Energy Business Modelling

8/12/2019 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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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


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


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


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


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


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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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


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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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


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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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


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


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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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


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


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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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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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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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


On Hand 50 50 20 0 0 0 0 0




3

Table Top Lead Time = 1


Gross Requirements 160 100 0 0 0 0 0 0


On Hand 180 20 0 0 0 0 0 0




Figure 8.20 MRP model for the kitchen table example.


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Drawer Lead Time = 1




On Hand 200 40 0 0 0 0 0 0




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Leg Assembly Lead Time = 1




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


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Legs Lead Time = 1




On Hand 250 130 0 0 0 0 0 0




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Side Rung Lead Time = 1



Scheduled Receipts 10 0 0 0 0 0 0 0 0

On Hand 50 0 0 0 0 0 0 0




8

Connecting Rung Lead Time = 1 Week Number Overdue 1 2 3 4 5 6 7 8



On Hand 110 80 0 0 0 0 0 0






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Drawer Lead Time = 1




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


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Leg Assembly Lead Time = 1




On Hand 100 100 0 0 0 0 0 0




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Legs Lead Time = 1




On Hand 250 130 0 0 0 0 0 0




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Side Rung Lead Time = 1



Scheduled Receipts 10 0 0 0 0 0 0 0 0

On Hand 50 0 0 0 0 0 0 0




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Connecting Rung Lead Time = 1


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




Figure 8.20 (cont.)


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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


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


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

5

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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Energy Business Modelling