Free Essay

Stateline Shipping Assignment

In: Other Topics

Submitted By Nieceyb23
Words 1320
Pages 6
(1) Original problem
This is a Transportation problem for cost minimization. The problem is that the company has six collection centres from where company wants to collect waste and then transported to three disposable centres at a minimum cost. The different costs from collection centres to disposable sites are given in a table as shown in the following table.

White water Los Canos Duras Availability (bbl)
Kingsport $12.00 $15.00 $17.00 35
Danville $14.00 $9.00 $10.00 26
Macon $13.00 $20.00 $11.00 42
Selma $17.00 $16.00 $19.00 53
Columbus $7.00 $14.00 $12.00 29
Allentown $22.00 $16.00 $18.00 38
Capacity (barrels) 65 80 105

Model in the mathematical form

Let Xij i=1,2,3,4,5,6; j=1,2,3 denote the quantity of waste transported from i-th plant to j-th waste disposal centre. The objective function Z and constraints can be expressed as

Minimize Z=12X11+15X12+17X13+14X21+9X22+10X23+13X31+20X32+11X33+17X41+16X42+19X43+7X51+14X52+12X53+22X61+16X62+18X63
Subject to
X11+X12+X13=35
X21+X22+X23=26
X31+X32+X33=42
X41+X42+X43=53
X51+X52+X53=29
X61+X62+X63=38
X11+X21+X31+X41+X51+X61 65
X12+X22+X32+X42+X52+X62 80
X13+X23+X33+X43+X53+X63 105
Xij 0, i=1,2,3,4,5,6; j=1,2,3.

(2) The original Problem

The above problem without considering the intermediates sites are solved using excel solver and the final solution are given as follows

White water Los Canos Duras
Kingsport 35
Danville 26
Macon 42
Selma 1 52
Columbus 29
Allentown 28 10
Dummy 27

Therefore, the optimal transportation procedure is to transport
(1) 35 bbl from Kingport, 1 bbl from Selma and 29 bbl from Columbus to the White water waste disposal plant
(2) 52 bbl from Selma and 28 bbl from Allentown to Los Canos waste disposal plant
(3) 26 bbl from Danville, 42 bbl from Macon and 10 bbl from Allentown to the Duras waste disposal plant

The minimum cost=35*12+26*10+42*11+1*17+52*16+29*7+28*16+10*18
=$2822.

(3) Modified Problem

Since the company having another option to drop a load at a plant or disposal sites and then picked up and carried on the final destination without extra cost, we can find certain roots in this model, it is cheaper to drop and pick up loads at intermediate points rather than ship them directly. So dropping the waste at certain intermediate position as described below will give certain cost advantage to the shipping company. So by considering all such possibilities some intermediate points are identified to drop the waste to minimize cost of transportation. All such roots with the lowest cost are given in the following table. Among the new roots, the roots with minimum cost are marked in green.

Sl. No. Plant From Intermediate Position Disposal centre Cost Minimum cost
1 Kingsport ------------- Duras $17 $15 Kingsport Danville Duras $15
2 Macon -------------- Los Canos $20 $19 Macon Selma Los Canos $19
3 Selma ------------- White water $17 $10 Selma Columbus White water $10
4 Selma ------------- Duras $19 $14 Selma Macon Duras $14
5 Allentown ------------ White water $22 $20 Allentown Kingsport White water $20
6 Allentown ------------ Duras $18 $17 Allentown Danville Duras $17

Therefore, the original transportation problem can be modified using the intermediate points as follows. The reduced costs from the original model is marked in brown colour.

White water Los Canos Duras Availability (bbl)
Kingsport $12.00 $15.00 $15.00 35
Danville $14.00 $9.00 $10.00 26
Macon $13.00 $19.00 $11.00 42
Selma $10.00 $16.00 $14.00 53
Columbus $7.00 $14.00 $12.00 29
Allentown $20.00 $16.00 $17.00 38
Capacity (barrels) 65 80 105

Then the objective function Z of the modified problem and constraints are written as
Minimize Z=12X11+15X12+15X13+14X21+9X22+10X23+13X31+19X32+11X33+10X41+16X42+14X43+7X51+14X52+12X53+20X61+16X62+17X63
Subject to
X11+X12+X13=35
X21+X22+X23=26
X31+X32+X33=42
X41+X42+X43=53
X51+X52+X53=29
X61+X62+X63=38
X11+X21+X31+X41+X51+X61 65
X12+X22+X32+X42+X52+X62 80
X13+X23+X33+X43+X53+X63 105
Xij 0, i=1,2,3,4,5,6; j=1,2,3.

(4) The modified transportation problem can be solved using excel solver and the following solutions were obtained

The new solution is given below.

White water Los Canos Duras
Kingsport 16 19
Danville 26
Macon 42
Shelma 36 17
Columbus 29
Allentown 38
Dummy 27

The minimum cost=16*15+19*15+26*9+42*11+36*10+17*14+29*7+38*16
=$2630.

Therefore, the new optimal transportation procedure using the intermediate sites is to transport
(1) 36 bbl from Shelma and 29 bbl from Columbus to the White water waste disposal plant
(2) 16 bbl from Kingsport, 26 bbl from Danville and 38 bbl from Allentown to Los Canos waste disposal plant
(3) 19 bbl from Kingsport, 42 bbl from Macon, 17 bbl from Shelma and 10 bbl from Allentown to the Duras waste disposal plant.
To get this cost advantage company must use the following roots for transportation. Waste from Kingsport to Duras (19 bbl) must take to Danville first and then from take Danville to Duras. Waste from Shelma to White water (36 bbl) must be transported and dropped at Columbus first and from there it must be shipped to White water. Waste from Shelma to Duras ($17 bbl) must be transported and dropped at Macon first and from there it must be shipped to Duras.

(5) Conclusion

Using the original problem the minimum cost of the company was estimated as $2822. But, using certain intermediate points to drop the waste to get cost advantage the original problem was modified and again solve using solver. The result showed that the new model caused a considerable reduction in transportation costs. The optimum cost of the Stateline Shipping Company reduced to $2630. To get this cost advantage company must use the following roots for transportation. Waste from Kingsport to Duras must take to Macon first and then from take Macon to Duras. Waste from Macon Los Canos should be transported to Selma first and then from Shelma to Los Canos. Waste from Shelma to White water must be transported and dropped at Columbus first and from there it must be shipped to White water. Waste from Shelma to Duras must be transported and dropped at Macon first and from there it must be shipped to Duras. Waste from Allentown to White water must be transported and dropped at Kingsport first and from there it must be shipped to White water. Finally waste from Allentown to Duras must be transported and dropped at Danville first and from there it must be shipped to Duras.

Limitations
The main limitation is that, in the above calculations, we have considered the cost aspect only. Handling of very dangerous industrial wastes cannot be considered based on cost aspect alone. In our problem, it should be noted that this waste contains hazardous elements and hence transportation of waste to many intermediate positions will increase the risk of the company. Another important limitation of this study is we have not considered the time required to transport waste from one station to another. If the waste from the sites do not reach at the disposable sites at proper time, dispose of wastes may become difficult. If we use intermediate sites to drop waste for cost advantage this delay become more serious. Also note that transporting and dumping of waste from one plant to another plant which is not meant for waste disposable may become legal problems.…...

Similar Documents

Free Essay

Assignment # 4

...• Assignment #4: Case Problem "Stateline Shipping and Transport Company" Read the 'Stateline Shipping and Transport Company" Case Problem on pages 273-274 of the text. Analyze this case, as follows: 1. In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. 2. Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program, Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. 3. Solve the model you developed in #3 (above) and clearly describe the results. 4. Interpret the results and draw conclusions that address the question posed in the case problem. What are the limits of the study? Write at least one paragraph. There are two deliverables for this Case Problem, the Excel spreadsheets and an accompanying written description/explanation. Please submit both of them electronically via the dropbox. The assignment will be graded using the associated rubric. |Outcome Assessed: |Develop solutions for transshipment problems. | | |Communicate issues in Management Science  | |Grading Rubric for Stateline Shipping & Transport Case Problem ...

Words: 586 - Pages: 3

Free Essay

Shipping Industry

...SHIPPING TRENDS Capt. S. Pullat BA, MCIT, MCIArb, FICS AUMNI Shipping Consultants In the midst of technological developments, its application and futuristics, the Customers seem to be relegated to the back seat. Beware, if one does not treat them like a King or at least a la Prince, they could be King makers, and any case has a decisive role to play in all our endeavours for success. For, if we are driven by technology alone –as predominantly this forum is- we must ensure that it is affordable, safe, has redundancy and environmentally and user friendly as well. Technology per se does not solve problems, it enables problem solving and must be proactive too so that obsolescence can be planned and replacement provided for. Perhaps there is a lot to learn from the Computer industry, software sector in particular, as to how upgradation or newgradation is to be effected frequently. A cyclical and capital-intensive industry such as shipping has been slow to change and innovate, so much so it is driven by regulators and not industry itself. Such hindsight methodology has considerable time lag before ushering in corrective measures and in the interim the industry’s image and perception has suffered in the eyes of users and the public at large. Handful are the cases where ships are built to higher specifications than the bare minimum that Class calls for. A major operator recently citing experience criticised the need to shell out huge sums to overcome the cost saving nexus...

Words: 1659 - Pages: 7

Free Essay

International Shipping

...Assignment – (Individual) Course: Diploma in Logistics Management Batch: DLM 12/41 Module: International Shipping Management ------------------------------------------------- Lecturer: Mr Eddie Tan Assignment On: What risks and perils are present in global transportation? Discuss how exporters and importers can manage these risks. Submission Date: 27th Feb 2013 Name(s) of Student: Norhazura Binti Zulkafly (Word count –1,882) Table of Content Chapter | Title | Page | 1 Introduction 3 2 Global trends and challenges in transport sector 4 3 Cargo Insurance 8 4 Transportation Perils 10 5 Managing Risks 11 6 Insurable interest 12 7 Summary 13 9 Bibliography 14 1. Introduction The global economy is going through a highly volatile period as highlighted in the Transportation Profile. Diesel and bunker fuel prices have been largely unpredictable, thanks to the wild swings in crude oil prices (peaking at nearly $150 per barrel before plummeting to less than $40 per barrel in 2008). Demand for industrial and consumer products has contracted after years of unprecedented growth, due to rising prices and a global recession, and companies have struggled to secure needed financing because of the global credit crunch. They create extreme challenges in the market for global transportation services. Just a few short years ago during the global trade boom, ports were testing......

Words: 1948 - Pages: 8

Free Essay

Stateline Shipping and Transport Company

...Stateline Shipping and Transport Company The transportation model will be set up by assigning a variable to each site. The plants Danville, Selma, and Columbus are 1, 2 and 3 respectively. This makes the waste disposal sites at White Water, Los Canos, Duras variables A, B and C, respectively. Decision variables: 1. Ship from 1: x1A, x1B, x1C 2. Ship from 2; x2A, x2B, x2C, 3. Ship from 3: x3A, x3B, x3C, The objective function is: Min. cost Z= 14x1A+9x1B+10x1C+17x2A+16x2B+19x2C+7x3A+14x3B+12x3C There will be one constraint for each location regardless of how many variables. Plant constraints: Output from plant 1: x1A + x1B + x1C =26 Output from plant 2: x2A + x2B + x2C = 53 Output from plant 3: x3A + x3B + x3C = 29 Waste disposal site constraints: Intake at site A: x1A + x2A + x3A ≤65 Intake at site B: x1B + x2B + x3B ≤80 Intake at site C: x1C + x2C + x3C ≤105 Once the data solver is set up the model comes up with this solution: Ship all Danville and Selma waste to Los Canos and all Columbus Waste to White Water to get a shipping cost of $1285.00 3. The transshipment model will follow the same logic as the transportation when setting up the variables. There will be a variable for each shipment from plant to plant, plant to waste disposal site and waste disposal site to waste disposal site. I started out Decision......

Words: 587 - Pages: 3

Premium Essay

Stateline Shipping and Transport Company

...Stateline Shipping and Transport Company School of Business MAT 540 This paper was presented in submission for MAT 540 assignment four (Part 1 Only). Abstract This paper serves as a written response to the instructions and questions asked in assignment four. Assignment four instructed the writer to read the case problem Stateline Shipping and Transport Company from pages 273-274 in the text, Introduction to Management Science by Bernard W. Taylor. The assignment then directed the writer to Formulate and Solve and linear transportation programming model, this step was done in QM. The linear programming model is attached herein. Keywords: Linear Programming, Transportation, Shipping, Model Introduction This Case Problem, Stateline Shipping and Transport Company, is based on a girl named Rachel Sundusky who is a manager of the South-Atlantic office for Stateline Shipping and Transport (Taylor, 2010). Rachel is negotiating a contract with Polychem an industrial use chemical company (Taylor, 2010). Polychem has six sites that it would like for Stateline to pick up waste from (Taylor, 2010). Polychem would then like for Stateline to transport the waste for disposal to one of three sites (Taylor, 2010). Polychem has agreed to handle all of the waste at all sites therefore Stateline needs only transport the materials and incur costs for the same (Taylor, 2010). Rachel would like to see what the less costly shipping routes are (Taylor, 2010). Rachel will need all of......

Words: 1105 - Pages: 5

Premium Essay

Case Problem: Stateline Shipping and Transport Company

...Case Problem: Stateline Shipping and Transport Company Assignment #4 Case Problem: Stateline Shipping and Transport Company MAT540: Quantitative Methods Vargha Azad 09/08/13 In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program. Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. 6 Plants labeled 1 through 6, 3 waste facilities labeled A through C Objective function: Minimize Z = 1A(12) + 1B(15) + 1C(17) + 2A(14) + 2B(9) + 2C(10) + 3A(13) + 3B(20) + 3C(11) + 4A(17) + 4B(16) + 4C(19) + 5A(7) + 5B(14) + 5C(12) + 6A(22) + 6B(16) + 6C(18); Subject to: 1A + 1B + 1C = 35 2A + 2B + 2C = 26 3A + 3B + 3C = 42 4A + 4B + 4C = 53 5A + 5B + 5C = 29 6A + 6B + 6C = 38 1A + 2A + 3A + 4A + 5A + 6A ≤ 65 1B + 2B + 3B + 4B + 5B + 6B ≤ 80 1C + 2C + 3C + 4C + 5C + 6C ≤ 105 All Combinations ≥ 0 Solver add-on solution in MS Excel yielded the following results: 35 bbl of wastes shipped from Kingsport to Whitewater, 26 bbl of waste shipped from Danville to Duras, 42 bbl of wastes shipped from Macon to Duras, 1 bbl of wastes shipped from Selma to Whitewater, 52 bbl of wastes shipped from Selma to Los Canos, 29 bbl of wastes shipped......

Words: 1072 - Pages: 5

Premium Essay

Stateline Shipping

...Stateline Shipping and Transport Company Carla Coleman Strayer University MAT 540: Quantitative Method Dr. Luke Howard March 20, 2014 2014 Case Study: Stateline Shipping and Transport Company In this case study, we are introduced to Rachel Sundusky, the manager of the South-Atlantic office of the Stateline Shipping and Transport Company. The information we are given is that Rachel is in the process of negotiating a new contract to haul hazardous chemical waste from six (6) locations to three (3) waste disposal sites for Polychem, a manufacturer or chemicals for industry use. Rachel has estimated both the cost to transport one barrel from each location to each disposal site, as well as between each location. In estimating these costs, Rachel took into account that some towns and municipalities where the six plants are located restrict the transportation of hazardous material within municipal limits, so costs in some cases had to include traversing circutous routes. Rachel is given the number of barrels of waste each of the six plant locations will need picked up and how many barrels each of the waste disposal sights can accept. Given this information, and the esimated shipping costs she has developed, Rachel would like to determine which shipping routes will minimize Stateline’s total cost. She would like to consider the cost to move the waste directly from each plant location to a...

Words: 525 - Pages: 3

Free Essay

Shipping Industry

...Indian shipping industry growth and constraints The Indian shipping industry accounts for 95% of the Indian trade by volume and approx. 70% of Indias trade by value. This industry mainly relies on Indian exports and imports and has been severely impacted by the recession of 2008-09 as felt by the Indian industries. The main components of industry include Dry cargo which is required for the import of iron ore , coal etc ( accounting for 66% of indias shipping trade). and the wet cargo which includes crude oil etc (34.7%).The Indian shipping industry with its fleet of 1029 ships as on 2012 is the 15th largest in the world and has grown at a CAGR of 3.3% since 1970’s, but however there are plenty of new opportunities for growth as well as severe constraints facing the industry. With the liberalization of the Indian economy and during the period of economic boom, there has been an ever increasing demand for LNG to be imported in the country in order to sustain Indias fertilizer and power plants. This is followed by a need to integrate and develop multimodal logistics in order to ensure that the cargo once unloaded is delivered to the desired location in a speedy manner. This is being taken up by India by planning 16 multimodal logistic parks along Delhi to Mumbai highways and also with the Modi government’s vision of connecting all the rivers in India in order to boost up intra country trade. Another opportunity for growth for the Indian shipping industry which is primarily......

Words: 610 - Pages: 3

Premium Essay

Stateline Shipping

...Assignment #4: Case Problem “Stateline Shipping and Transport Company” 1. In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. White water Los Canos Duras Availability Kingsport $12.00 $15.00 $17.00 35 Danville $14.00 $9.00 $10.00 26 Macon $13.00 $20.00 $11.00 42 Selma $17.00 $16.00 $19.00 53 Columbus $7.00 $14.00 $12.00 29 Allentown $22.00 $16.00 $18.00 38 Capacity 65 80 105 223 The objective of the problem is to develop a shipping schedule that minimizes the total cost of transportation. Suppose Xij denotes the number of barrels of wastes to be transported from the “i” plant to “j” site. Then the total cost of transportation is: Z = 12 X11 + 15 X12 + 17 X13 + 14 X21 + 9 X22 + 10 X23 + 13 X31 + 20 X32 + 11 X33 + 17 X41+ 16 X42 + 19 X43 + 7 X51 + 14 X52+ 12 X53 + 22 X61 + 16 X62 + 18 X63. Thus the objective function of the problem is to minimize Z = 12 X11 + 15 X12 + 17 X13 + 14 X21 + 9 X22 + 10 X23 + 13 X31 + 20 X32 + 11 X33 + 17 X41+ 16 X42 + 19 X43 + 7 X51 + 14 X52+ 12 X53 + 22 X61 + 16 X62 + 18 X63. Constraints Availability in plants: X11 + X12 + X13 = 35 X21 + X22 + X23 = 26 X31 + X32 + X33 = 42 X41 + X42 + X43 = 53 X51 + X52 + X53 = 29 X61 + X62 + X63 = 38 Capacity of the sites: X11 + X21+ X31+X41 + X51 + X61 ≤ 65 X12 + X22+ X32+X42 + X52 + X62 ≤ 80 X13 + X23+ X33+X43 + X53 + X63 ≤ 105 Non- Negativity restrictions Xij ≥ 0 , i = 1,2,3,4,5,6 ; j = 1,2,3...

Words: 2300 - Pages: 10

Premium Essay

Stateline Shipping

...Stateline Shipping and Transport In the “Stateline Shipping and Transport Company” case there is the manager Rachel Sundusky of the South –Atlantic office of the Stateline Shipping and Transport Company. She is trying to negotiate a new shipping contract with Polychem where Stateline picks up and transport waste product form its six plants to three waste disposal sites. In this problem we are trying to determine the shipping routes the will minimize Stateline total cost. In the first part I set up the problem in excel showing the shipping to the waste directly from the six plants to the three waste disposal site. In the result I had a Z value which is the minimum cost of $3090.00 that Polychem will pay Stateline to transport their products. It also shows that Danville and Columbus is not safe to ship from because they cannot provide the supply that is needed. In the second part I develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. In the results it shows that I had a Z value which is the minimum cost of 2884.00 that Polychem will pay Stateline to transport their products. Also shows that Danville is not worth using to ship from because they cannot provide the supply that is needed. The overall results show that it is cheaper for Stateline to use the routes where the plants and disposal sites can be used as intermediate points. In both models it shows that Danville is not a good shipping site. Over all......

Words: 292 - Pages: 2

Free Essay

Stateline Transhipment Models

...from sources to destinations, or some combination of these alternatives. Therefore we can apply the transshipment models to inventory applications because deals with a source and destinations and they are similar. The transportation model is an example of decision making under certainty because the sources and destination are known factors before making the decision. Author: Anonymous Date: Thursday, April 28, 2011 4:35:45 PM EDT Subject: Week 10 Discussion 2 Explain the assignment model and how it facilitates in solving transportation problems. What benefits would be gained from using this model? Explain the assignment model and how it facilitates in solving transportation problems. The assignment model is for a specific form of transportation model in which all supply and demand values are equal to one. Is basically tells you which value X- needs to go to which destination Y-. Assignment #4: Case Problem "Stateline Shipping and Transport Company" The model developed describes the shipping of the waste from the plants to the three waste disposal sites. The results for the model are that of the numbers for the six plants and the three waste. The waste received is broken down in the other two models. The limits to the study are that it doesn’t state how long it took to accumulate a cost of 2630. Also out of the six plants only three of them were taken to a disposal site....

Words: 403 - Pages: 2

Premium Essay

Assignment 4

...Week 10 Assignment Click the link above to submit your assignment Assignment #4: Case Problem "Stateline Shipping and Transport Company" Read the 'Stateline Shipping and Transport Company" Case Problem on pages 273-274 of the text. Analyze this case, as follows: In Excel, or other suitable program, develop a model for shipping the waste directly from the 6 plants to the 3 waste disposal sites. Solve the model you developed in #1 (above) and clearly describe the results. In Excel, or other suitable program, Develop a transshipment model in which each of the plants and disposal sites can be used as intermediate points. Solve the model you developed in #3 (above) and clearly describe the results. Interpret the results and draw conclusions that address the question posed in the case problem. What are the limits of the study? Write at least one paragraph. There are two deliverables for this Case Problem, the Excel spreadsheets and an accompanying written description/explanation. Please submit both of them electronically via the dropbox. The assignment will be graded using the associated rubric. Outcome Assessed: Develop solutions for transshipment problems. Communicate issues in Management Science Grading Rubric for Stateline Shipping & Transport Case Problem There are 12 points in each of the five criteria for a total of 60 points possible Criteria 0 Unacceptable (0 points) 1 Developing (6 points) 2 Competent (9 points) 3 Exemplary (12 points) 1.......

Words: 589 - Pages: 3

Free Essay

Shipping

...Exclusive Summary Shipping has been an important human activity, especially where prosperity depended primarily on international trade and interregional trade. Transportation has been one of the main factors of globalization, along with communications, international standardization, and trade liberalization. Due to a number of technological, economic, and socio-cultural forces, only limited country can keep itself fully isolated from the economic activities of other countries. Many countries have seen enormous economic growth in the recent past due to their willingness to open their borders and markets to foreign investment and trade. This increased flow of knowledge, resources, goods, and services among world’s nations is called “globalization”, formally defined as the development of an increasingly integrated global economy marked especially by free trade, free flow of capital, and the tapping of cheaper foreign labor markets. Introduction Marine transportation is an integral, if sometimes less publicly visible, part of the global economy. The marine transportation system is a network of specialized vessels, the ports they visit, and transportation infrastructure from factories to terminals to distribution centers to markets. Maritime transportation is a necessary complement to and occasional substitute for other modes of freight transportation. For many commodities and trade routes, there is no direct substitute for waterborne commerce. The Important of Maritime......

Words: 1767 - Pages: 8

Free Essay

Assignment #4: Case Problem “Stateline Shipping and Transport Company”

...Stateline Shipping And Transport Company 1. Formulation of the Problem The Stateline Shipping and Transport Company wanted to transport industrial wastes from the 6 plants to the 3 waste disposable sites. The problem can be represented in as a Transportation table as shown below. Our problem is to find roots to disposable sites, such that the cost of transportation is minimized.. White water Los Canos Duras Availability (bbl) Kingsport $12.00 $15.00 $17.00 35 Danville $14.00 $9.00 $10.00 26 Macon $13.00 $20.00 $11.00 42 Selma $17.00 $16.00 $19.00 53 Columbus $7.00 $14.00 $12.00 29 Allentown $22.00 $16.00 $18.00 38 Capacity (barrels) 65 80 105 Mathematical Formulation Let Xij i=1,2,3,4,5,6; j =1,2,3 denote the quantity of waste transported from i-th plant to j-th waste disposal centre. Then the objective function Z representing the cost and different constraints of the problem can be written as Minimize Z=12X11+15X12+17X13+14X21+9X22+10X23+13X31+20X32+11X33+17X41+16X42+19X43+7X51+14X52+12X53+22X61+16X62+18X63 Subject to X11+X12+X13 = 35 Is this essay helpful? Join OPPapers to read more and access more than 600,000 just like it! get better grades X21+X22+X23 = 26 X31+X32+X33 = 42 X41+X42+X43 = 53 X51+X52+X53 = 29 X61+X62+X63 = 38 X11+X21+X31+X41+X51+X61 65 X12+X22+X32+X42+X52+X62 80 X13+X23+X33+X43+X53+X63 105 Xij 0, i=1,2,3,4,5,6; j=1,2,3. 2. The transportation problem described above can be solved mathematically using a......

Words: 385 - Pages: 2

Premium Essay

Stateline Shipping and Transport Company

...The first time we touched it meant so much been so long since I felt a bond so strong, I know we are just trying to figure this out but a relationship is what its all about. I got you and you me thats the way god meant it to be So when we go through hard times times and our rhythm has no rhyme and our space seems dark just know in your heart that there is no beginning without a start. If you believe in me like I believe in you there is nothing in this world that we cant do. If all we can be is happy be a little nasty and share the joys and pain this life would not be in vain cause that’s what life is about Trying to clear my head listen to all the things you said and placing it on my mind cause I think we are one of kind. I need you I hope that you need me from a small seed grows a tree strong enough to break the earth and bear fruit to feed And that is what I want with you. Promise to be true just give me a seed see if we can grow at tree strong enough to hold me and you and feed our hearts desire cause you know that I admire all that you are you are a shining star. Brighten up my day in so many ways share in my goals and my pain I really cant explain but I only hope I can do the same...

Words: 265 - Pages: 2