Feel free to download my pdf for full reading =)
The following solution was used to demonstrate the formulation of the transportation model. LPG is process and stored in Petronas refinery in three different places—Malacca refinery, Klang Port, and Kertih Port. These refineries supply three different zone in peninsular Malaysia. North Zone (Perlis, Penang, Kedah, Kelantan & Terengganu), Center Zone (Perak, Sekangor, Kuala Lumpur & Pahang), South Zone (Malacca, Negeri Sembilan & Johor Bahru). LPG is shipped to the customer in road cars, using lorry tanker each of which is capable of holding ten ton of LPG. Each grain refinery is able to supply the following number of ton of LPG to the customer on a daily basis:
Petronas Refinery Supply
1. Malacca
refinery 175
2. Klang
Port 275
3. Kertih
Port 350
-----
800
tons
Figure 4.1
: Petronas Refinery supply of LPG on daily basis
Each
zone demands the following number of tons of LPG per day.
Zone Demand
1. North 200
2. Center 300
3. South 300
----
800
tons
Figure 4.2
: LPG demand per day
The
cost of transporting ten tons of LPG from each refinery (source) to each zone
(destination) differs according to the distance and type of road used. These
costs are shown in the Table 4.1. For example, the cost of shipping ten tons of
LPG from the Klang Port to the North Zone is RM1300
Table 4.1
: Cost for shipment of 10 tons LPG from refinery to peninsular zone in Malaysia.
ZONE
|
|||
REFINERY
|
North
|
Center
|
South
|
Malacca
|
RM 1300
|
800
|
900
|
Klang Port
|
1100
|
900
|
1200
|
Kertih Port
|
600
|
1600
|
2000
|
*To
make an easy calculation, we change the data into a single digit :
**Note
: real cost for each tons = cost x
Table 4.2
: Adjusted cost for shipment from refinery to zone in peninsular Malaysia.
ZONE
|
|||
REFINERY
|
A.
North
|
B.
Center
|
C.
South
|
1. Malacca
|
13
|
8
|
9
|
2. Klang
Port
|
11
|
9
|
12
|
3. Kertih
Port
|
6
|
16
|
20
|
The
problem is to determine how many tons of LPG to transport from each refinery to
each zone on daily basis in order to minimize the total cost of transportation.
The linear programming model for this problem is formulated in the equations
that follow:
..........................download Minimizing Cost in Transportation using Linear Transportation Method pdf for full reading......................
4.3 DISCUSSION
In
this model the decision variables,
, represent the number of tons of LPG transported from each
refinery, i (where i = 1,2,3
),to each zone, j (where j =
A, B, C). The objective function represents the total transportation cost for
each route. Each term in the objective function reflects the cost of the
tonnage transported for one route. For example, if 20 tons are transported from
refinery 1 to zone A, the cost of 13 is multiplied by 20 which equals RM260.
(Real cost = 260x10 = RM2600). The first three constraints in the linear
programming model represent the supply at each refinery; the last three
constraints represent the demand at each zone.
..........................download Minimizing Cost in Transportation using Linear Transportation Method pdf for full reading......................
