Energy Business Modelling
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Transcript of Energy Business Modelling
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A B C D E F G H I J
Example 9.1 - An EOQ Model for Bedrock's Problem
Input Cells are shaded 100
Annual Demand 12,000
Ordering Cost 50.00 Order Holding Ordering Annual
Unit Cost 25.00 size cost cost cost
Unit holding cost per year (two options) 100 375 6,000 6,375
(i) in s per year 200 750 3,000 3,750
(ii) as % of unit cost 30.0% 300 1,125 2,000 3,125
Unit holding cost per year = 7.50 400 1,500 1,500 3,000
500 1,875 1,200 3,075
Output 600 2,250 1,000 3,250
EOQ 400.00 700 2,625 857 3,482
No. of Orders/Year 30.0 800 3,000 750 3,750
Total cost 303,000 Plot cell range F5:I14
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
100 200 300 400 500 600 700 800
A
nnualcost
Order quantity
EOQ graph
Holding cost Ordering cost Annual cost
Figure 8.4 Economic order quantity (EOQ) model.
(Note that this model has been modified)
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A B C D E F G
Example 9.2 - The PROQ Model and Solution to Gizmo's Problem.
Input Annual Demand 2,100
Setup Cost 450.00
Unit Cost 30.00
Annual production rate 2,500
Unit holding cost per year (two options)
(i) in s per year
(ii) as % of unit cost 20.0%
Annual unit holding cost = 6.00
Output PROQ 1403.12
Production run time,Ro(in weeks) 29.18
Optimal cycle time, To(in weeks) 34.74
Maximum inventory level 224.5Annual holding cost 673
Annual setup cost 673
Total cost 64,347
Cell Formula Copied to
E10 IF(E9="",E8,E5*E9)
E11 IF(E10=0,"Holding cost cannot be zero!","")
E12 SQRT(2*E3*E4/E10)*SQRT(E6/(E6 - E3))
E13 52*E12/E6
E14 52*E12/E3
E15 E12*(E6 - E3)/E6
E16 0.5*E10*E15E17 E3*E4/E12
E18 E16 + E17 + E3*E5
Figure 8.5 Production order quantity (PROQ) model.
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H I J K L M N O P Q
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Figure 8.5 Production order quantity (PROQ) model.
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A B C D E F G H I
Example 9.3 - A Quantity Discount Model for the Wheelie Company
InputAnnual Demand 1,500 User input cells
Ordering Cost 80.00 are shaded
Unit holding cost per year (two options)
(i) in s per year
(ii) as % of unit cost 30.0%
DISCOUNT TABLE Unit Cost = 10.00 8.00 6.00
Minimum discount quantity, Min i= 0 1000 2000
Annual unit holding cost = 3.00 2.40 1.80
Output Qi = 282.8 316.2 365.1
Adjusted order quantities = 282.8 1000.0 2000.0
Total costs = 15,849 13,320 10,860
Minimum total cost is 10,860 2
Optimal order quantity is 2000.0
Cycle time is 69.3 weeks
Cell Formula Copied to
F11 IF($G6="",$G7*F9,$G6) G11:H11
F12 IF(F11=0,"Holding cost cannot be zero!","")
F13 SQRT(2*$G3*$G4/F11) G13:H13
F14 IF(F13>F10,F13,F10) G14:H14
F15 $G3*$G4/F14 + 0.5*F14*F11 + $G3*F9 G15:H15
F17 MIN(F15:H15)H17 MATCH(F17,F15:H15,0) - 1
F18 OFFSET(F18,-4,H17)
F19 52*F18/G3
Figure 8.6 Quantity discount model for the Wheelie Company.
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A B C D E F G H I
Example 9.4 - A Delivery Charge Model for the Farmers' Co-operative
InputDaily Demand (in tonnes) 3.0 User input cells
Unit Cost 100.00 are shadedUnit holding cost per day (two options)
(i) in s per day 1.50
(ii) as % of unit cost
DELI VERY TABLE Reorder Cost = 80.00 130.00 180.00
Maximum delivery quantity, Maxi= 10 20 30
Daily unit holding cost = 1.50 1.50 1.50
Output Qi = 17.9 22.8 26.8
Adjusted order quantities = 10.0 20.0 26.8
Total costs = 332 335 340
Minimum total cost is 332 0
Optimal order quantity is 10.0
Cycle time is 3.3 days
Cell Formula Copied to
F13 SQRT(2*$G3*F9/F11) G13:H13
F14 IF(F13
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A B C D E F G H
Example 9.5 - An Inventory Model with Shortages Allowed
Input Annual Demand 12,000
Setup/Ordering Cost 50.00 User input cells
Unit Cost 25.00 are shaded
Holding cost (two options)
(i) in s per year
(ii) as % of unit cost 30.0%
Shortage cost per unit per year 4.00
Unit holding cost per year = 7.50
Output Optimal order size, Qo 678.2
Maximum stock level 235.9
Back-order size 442.3
No. of orders/year 17.7Cycle time 2.9 weeks
Annual Costs..
Setup/ordering cost 884.65
Holding cost 307.70
Shortage cost 576.95
Purchase cost 300,000
Total cost 301,769
Cell Formula Copied to
E10 IF(E8="",E7,E8*E5)
E11 IF(E10=0, "Enter a value in either cell E7 or E8!","")E13 SQRT(2*E3*E4*(E9 + E10)/(E9*E10))
E14 E9*E13/(E9 + E10)
E15 E13 - E14
E16 E3/E13
E17 52/E16
E19 E3*E4/E13
E20 0.5*E10*E14*E14/E13
E21 E9*(E13 - E14)^2/(2*E13)
E22 E3*E5
E23 SUM(E19:E22)
Figure 8.8 Deterministic model with planned storages.
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I J K L M N O P Q
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Figure 8.8 Deterministic model with planned storages.
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A B C D E F G H I J
Example 9.6 - An Inventory Model with Storage Space Constraints
Setup cost 1,500.0 User input cellsHolding cost (as % of unit cost) 30.0% are shaded
Product Demand Unit Space EOQ Average Variable
cost (per unit) (Qo) space costs
Widget 10,000 18.00 0.3 2357.0 353.6 12,728
Gadget 8,000 15.00 0.2 2309.4 230.9 10,392
P 3,000 10.00 0.15 1732.1 129.9 5,196
Totals = 714.4 28,316
Product Demand Unit Space EOQ Average Variable
cost (per unit) (Qo) space costs
Widget 7054 18.00 0.3 1979.6 296.9 12,922Gadget 5643 15.00 0.2 1939.6 194.0 10,551
P 2116 10.00 0.15 1454.7 109.1 5,275
Totals = 600.0 28,749
Percentage increase in variable costs = 1.53%
Scaling Factor = 0.705 (Initially, set Scaling Factor = 1)
Solver Par ameters
Set Tar get Cell :E23
Equal to:Max
By Changing Cell s:E23
Subject to Constrai nts:H18 =0 = Answer must be positive
Cell Formula Copied to
G8 SQRT(2*C8*G$3/(G$4*D8)) G9:G10
H8 0.5*E8*G8 H9:H10
I8 C8*G$3/G8 + 0.5*G8*D8*G$4 I9:I10
H11 SUM(H8:H10) I11
Copy range B6:I11 into B13:I18
C15 C8*E$23 C16:C17I15 C8*G$3/G15 + 0.5*G15*D15*G$4 I16:I17
I20 (I18 - I11)/I11
Figure 8.9 Multiple-product model with storage space constraint.
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K L M
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Figure 8.9 Multiple-product model with storage space constraint.
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A B C D E F G H I J
Example 9.7 - The Newsboy Problem: A Probabilistic Model with Discrete Demand
InputUnit Cost, C = 3.00Selling Price, S = 5.00 User input cells are shaded
Scrap value, V = 0.75
Output
Indiv. Cumul. profit, EPiDemand, Di Pi CUMi Sales Profit
1 10 0.05 1 10 20
2 20 0.1 0.95 19.5 38
3 30 0.15 0.85 28 52
4 40 0.2 0.7 35 59
5 50 0.2 0.5 40 58
6 60 0.15 0.3 43 487 70 0.1 0.15 44.5 32
8 80 0.05 0.05 45 11 4
Optimal demand, Qo= 40 Maximum prof it = 59
Cell Formula Copied to
E11 SUM(D11:D$18) E12:E18
F11 SUMPRODUCT(C$11:C11,D$11:D11) + C11*E12 F12:F17
F18 SUMPRODUCT(C$11:C18,D$11:D18)
G11 E$4*F11 - E$3*C11 + E$5*(C11 - F11) G12:G18
I18 MATCH(H20,G11:G18,0)
D20 OFFSET(C10,I18,0)
H20 MAX(G11:G18)
Figure 8.10 The Newsboy problem - a probabilistic model with discrete demand.
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A B C D E F G H I
Example 9.8 - A Probabilistic Model with Shortages
Input Holding cost, H = 40.00 All user input cellsShortage cost, B = 500.00 are shaded
B/(B + H) = 0.93
Output
Indiv. Sum
Demand, Di Pi SUMi1 3 0.4 0.4
2 4 0.25 0.65
3 5 0.13 0.78
4 6 0.11 0.89
5 7 0.05 0.94 = Optimal amount
6 8 0.04 0.987 9 0.01 0.99
8 10 0.01 1
Cel l Formula Copied to
E5 E4/(E4 + E3)
E11 SUM(D$11:D11) E12:E18
F11 IF(E11>=H$5)," = Optimal amount","")
F12 IF(AND(E11=H$5)," = Optimal amount","") F13:F18
Figure 8.11 Probabilistic model with shortages.
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A B C D E F G H I J K
Example 9.9 - A Service-Level Model with Variable Demand/ Fixed Lead-Time
I nput - must be in consistent time units
Time (day, week, month, year) week Demandi s normally-distri buted
Ordering/Setup Cost 100.00 Mean = 500
Unit Cost 10.00 Standard deviation = 60Holding cost (two options) Service Level %, SL= 95%
(i) in s per year Lead Time, Lt= 5 week
(ii) as % of unit cost 30.0%
Unit holding cost per week 0.058 52
Output
Reorder level/point, R 2721.0 Holding cost of safety stock 13
Order quantity, Q 1316.6 Holding cost of normal stock 38
Safety stock 221.0 Ordering/setup costs 38
Total costs per week 89
Cell Formula Copied to
D8 E4 D10, K8, H16
E10 IF(E9="",E8/G10,E9*E6/G10)
G10 IF(E4="day",365,IF(E4="week",52,IF(E4="month",12,1)))
E11 IF(E10=0,"Enter a value in either cell E8 or E9!","")
D13 J5*J8 + D15
D14 SQRT(2*J5*E5/E10)
D15 ROUNDUP(NORMSINV(J7)*J6*SQRT(J8),0)
J13 D15*E10
J14 D14*E10/2
J15 IF(D14=0,"",E5*J5/D14)
J16 SUM(J13:J15)
Figure 8.12 Service-level model with variable demand/fixed lead-time.
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A B C D E F G H I J K
Example 9.10 - A Service-Level Model with Fixed Demand/ Variable Lead-Time
I nput - must be in consistent time units
Time (day, week, month, year) week Lead-timeis normally-distributedDemand 500 Mean = 5
Ordering/Setup Cost 100.00 Standard deviation = 1
Unit Cost 10.00 Service Level %, SL= 95%
Holding cost (two options)
(i) in s per year User input cells are shaded
(ii) as % of unit cost 30.0%
Unit holding cost per week 0.058 52
Output
Lead time 6.6 week Holding cost of normal stock 38
Reorder level/point, R 3322.4 Ordering/setup costs 38
Order quantity, Q 1316.6 Total costs per week 76
Cell Formula Copied to
D14 J5 + NORMSINV(J7)*J6
E14 E4
D15 E5*D14
D16 SQRT(2*E5*E6/E11)
J14 D16*E11/2
J15 E6*E5/D16
J16 SUM(J14:J15)
Figure 8.13 Service-level model with variable demand/variable lead-time.
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A B C D E F G H I J K
Example 9. 11 - A Periodic Review (i.e. Fixed-Period) Model
I nput - must be in consistent time units Demandi s normally-distributed
Time (day, week, month, year) day Mean = 40
Ordering/Setup Cost 50.00 Standard deviation = 15Unit Cost 10.00 Service Level %, SL= 95%
Holding cost (two options) Lead Time, Lt= 8 day
(i) in s per year 20.00 Review Period = 16 day
(ii) as % of unit cost Stock On-hand = 60
Unit holding cost per day 0.055 365
Output
Reorder level/point, R 1081.0 Holding cost of safety stock 6.63
Order quantity, Q 1021.0 Holding cost of normal stock 27.97
Safety stock 121.0 Ordering/setup costs 1.96
Total costs per day 36.56
Cel l Formula Copied to
D13 J4*(J7 + J8) + D15
D14 D13 - J9
D15 ROUNDUP(NORMSINV(J6)*J5*SQRT(J7+J8),0)
Figure 8.14 Periodic review (fixed-period) model.
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A B C D E F G H I J
Example 9.12 - A Multi-Period Model with Several Constraints
Input All user input cells are shadedAnnual Demand 3,600
Ordering Cost 5.00 Output
Unit Cost 2.00 EOQ 300.00
Unit holding cost per year (two options) Cycle time
(i) in s per year (in months) 1.0
(ii) as % of unit cost 20.0% Total cost 7,320
Unit holding cost per year 0.40
Monthly Order Ending Cost per
Month Demand Quantity Inventory Period
1 240 270 30 546
2 270 330 90 668
3 450 360 0 725
4 210 270 60 547
5 240 270 90 548
6 300 270 60 547
7 330 330 60 667
8 420 360 0 725
9 240 270 30 546
10 330 300 0 605
11 300 300 0 605
12 270 270 0 545
Annual demand = 3,600 7,274 = Annual cost
Objective: M inimize surplus stock = 420
Note: Switch on the "Assume Linear Model" parameter in the Solver Options dialog box
Figure 8.15 Multi-period model with several constraints.
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K
Figure 8.15 Multi-period model with several constraints.
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Figure 8.15 Multi-period model with several constraints.
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A B C D E F G H I J K L M
Example 9.13 - A Simulation Model for Inventory Control
Demand table Lead-time table Dem- No. of
Lower Upper and Pi Lower Upper days Pi0 0.03 0 0.03 0 0.20 1 0.20 User input
0.03 0.08 1 0.05 0.20 0.70 2 0.50 cells are
0.08 0.21 2 0.13 0.70 1.00 3 0.30 shaded
0.21 0.46 3 0.25 1.00
0.46 0.68 4 0.22
0.68 0.88 5 0.20 Reorder level = 15
0.88 1.00 6 0.12 Order quantity = 30
1.00
Output table
Units Begin. RAND Dem- Ending New Lost Lead Recpt.Day Recvd. Invntry. No. and Invntry. Level sales Order? time Day
1 30 0.31 3 27 27 0 No
2 0 27 0.48 4 23 23 0 No
3 0 23 0.52 4 19 19 0 No
4 0 19 0.52 4 15 15 0 Yes 1 6
5 0 15 1.00 6 9 39 0 No
6 30 39 0.05 1 38 38 0 No
7 0 38 0.20 2 36 36 0 No
8 0 36 0.97 6 30 30 0 No
9 0 30 0.74 5 25 25 0 No
10 0 25 0.49 4 21 21 0 No
11 0 21 0.22 3 18 18 0 No
12 0 18 0.77 5 13 13 0 Yes 3 1613 0 13 0.95 6 7 37 0 No
14 0 7 0.15 2 5 35 0 No
55 0
Service Level = 100.0%
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A B C D E F G H I J K L
Case Study 9.1 - A Material Requirements Planning (MRP) Model
The BOM Table
Part Number: Descr iption BOM I d. No. of Lead On Planned
Level Code Units Time Hand Order User input
Table 0 1 1 1 50 Rel. Row cells are
Top Assembly 1 1001 1 2 50 25 shaded
Table Top 2 2001 1 1 180 35
Drawer 2 2002 1 1 200 35
Leg Assembly 1 1002 1 1 100 25
Legs 2 2003 4 1 250 65
Side Rung 2 2004 2 1 50 65
Connecting Rung 2 2005 1 1 110 65
The MRP Output Table
1Table Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Master Production Schedule 0 0 180 180 100 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 50 50 50 0 0 0 0 0
Net Requirements 0 0 130 180 100 0 0 0
Planned Order Receipts 0 0 130 180 100 0 0 0
Planned Order Releases 0 0 130 180 100 0 0 0 0
2
Top Assembly Lead Time = 2
Week Number Overdue 1 2 3 4 5 6 7 8Gross Requirements 0 130 180 100 0 0 0 0
Scheduled Receipts 0 100 0 0 0 0 0 0
On Hand 50 50 20 0 0 0 0 0
Net Requirements 0 0 160 100 0 0 0 0
Planned Order Receipts 0 0 160 100 0 0 0 0
Planned Order Releases 0 160 100 0 0 0 0 0 0
3
Table Top Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 160 100 0 0 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 180 20 0 0 0 0 0 0
Net Requirements 0 80 0 0 0 0 0 0
Planned Order Receipts 0 80 0 0 0 0 0 0
Planned Order Releases 0 80 0 0 0 0 0 0 0
Figure 8.20 MRP model for the kitchen table example.
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A B C D E F G H I J K L
4
Drawer Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 160 100 0 0 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 200 40 0 0 0 0 0 0
Net Requirements 0 60 0 0 0 0 0 0
Planned Order Receipts 0 60 0 0 0 0 0 0
Planned Order Releases 0 60 0 0 0 0 0 0 0
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Leg Assembly Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 0 130 180 100 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 100 100 0 0 0 0 0 0
Net Requirements 0 30 180 100 0 0 0 0Planned Order Receipts 0 30 180 100 0 0 0 0
Planned Order Releases 0 30 180 100 0 0 0 0 0
6
Legs Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 120 720 400 0 0 0 0 0
Scheduled Receipts 0 100 0 0 0 0 0 0
On Hand 250 130 0 0 0 0 0 0
Net Requirements 0 490 400 0 0 0 0 0
Planned Order Receipts 0 490 400 0 0 0 0 0
Planned Order Releases 0 490 400 0 0 0 0 0 0
7
Side Rung Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 60 360 200 0 0 0 0 0
Scheduled Receipts 10 0 0 0 0 0 0 0 0
On Hand 50 0 0 0 0 0 0 0
Net Requirements 10 360 200 0 0 0 0 0
Planned Order Receipts 10 360 200 0 0 0 0 0
Planned Order Releases 10 360 200 0 0 0 0 0 0
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Connecting Rung Lead Time = 1 Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 30 180 100 0 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 110 80 0 0 0 0 0 0
Net Requirements 0 100 100 0 0 0 0 0
Planned Order Receipts 0 100 100 0 0 0 0 0
Planned Order Releases 0 100 100 0 0 0 0 0 0
Figure 8.20 MRP model for the kitchen table example.
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Figure 8.20 MRP model for the kitchen table example.
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Page-break
Figure 8.20 MRP model for the kitchen table example.
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A B C D E F G H I J K L
4
Drawer Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 160 100 0 0 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 200 40 0 0 0 0 0 0
Net Requirements 0 60 0 0 0 0 0 0Planned Order Receipts 0 60 0 0 0 0 0 0
Planned Order Releases 0 60 0 0 0 0 0 0 0
5
Leg Assembly Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 0 130 180 100 0 0 0 0
Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 100 100 0 0 0 0 0 0
Net Requirements 0 30 180 100 0 0 0 0
Planned Order Receipts 0 30 180 100 0 0 0 0
Planned Order Releases 0 30 180 100 0 0 0 0 0
6
Legs Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 120 720 400 0 0 0 0 0
Scheduled Receipts 0 100 0 0 0 0 0 0
On Hand 250 130 0 0 0 0 0 0
Net Requirements 0 490 400 0 0 0 0 0
Planned Order Receipts 0 490 400 0 0 0 0 0
Planned Order Releases 0 490 400 0 0 0 0 0 0
7
Side Rung Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 60 360 200 0 0 0 0 0
Scheduled Receipts 10 0 0 0 0 0 0 0 0
On Hand 50 0 0 0 0 0 0 0
Net Requirements 10 360 200 0 0 0 0 0
Planned Order Receipts 10 360 200 0 0 0 0 0
Planned Order Releases 10 360 200 0 0 0 0 0 0
8
Connecting Rung Lead Time = 1
Week Number Overdue 1 2 3 4 5 6 7 8
Gross Requirements 30 180 100 0 0 0 0 0Scheduled Receipts 0 0 0 0 0 0 0 0
On Hand 110 80 0 0 0 0 0 0
Net Requirements 0 100 100 0 0 0 0 0
Planned Order Receipts 0 100 100 0 0 0 0 0
Planned Order Releases 0 100 100 0 0 0 0 0 0
Figure 8.20 (cont.)
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A B C D E F G H I J K L M
Example 9. 14 - A Model for the Part Period Balancing (PPB) Method
Input Ordering (or Setup) Cost = 200 User input cells
Unit holding cost = 1.00 are shadedEconomic part period (EPP) = 200
REQP 150 100 150 0 50 75 100 25 20
Per iod, P 1 2 3 4 5 6 7 8 9
Weighted REQi 0 100 300 0 200 375 600 175 160
CUMi 0 100 400 400 600 975 1575 1750 1910
(CUMi- EPP)/EPP -1.0 -0.5 1.0 1.0 2.0 3.9 6.9 7.8 8.6
0.5 1.0 0.5 1.0 1.0 2.0 3.9 6.9 7.8 8.6
Order Data = 150 100
0 Answer: Place an order for 250 uni ts in per iod 1
New Factor, NFi 0 0 1 2 3 4 5 6 7
Weighted REQi -150 -100 0 0 100 225 400 125 120
CUMi 0 0 0 0 100 325 725 850 970
(CUMi- EPP)/EPP -1.0 -1.0 -1.0 -1.0 -0.5 0.6 2.6 3.3 3.9
0.5 1.0 1.0 1.0 1.0 0.5 0.6 2.6 3.3 3.9
Order Data = 150 0 50
2 Answer: Place an order for 200 uni ts in per iod 3
New Factor, NFi 0 0 0 0 0 1 2 3 4
Weighted REQi
-150 -100 -150 -1 -50 0 100 50 60
CUMi 0 0 0 0 0 0 100 150 210
(CUMi- EPP)/EPP -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -0.5 -0.3 0.1
0.1 1.0 1.0 1.0 1.0 1.0 1.0 0.5 0.3 0.1
Order Data = 75 100 25 20
5 Answer: Place an order for 220 uni ts in per iod 6
New Factor, NFi 0 0 0 0 0 0 0 0 0
Copy cell range B11:L17 repeatedly down the spreadsheet, placing the cursor in cells B19,
B27. until the 'New Factor, NFi' row contains nothing but zeros (e.g. see row 33 above).
Figure 8.21 Model for the part-period balancing (PBB) method.
(Note that this model has been modified)
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A B C D E F G H
Product No. in Product Year Cash
name stock price flow
Gizmo 10 10.00 1 1
Gadget 25 12.50 2 4
Widget 8 20.00 3 8
Sprocket 40 4.50 4 16
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Sample F igur e
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A B C D E F G H
Column(B3) = 2 Row(B3) = 3
Column(D5:D9) = 4 Row(D5:D9) = 5
INDEX(B4:D7,2,3) = 12.50 NORMSINV(0.95) =
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1.6449