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Need an research paper on 4: case problem stateline shipping and transport company. Needs to be 2 pages. Please no plagiarism.
Need an research paper on 4: case problem stateline shipping and transport company. Needs to be 2 pages. Please no plagiarism. Case Study John Doe Case Study The scope is to study to create two models. one will show how to minimize the shipping cost of transportation of waste from six plants to three disposal sites, the other one will illustrate how to organize the same work using transshipment concept. The objects for transshipments are the six plants and three disposal sites.
Transportation Model
From the viewpoint of demand and supply, the six plants are considered as supply sources and three waste sites are demands sites. both of them have limitation, which is expressed as a quantity that can be supplied and stored. The objective is to achieve cost minimization under the given limitations (Reeb & Leavengood, 2002)
The solution is approached by creating a 6 x3 matrix illustrated in Table 1. Each cell of transportation expressed through Xij depicts quantity from the supply source to waste disposal site. The matrix also shows that total supply quantity is 223 bbls per week and the total demand quantity is 250 bbls per week. Supply and demand are not balanced. the solution requires to implement a dummy supply source of 27 bbls. Decision variable, in this case, is the quantity for a site, and objective function is cost minimization. The model is represented through the following linear equations (“Linear programing”, n.d).
Minimization is solved using the following equation, subject to: Z=12X11+15X12+17X13+14X21+9X22+10X23+13X31+20X32+11X33+17X41+16X42+19X43+7X51+14X52+12X53+22X61+16X62+18X63.
X11 + X12 + X13 = 35X11 + X21 + X31 + X41 + X51 + X61 = 65
X21 + X22 + X 23 = 26X12 + X22 + X32 + X42 + X52 + X62 = 80
X31 + X32 + X33 = 42X13 + X23 + X33 + X43 + X53 + X63= 105
X41 + X42 + X43 = 53
X51 + X52 + X53 = 29
X61 + X62 + X63 = 38
The solution was obtained using the “Transportation” module of POM - OM software (“The Transportation model”, n.d.) The shipment from the supply source to waste the side is illustrated in Table 3. The POM – OM solution includes a dummy supply source for 27 bbls. The minimum cost is $2,832. it does not include dummy supply source quantity.
Table 3. Shipment from supply sources to the disposal sites
Transportation Solution
Optimal solution value = $2832
Whitewater
Los Canos
Duras
Kingsport
35
 .
 .
Danville
 .
 .
26
Macon
 .
 .
42
Selma
1
42
10
Columbus
29
 .
 .
Allentown
 .
38
 .
Dummy
 .
 .
27
Note: Quantity in barrels
Table 4. Cost of transportation from the plants to the disposal sites
Transportation Solution
 .
Whitewater
Los Canos
Duras
Kingsport
35/$420
 .
 .
Danville
 .
 .
26/$260
Macon
 .
 .
42/$462
Selma
1/$17
42/$672
10/$190
Columbus
29/$203
 .
 .
Allentown
 .
38/$608
 .
Dummy
 .
 .
27/$0
Transshipment Model
The idea is based on the concept that shipping line will use an intermediary supply center, which could be either a plant or waste disposal site. This concept gives a 9 x 9 matrix where supply plus disposal sources together act as supply sources and disposal sources (Rajendran & Pandian, 2012). Table 5 displays the feed matrix to achieve a solution. The values for supply and demand quantities of the matrix are based on the following assumptions:
Table 5. Transshipment solution matrix
Demand Sites
 .
Supply Q-ty
Supply Sites
1
2
3
4
5
6
A
B
C
Kingsport
Danville
Macon
Selma
Columbus
Allentown
Whitewater
Los Canos
Duras
1
285
Kingsport
X11
X12
X13
X14
X15
X16
X1A
X1B
X1C
2
276
Danville
X21
X22
X23
X24
X25
X26
X2A
X2B
X2C
3
292
Macon
X31
X32
X33
X34
X35
X36
X3A
X3B
X3C
4
403
Selma
X41
X42
X43
X44
X45
X46
X4A
X4B
X4C
5
279
Columbus
X51
X52
X53
X54
X55
X56
X5A
X5B
X5C
6
288
Allentown
X61
X62
X63
X64
X65
X66
X6A
X6B
X6C
A
250
Whitewater
XA1
XA2
XA3
XA4
XA5
XA6
XAA
XAB
XAC
B
250
Los Canos
XB1
XB2
XB3
XB4
XB5
XB6
XBA
XBB
XBC
C
250
Duras
XC1
XC2
XC3
XC4
XC5
XC6
XCA
XCB
XCC
250
250
250
250
250
250
315
330
355
1. Each plant may absorb total demand quantity 250 bbls. in addition to its own supply quantity,
2. Each waste site may absorb total demand quantity 250 bbls in addition to its own demand quantity.
Table 6. Transshipment cost matrix
Demand Sites
1
2
3
4
5
6
A
B
C
Supply sites
From Sites
To Sites
Kingsport
Danville
Macon
Selma
Columbus
Allentown
Whitewater
Los Canos
Duras
1
Kingsport
0
6
4
9
7
8
12
15
17
2
Danville
6
0
11
10
12
7
14
9
10
3
Macon
5
11
0
3
7
15
13
20
11
4
Selma
9
10
3
0
3
16
17
16
19
5
Columbus
7
12
7
3
0
14
7
14
12
6
Allentown
8
7
15
16
14
0
22
16
18
A
Whitewater
12
14
13
17
7
22
0
12
10
B
Los Canos
15
9
20
16
14
16
12
0
15
C
Duras
17
10
11
19
12
18
10
15
0
The solution is achieved by solving the 9x9 matrix for cost minimization. Each Xij of the matrix depicts the quantity it may contain in determining the minimum transportation cost. The supply and demand constraints are obtained, in the same way as shown in the previous example. The summation of each row of the matrix presents a supply constraint equation. The summation of each column of the matrix presents a demand constraint. The minimization solution is achieved using the “Transportation” module of POM - OM software. The results are presented in Tables 7 and 8. The results illustrate the required shipment directions and associated cost.
Table 7. Transshipment cost from one place to another
 .
Kingsport
Danville
Macon
Selma
Columbus
Allentown
Whitewater
Los Canos
Duras
Kingsport
16/$96
19/$76
 .
 .
 .
 .
 .
 .
Danville
 .
 .
 .
 .
 .
 .
80/$720
 .
Macon
 .
 .
 .
 .
 .
 .
 .
78/$858
Selma
 .
 .
17/$51
36/$108
 .
 .
 .
 .
Columbus
 .
 .
 .
 .
 .
65/$455
 .
 .
Allentown
 .
38/$266
 .
 .
 .
 .
 .
 .
Whitewater
 .
 .
 .
 .
 .
 .
 .
 .
Table 8. Transshipment solution
Transshipment Solution
Optimal solution value = $2630
Kingsport
Danville
Macon
Selma
Columbus
Allentown
Whitewater
Los Canos
Duras
Kingsport
250
16
19
 .
 .
 .
 .
 .
 .
Danville
 .
196
 .
 .
 .
 .
 .
80
 .
Macon
 .
 .
214
 .
 .
 .
 .
 .
78
Selma
 .
 .
17
250
36
 .
 .
 .
 .
Columbus
 .
 .
 .
 .
214
 .
65
 .
 .
Allentown
 .
38
 .
 .
 .
250
 .
 .
 .
Whitewater
 .
 .
 .
 .
 .
 .
250
 .
 .
Los Canos
 .
 .
 .
 .
 .
 .
 .
250
 .
Duras
 .
 .
 .
 .
 .
 .
 .
 .
250
Dummy
 .
 .
 .
 .
 .
 .
 .
 .
27
POM-QM for Windows
Conclusion
In this assignment, the demand quantity is 250 bbls whereas the supply quantity is 223 bbls. In approaching cost minimization, software POM –QM used a dummy supply source in the quantity of 27 bbls. The unbalanced demand and supply quantity is considered to be a limitation of the study. The study shows that using transshipment the company management can reduce the shipment cost. The shipment cost of shipment of 223 bbls without the transshipment option is $2832 whereas with the option is $2630. Hence, transshipment, in this case is a better solution.
References
Linear Programming: Introduction. (n.d.). Retrieved from http://www.purplemath.com/modules/linprog.htm
Rajendran, P., & Pandian, P. (2012). Solving Fully Interval Transshipment Problems. Retrieved from http://www.m-hikari.com/imf/imf-2012/41-44-2012/pandianIMF41-44-2012.pdf
Reeb, J., & Leavengood, S. (2002). Transportation Problem: A Special Case for Linear Programming Problems. Retrieved from http://ir.library.oregonstate.edu/xmlui/bitstream/handle/1957/20201/em8779-e.pdf
http://www.prenhall.com/weiss_dswin/html/trans.htm
The Transportation Model. (n.d.). Retrieved from http://www.prenhall.com/weiss_dswin/html/trans.
