[CUTTING STOCK]Steel mill producer

DiketahuiSize of production: 100 "

80 "55 "

Demand: Size Unit45 " 15030 " 20018 " 175

Ditanyakan: How should the steel mill cut the sheets to minimize waste?

Solution100" steel mill

UkuranSisa Jumlah

45 30 182 10 01 1 1 7 01 3 1 150

3 10 02 2 4 01 3 16 0

5 10 0

Total Panjang 150 0 450Sisa 150

45" 30" 18"Jumlah Steel 150 200 550

≥ ≥ ≥150 200 175

Fungsi objektif: Total sisa steel 350

How should the steel mill cut the sheets to minimize waste?

80" steel mill 55" steel millUkuran

Sisa JumlahUkuran

45 30 18 451 1 5 0

2 1 2 1001 2 14 0 1

4 8 01 1 17 0

0 200 100 0200

55" steel millUkuran

Sisa Jumlah30 18

1 1 7 03 1 0

10 0

0 00

[SUPPLIER SHIPPING/PURCHASING COST]

Diketahui

Per unit shipping cost ($) of Product A from each of 4 suppliers to factories

Supplier 1 Supplier 2 Supplier 3

Factory 1 4 3 6Factory 2 7 4 4Factory 3 2 5 5Factory 4 6 6 8

Per unit price($) of product A from each of 4 suppliersSupplier 1 Supplier 2 Supplier 3 Supplier 4

12 11 11 12

1The number of units required of factories 20The number of units available of suppliers 100

Ditanyakan

Solution Supplier 1 Supplier 2Factory 1 0 5Factory 2 0 10Factory 3 40 0Factory 4 0 0Jumlah 40 15

≤ ≤100 15

Optimal amounts of product A to purchase and ship between each supplier and each factory in order to minimize total purchase and shipping cost

Supplier 4

3564

2 3 430 40 5015 20 150

Supplier 3 Supplier 4 Jumlah0 15 20 ≥ 20

20 0 30 ≥ 300 0 40 ≥ 400 50 50 ≥ 50

20 65≤ ≤

20 150

Optimal amounts of product A to purchase and ship between each supplier and each factory

Shipping cost Raw material cost60 235

120 33080 480

200 600Total 460 1645

Fungsi objektif: Total Cost 2105

MachineSpeed

Number of Bolts / minuteMachine 1 5Machine 2 9Machine 3 25

Machine Bolts yang dihasilkan1" Bolts

Machine 1 1157Machine 2 2343Machine 3 12500

16000>=

16000

Operating Cost / Output Unit Capability (Ability to make)Operating Cost / 100 bolts produced 1" Bolts 2" Bolts 3" Bolts

$25 1 1 1$14 1 1 0$4 1 0 0

Bolts yang dihasilkan Operating Cost2" Bolts 3" Bolts

843 400 2400 6002157 4500 630

12500 500Total Cost 1730

3000 400>= >=

3000 400

Banyaknya Bolts dalam satu mesin

Operating CostWaktu (min)

480 <= 500500 <= 500500 <= 500

[BLENDING PROBLEMS]

Diketahui

Minimum output (tons/year) =

Information on rock:

Calcium Content Magnesium Content

Quarry 1 1 2.3Quarry 2 0.7 1.6Quarry 3 1.5 1.2Quarry 4 0.7 4.1

Ditanyakan

Solution

Kapasitas produksiQuarry 1 1000 ≤Quarry 2 2295 ≤Quarry 3 1125 ≤Quarry 4 1580 ≤Total 6000

≥6000

What rock quarries should be used and how much should they produce to meet a certain quality of limestone (calcium content 0.9 per ton and magnesium content 2.3 per ton) and minimize cost?

6000

2000 3.52500 41300 43000 2

Calcium Content Magnesium content2000

0.9 2.3250013003000

= =0.9 2.3

Fungsi objektif Total Cost

Maximum production per year (ton)

Cost to keep quarry open per year ($ million)

What rock quarries should be used and how much should they produce to meet a certain quality of limestone (calcium content 0.9 per ton and magnesium content 2.3 per ton) and minimize cost?

Cost ($ million)3.5

442

13.5