1. 1
Linear Programming modelling in a supply networkoptimisation project to find the best
possible solution in allocating materials to achieve minimum cost.
Minimum cost supply network flow
Total Demand Manuf. capacity Shipping cost DC's Shipping cost Nodes storage cost Customer Demand
APAC Plant APAC APAC
1000 4 5 2 Node APAC 1100
9 4 Node AMER
11 5 Node EMEA
AMER Plant AMER AMER
Company 2500 750 2 5 4 Node AMER 600
11 2 Node APAC
9 5 Node EMEA
EMEA Plant EMEA EMEA
750 3 6 5 Node EMEA 800
12 4 Node AMER
15 2 Node APAC
COST MATRIX APAC>APAC APAC>AMER APAC>EMEA AMER>AMER AMER>APAC AMER>EMEA EMEA>EMEA EMEA>AMER EMEA>APAC
Plant > DC shipping cost 4 0 0 2 0 0 3 0 0
DC > Nodes shipping cost 5 9 11 5 11 9 6 12 15
Storage cost 2 4 5 4 2 5 5 4 2
Total 11 13 16 11 13 14 14 16 17
Capacity/Demand matrix Capacity Demand
APAC 1000 1100
AMER 750 600
EMEA 750 800
Total 2500 2500
Total cost matrix APAC Plant AMER Plant EMEA Plant Demand
APAC 11 13 17 1100
AMER 13 11 16 600
EMEA 16 14 14 800
Supply capacity 1000 750 750
Delivery matrix APAC Plant AMER Plant EMEA Plant Demand
APAC 1000 100 0 1100
AMER 0 600 0 600
EMEA 0 50 750 800
Supply capacity 1000 750 750
Optimal cost solution
APAC 12300
AMER 6600
EMEA 11200
MIN Cost 30100

2. 2
Linear Programming modelling in factory planning minimizing overtime costs
Machines
normal t overtime normal t overtime normal t overtime Total Demand
prod a 0.0 0.0 20.0 0.0 0.0 0.0 20 20
prod b 4.0 0.0 16.0 0.0 0.0 0.0 20 20
prod c 26.0 0.0 0.0 4.0 0.0 0.0 30 30
prod d 0.0 6.0 4.0 0.0 30.0 0.0 40 40
Cost mach. 30 6 40 4 30 0 110
Max cost 30 6 40 8 30 6 120
cost/hour 50
Minimize 5500
mach. running costs
LB R N
Cost` normal t overtime normal t overtime normal t overtime
prod a 0.0 0.0 1000.0 0.0 0.0 0.0
prod b 200.0 0.0 800.0 0.0 0.0 0.0
prod c 1300.0 0.0 0.0 200.0 0.0 0.0
prod d 0.0 300.0 200.0 0.0 1500.0 0.0
Total 1500 300 2000 200 1500 0
A B B

3. 3
Linear Programming Factory planning, maximizing product revenue under capacity
constraints
Considering the lack of capacity at ME for Prod D, the optimum solution that maximized
revenue was to use the free capacity at CH to assemble extra 10 and transfer them to
AMER.
Capacity CH CZ ME Total capacity
Prod A 30 15 10 55
Prod B 30 25 20 75
Prod C 150 120 80 350
Prod D 30 20 10 60
Total 240 180 120 540
Demand APAC EMEA AMER Total demand
Prod A 30 15 10 55
Prod B 30 25 20 75
Prod C 150 120 50 320
Prod D 20 20 20 60
Total 230 180 100 510
Production CH CZ ME Total production
Prod A 30 15 10 55
Prod B 30 25 20 75
Prod C 150 120 50 320
Prod D 30 20 10 60
240 180 90 510
Product cost matrix $
Prod A 1000
Prod B 750
Prod C 150
Prod D 780
MAX $ 206,050

4. 4
Queue Theory modelling analysing supply capacity and production machine
Supplier Capacity Analysis
week
Supply 1000
Demand 1250
Traffic intensity: 0.8
Average number of units in the queue: 3.20000
Probability of having to wait for service: 0.80000
Average time in the system (minutes): 0.00400
Probability that there are n units (≥ 0) in the system: n
0 0.20000
1 0.16000
2 0.12800
3 0.10240
4 0.08192
5 0.06554
Machine Capacity Analysis
Products
Interarrival
time
Service
time
Arrival
time
Start of
service
End of
service
Overall
queuing
time
Time in
the
system
1 5 9 5 5 14 0 9
2 11 13 16 16 29 0 13
3 10 12 26 29 41 3 15
4 10 12 36 41 53 5 17
5 11 9 47 53 62 6 15
6 6 12 53 62 74 9 21
7 6 11 59 74 85 15 26
8 8 14 67 85 99 18 32
Average: 7 18.5

5. 5
1) Initial logistics material flow network
2) Optimized distribution network with a mini-logistics shortest path least cost strategy
with minimum flow, shortest path at least cost
HAM
ZUR
2
AMS 2
5 BER GVA
3
BRU 2 2
3 FRA 4 PAR 5
PRA
4
3 3 3
2 MUN 5
LUX MIL
POR
3 2
VIE MAD
2
2 3 ROM
2
2 BUD LIS
LJU
2 3 5
ZAG 3
BEL BUC
2
4
SAR 6
5 SOF
IST
ATH