/lecture...
1
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
2
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)
2
3
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
4
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)
3
5
Course Topics
PART III – Job scheduling
Chapter 9:
Scheduling and SequencingChapter 10:
Single Machine SchedulingChapter 11:
Parallel Machine, Flow Shop and Job ShopScheduling
6
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)
4
IE652 - Chapter 1
Aggregate Production Planningthrough Spread Sheet andTransportation Models
8
Aggregate Production Planning
� Aggregate production planning is usedto satisfy the intermediate-range demandforecasts.
5
9
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
10
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
6
11
Holding inventories
time
dem
and
Producion capacity
+inventory
–inventory
+inventory
12
Allowing for backlogging(backordering)
time
dem
and
Producion capacity
–backordering
backordering+
7
13
Allowing overtime or subcontracting
time
dem
and
Producion capacity
Overtime and/orsubcontracting
+
14
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
8
15
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)
16
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
9
17
Planning Strategies2nd Strategy: Changing production levels
Additional costs of subcontracting
Use subcontracting
Overtime compensationsIntroducing overtime withoutchanging workforce levels
Relevant CostsMethod
18
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
10
19
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
20
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
11
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
22
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
13
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
26
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
30
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
16
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
32
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
34
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
36
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
19
37
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
38
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
20
39
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
40
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
21
41
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
42
Transportation Costs
25Subcontract
15Overtime4
10Regular Time
3025Subcontract
2015Overtime3
1510Regular Time
353025Subcontract
252015Overtime2
201510Regular Time
40353025Subcontract
30252015Overtime1
25201510Regular Time
151050Beginning InventoryProduction Period
4321Demand Period
22
43
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