Quantative Analysis Assignment 1
Question:
A supply chain for refrigerator contains a number of plants, warehouses, collection centers, disposal
center, and a set of customers as shown in Figure 1. The refrigerators are manufactured at plants
located in three different sites in Saudi Arabia. Then they are transported to three (3) warehouses in
different cities. After that, the refrigerators are shipped to seven customers to satisfy their needs. Some
of these refrigerators are returned due to some faults. The returned items are collected and inspected
at two collection centers to specify if they need recovery or not. The recoverable return products are
sent to the plants and the unrecoverable return products are sent to the disposal center. From historical
data, the rate of return refrigerators from the customers is 4 % of the demand and the rate of
recoverable return refrigerators is (2% of the refrigerators inspected at collection centers). The unit
transportation cost between the other nodes in the network is estimated to be SR 7.
Part 1:
Develop a mathematical model (in general form) to help the company determine which plants
should be open, the number of refrigerators to produce in each factory, flow between each
two nodes, number of refrigerators returned per day while minimizing the total cost including
(fixed cost, production cost, rework cost, and transportation cost).
P 1=W 1 ,700=700
P 2=W 2 , 800=800
P 3=W 3 , 600=600
R=P 1 W 1+ P 2W 2+ P 3 W 3=1319
R=0+800+519=1319
Quantative Analysis Assignment 2
Why plant P2 and P3 should be opened instead of P1,
Plant 1 cost=7000000+ 60∗950+53∗10 +7∗950=7057000
Plant 2 cost=6500000+65∗800+53∗10+7∗800=6558130
Plant 3 cost =6000000+50∗750+53∗10+ 7∗750=6043280
Therefore, according to analysis plants P2 and P3 should be opened because they can cover the daily
refrigerators demand of all customers. Plus, they have lower overall cost as compared to plant 1.
Plant 2 will produce=800 refrigerators
Plant 3 will produce=519 refrigerators
Flow of nodes,
Plant 2 →Warehouse 2→ Customers
Plant 3 → Warehouse 3→ Customers
Number of refrigerators returned per-day,
Number of Refrigerators Returned Daily=1319∗4 %=53
Find the optimal solution using software:
MS Excel was used for this analysis,
Plant P1 P2 P3
Daily Production Capacity (Refrigerators) 950 800 750
Production cost(SRJ Refrigerators) 60 65 50
Rework cost(SRJ Refrigerators) 10 10 10
700000 650000 600000
Fixed cost 0 0 0
706418 655813 604328
0 0 0
Warehouse W1 W2 W3
Capacity 700 850 600
Total Daily Demand Refrigerators Returned daily Daily Recoverable Refrigerators
1319 52.76 1.0552
Quantative Analysis Assignment 3
Part 2:
Assume that three types of trucks are available to transport the products from the plants to
warehouse. Each truck type has a limited capacity. The transportation cost between the
suppliers and plants depends on the truck type, which is given in Table below:
R=0+800+519=1319
Considering the model above the Type 1 truck will be used for plant 2 and warehouse 2 transportation
and Type 2 truck will be used for transportation from Plant 3 to Warehouse 3,
Type 1 Truck cost=800∗10=8000
Type 2 Truck cost=519∗7=3633
The first policy that the manager wants to test is an order quantity of 300 refrigerators with a
reorder point of 70 refrigerators. Conduct the simulation for a 20-day period? Use excel.
Timeline Values Forecast Lower Confidence Bound Upper Confidence Bound
1 300
2 450
3 250 250 250.00 250.00
4 270.21983 68.31 472.13
5 259.09715 53.23 464.97
6 247.97448 33.49 462.46
7 236.8518 7.88 465.82
8 225.72913 -24.19 475.64
9 214.60645 -62.68 491.90
10 203.48378 -107.20 514.17
11 192.3611 -157.16 541.88
12 181.23843 -211.95 574.43
13 170.11575 -271.06 611.29
14 158.99308 -334.03 652.02
15 147.8704 -400.50 696.24
16 136.74773 -470.16 743.66
17 125.62505 -542.78 794.03
18 114.50238 -618.16 847.16
19 103.3797 -696.13 902.89
20 92.257025 -776.55 961.06
Quantative Analysis Assignment 4
The warehouse is open 200 days a year. Estimated ordering cost is SR 3000 per order. Holding
cost is SR 220 per refrigerator per year. Lost sales cost SR 2500. Find total daily cost.
( 3000+ 220+2500 )
Warehouse Cost Daily=
200
5720
Warehouse Cost Daily=
200
Warehouse Cost Daily=28.6 SR
