Transporatation problems exercises

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TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEMS 
EXERCISES 
 
 
 
 
Vassilis Kostoglou 
 E-mail: vkostogl@it.teithe.gr 
 URL: www.it.teithe.gr/~vkostogl 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 1 
 
A factory producing aluminum is supplied with bauxite from three mines (01, 02 and 03) 
which produce 3, 7 and 5 thousand tones of mineral per week respectively. There are 4 
modes of transportation of bauxite to the factory: by ship (T1) - by trucks (T2) - by a 
simple railway wagon (T3) - by special railway wagons (T4). The total capacity per day 
is 4 thousand tones for ships, 3 thousand for cars and 4 thousands each one of 
the two types of rail. Transportation costs per tone are given in the following table. 
 
 
Vehicles 
 
Mines 
 
Τ1 
 
Τ2 
 
Τ3 
 
Τ4 
01 2 2 2 1 
02 10 8 5 4 
03 7 6 6 8 
 
Identify the quantities that must be transported by any means of transportation so as to 
minimize the total transportation cost. 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 2 
 
One of the main products of P & T Company, a large canning industry is canned beans. 
There are three canneries which send products to four distribution centers. Since 
transportation costs are particularly increased due to large distances, the administration 
decided to reduce it. There have been some estimates of the quantity production and 
transportation to distribution centers and as for the transportation costs of each load 
(fully loaded truck company) it is denominated in U.S. dollars. 
 
 Distribution 
centers 
 
 1 2 3 4 
1 464 513 654 867 75 
Canneries 2 352 416 690 791 125 
3 995 682 388 685 100 
 80 65 70 85 
 
Find the combination of the transportation load that minimizes the total transportation 
cost. 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 3 
 
A company that produces an innovative product has two branches and three main 
customers. The two branches will produce 60 units and 40 units respectively of the 
product during the next period. The company is committed to sell 50 units to the first 
customer and at least 20 units to the third customer. The second and the 
third customer also want to buy as many units from those remaining. The profit of the 
company (expressed in thousands of euro) depending on the transportation of its 
branches to customers is given in the following table. 
 
 
 Customer 
 1 2 3 
Branch 1 5 7 6 
Branch 2 2 3 5 
 
How should we distribute the products in order to maximize the total profit? 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 4 
 
Factories X, Y and Z of a business have a monthly production capacity of a chemical 
product 22, 15 and 8 tons respectively. This production covers the needs of four 
consumer centers, which need 7, 12, 17 and 8 tons per month. The cost of transporting 
one tone (in €) from the factories in the centers of consumption is indicated in the 
following table. 
 
Consumer 
center 
Factory 
 
Ι 
 
ΙΙ 
 
ΙΙΙ 
 
ΙV 
Χ 5 2 4 3 
Y 4 8 1 6 
Ζ 4 6 7 5 
 
The responsible officer has formed the following program based on his experience: Χ 
 ΙΙ: 12 tones, Χ  ΙΙΙ: 1 tone, Χ  ΙV: 9 tones, Y  ΙΙΙ: 15 tones, C  Ι : 7 tones, C  
ΙΙΙ : 1 tone. 
Consider whether the transportation program developed is the best possible. If not, then 
determine the optimum solution. 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 5 
 
A commercial company has three stores, let it be A, B and C, from which supplies its 
three main largest customers, let it be M, N and Q, with a consumer product. All 
warehouses have approximately the same size as with corresponding capacity of 50 
tones for this product. The three customers require a certain period of time 30, 45 
and 25 tones respectively. Transportation cost (in €) of each tone from each warehouse 
to each customer is as follows. 
 
Customer 
Warehouse 
Μ Ν Q 
A 30 40 10 
B 20 10 50 
C 70 20 20 
 
The company's management wants to know whether it would be desirable to eliminate 
one of the warehouses and sell the corresponding stock. What in your opinion is the 
most appropriate decision? 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 6 
 
A company has three branches which produce a particular product that after 
production is transported to distribution centers. Branches 1, 2 and 3 produce 12, 17 
and 11 loads per month respectively. Each distribution center needs to collect 10 loads 
per month. The distance from each branch in the respective distribution centers is given 
(in kms) in the following table. 
 
 Distribution center 
 1 2 3 4 
 1 800 1300 400 700 
Branch 2 1100 1400 600 1000 
 3 600 1200 800 900 
 
The fixed cost of each load is € 30 and the extra charge is € 1.50/km. 
a) Design the appropriate transportation model. 
b) Using the method of the northwest corner find the initial basic feasible solution. 
c) Starting with the initial basic feasible solution determined to the question b find the 
 optimal solution. How many loads must be transferred from each branch to each 
 distribution center in order to minimize the total transportation cost? 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 7 
 
Let us suppose that England, France and Spain produce the whole wheat, barley and 
oats in the world. The demand for wheat in the world requires 125 million hectares 
available for its production. Similarly, 60 million hectares of land are required for the 
production of barley and 75 for the production of oats. The total area available for this 
purpose in England, France and Spain is 70, 110 and 80 million hectares respectively. 
The number of hours required in England, France and Spain for the production of wheat 
in one hectare of land is 18, 13 and 16 hours respectively. The corresponding hours in 
the three countries for the production of barley in a hectare of land is 15, 12 and 12 
hours respectively. The number of hours required in England, France and Spain for the 
production of oats in one hectare of land is 12, 10 and 16 hours respectively. The 
cost for each working hour for the production of wheat in England, France and Spain 
is $ 3, $ 2.40 and $ 3.30 per hour respectively. The comparable costs for every working 
hour for the production of barley is $ 2.70, $ 3 and $ 2.80 respectively, while for the 
production of oats is $ 2.30, $ 2.50 and $ 2.10 respectively. 
 
The problem that must be addressed is the distribution of land used for each country so 
as to meet global needs and simultaneously minimize the total labor costs. Design and 
resolve the appropriate transportation model. 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 8 
 
The company SAS has a chain of stores that sell equipment, hi-fi. The shareholders are 
thinking of ordering new midi systems, which then would sell 430 pounds. The shops 
are separated into three geographical areas, north, west and south and SAS believes 
that the demand for the system in each area will be 170, 210 and 150 units 
respectively. The SAS has decided to order 100 units for each geographic area stores.
 
There are three potential suppliers for the system A, B and C. A is capable of supplying 
200 units for 400 pounds the one, the B 160 units for 420 pounds the one and C 180 
units for 410 pounds the one. These prices do not include the transportation costs that 
vary with the supplier and the supply contract according to the following table. 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 Stores 
Suppliers North West South 
Α 20 10 5 
Β5 15 20 
Γ 30 10 25 
 (Unit transportation cost in British pounds) 
 
The SAS wants to maximize the profit from the sales of the new system. 
Design and solve the corresponding transportation problem. 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 9 
 
An airline company buys fuel for the plane from three vendors. The company needs for 
each of the three airports that uses and for the next months 100000 gallons for the first, 
180000 gallons for the second and 35000 gallons for the third airport. Each vendor can 
supply fuel to any airport in the price (dollars per gallon) given in the table below. 
 
 Airport 1 Airport 2 Airport 3 
Seller 1 0.92 0.89 0.90 
Seller 2 0.91 0.91 0.95 
Seller 3 0.87 0.90 0.92 
 
 
Each seller has a restriction on the total amount of fuel that can be supplied each 
month. The potential is 320000 gallons for the seller 1, 1270000 gallons for the seller 
2 and190000 gallons for the seller 3. 
 
Find the right fuel purchasing policy so as to minimize the total cost of feeding the 
three airports. 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 10 
 
A farmer's association has launched public competition for the daily transportation of 
some cereal from the head offices of the three regional warehouses. The daily 
requirements of the warehouses are amounted to 18, 10 and 8 tones respectively. 
Overall offers were submitted by three carriers, each specifying the maximum amount 
of weight that can carry per day. These quantities are equal for all three companies with 
12, 16 and 24 tones respectively. The costs for the transportation of one tone 
of grain from each company in the three regional warehouses are presented (in €) in 
the following table. 
 
Warehouses 
 7000 4000 10000 
Companies 5000 3000 9000 
 6000 5000 9000 
 
What contracts exactly would you advise the administration of the partnership to sign, so 
that on the one hand to minimize the total transportation cost, on the other hand not the 
administration be accused for bias in favor of or against any of the carriers? 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 11 
 
A food industry produces chips at three factories, located in Birmingham, Glasgow and 
London. Since the customers should be supplied with fresh products, these are not 
stored in the factories. The monthly production ability of the factory in London is 750 
tones, while of the other two are 500 tones. Every day 300 tones are given to the five 
warehouses in order to subsequently be transferred to customers. The profit per sale 
tone from the first warehouse is 0.4 pounds if produced in London, 0.6 if produced in 
Glasgow and 2.2 pounds if produced in Birmingham. The corresponding gains for 
the second warehouse are 1.1, 1.2 and 2 pounds. 
 
The profit per tone of production in London is 1.7, 1.3 and 2.5 pounds when sold by the 
third, fourth and fifth warehouse respectively. The corresponding gains for Birmingham 
are 1.6, 1 and 0.5 pounds, while for Glasgow are 1.1, 0.8 and 2.1 pounds. 
 
What is the maximum monthly profit that can be achieved by the industry? 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 12 
 
One major producer wants to buy raw material that does not exist in large stock. He 
needs to purchase 100 tones per week for the operation of the three factories, which 
have regular weekly requirements 40, 15 and 45 tons respectively. It is possible to 
satisfy these requirements if it obtains 40, 35 and 25 tons per week from three different 
suppliers. The cost of each unit of raw material is charged the same from any supplier, 
but the buyer must pay the costs of transportation for the three factories 6, 3.6 and 4.8 
pounds for the first supplier, 2.4, 1.2 and 0.6 pounds for the second supplier and 6, 4.8 
and 3.6 pounds for the third supplier, respectively. 
 
(a) How should the producer make the orders to minimize the total transportation 
 cost and simultaneously meet requirements of the factory? 
(b) Assume that in the initial problem the requirement of the first factory is 50 tons 
 per week, of the second factory 15 tons a week and of the third factory 35 tones 
 per week. 
 
Determine the optimal solution and compare with that of the initial problem. 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 13 
 
A pastry company produces a special type of bread in two branches with the following 
production data. 
 
Branch Production 
capacity 
(kg) 
Production 
cost 
($/kg) 
Α 2500 0.23 
Β 2100 0.25 
 
Four restaurant chains want to purchase this special type of bread. Their requirements 
and the amount they offer are given in the table below. 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
Chain Maximum 
demand 
(in kg) 
Offering price 
($/kg) 
1 1800 0.39 
2 2300 0.37 
3 550 0.40 
4 1750 0.36 
 
Transportation costs (in $) of one kg of bread from each branch of the chain restaurants 
are: 
 
 Chain 1 Chain 2 Chain 3 Chain 4 
Branch Α 0.06 0.08 0.11 0.09 
Branch Β 0.12 0.06 0.08 0.05 
 
Design the delivery plan, which maximizes the net profit. 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 14 
 
A wholesaler sells some food in four major markets, let it be A, B, C and D. The weekly 
demand has been accurately predicted and is 40 bags for the market A, 30 for B and C 
and 20 bags for the market D. The wholesaler always orders the goods he markets from 
two local producers, P & R. The first of them charges €1 for the transportation of one 
bag in market A, € 4 for B, € 5 for C and € 6 for D. 
 
As expected the cost of food is charged separately. The producer P charges €1 for the 
transportation bags to the market A, €2 for B, €7 for C and €9 for D, without including the 
cost of the product. One particular week both producers can supply from 65 bags, but 
the producer P sells food for €1 more expensive per bag than P. 
 
Which are the orders which must be placed this week by the wholesalers? 
 
Next week the producers can still supply the same quantities, but now P sells €1 per bag 
more expensive than P, even though transport costs have not changed at all. 
 
Should the wholesaler change the orders? And if so, how exactly? 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 15 
 
The air company "Greek Air-transportations" uses four types of aircrafts (Β 727, Β 737, 
Β 707, Α 300) and aims to use them in four new routes of transportation of the fresh 
agricultural products: 
ΕΑ 101: Athens - Bucharest 
ΕΑ 108: Athens - Glasgow 
ΕΑ 205: Thessaloniki - Laussane 
ΕΑ 207: Thessaloniki - Hamburg 
 
The weekly demand of the products is calculated to 400 tons for Bucharest, to 530 for 
Glasgow, to 450 for Laussane and to 480 for Hamburg. The offering transportation 
ability for the same time period is 420 tones with Β 727, 390 tones with Β 737, 480 
tones with Β 707 and 570 tones with Α 300 (without the number of the aircrafts or the 
routes getting examined). 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
The Β 737 cannot be used to the route Athens - Glasgow due to restricted action radius 
(a medium supply is disadvantageous) while the Α 300 can’t fly to Bucharest, because 
there is not specialized technical land potential. The profit per tone (in €) for each flight-
type aircraft combination is: 
 
 Flight 
 
Aircrafts 
 
ΕΑ 101 
 
ΕΑ 108 
 
ΕΑ 205 
 
ΕΑ 207 
Α 300 8 16 13 14 
Β 727 9 7 13 12 
Β 737 10 10 14 12 
Β 707 12 14 13 14 
 
Design the routes so as to maximize the profit. 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 16An agricultural partnership has the following orders (in tones) for fresh and canned 
peaches. 
 
Month 
 
Product 
 
May 
 
June 
 
July 
 
August 
Fresh 
Can 
50 
45 
120 
40 
140 
35 
100 
55 
 
The collection of one peach tone requires four working hours, the sorting and their 
package for direct disposition (fresh) six working hours, while the canning of the same 
quantity requires five working hours. 
 
The partnership employs totally 10 employees, that work in average 25 days per month 
by full daily 8-hour. 5 of them should be moved to other cultivation for 13 days every 
month in May and for 16 days in July and in August. 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
Monthly wages are formed per four-month as follows: 
 
Labor - Month May June July August 
Collection 1000 1100 950 900 
Package 800 850 800 700 
Canning 800 800 900 800 
 
Late delivery of an order is not possible. Production that exceeds demand of the same 
period reflects a charge against salary of € 50 during the month that production exceeds 
demand. 
 
Design the most advantageous production to the partnership. 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
PROBLEM 17 
 
A company has decided to produce three new products. Its five branches are currently 
over production capacity. The construction cost of one unit of the first product will be $ 
31, $ 29, $ 32, $ 28 and $ 29 in 1st, 2nd, 3rd, 4th and 5th branch respectively. Construction 
cost of a unit of the second product will be $ 45, $ 41, $ 46, $ 42 and $ 43 
in 1st, 2nd, 3rd, 4th and 5th branch respectively. Construction cost of a unit of the third 
product will be $ 38, $ 35 and $ 40 in 1st, 2nd and 3rd branch, respectively, while 
the 4th and 5th branch do not have the ability to produce this product. The sales 
division is that they can be produced 6000, 10000 and 8000 units of products 1, 2 
and 3 respectively per day. Branches 1, 2, 3, 4 and 5 have the potential to produce 
4000, 6000, 4000, 6000 and 10000 units per day, respectively, without including the 
combination of products available. It is assumed that whichever branch has the 
ability and capacity to produce these products it can also produce combinations of 
these in any quantity. 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
The administration wants to know how to allocate new products to the branches in order 
to minimize construction costs. 
 
a) Design the problem as a transportation model. 
 
b) Starting with the Vogel method for finding the initial possible solution use the 
 Simplex method of transposition problems to determine the optimal solution. 
 
 
 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
PROBLEM 18 
 
A company which produces a unique product has three branches and four main 
customers. The three branches will produce 6, 8 and 4 units respectively during 
the following period. The company has pledged to sell 4 units to the first client, 6 units 
to the second client and at least 2 units to the third client. The third and fourth clients 
want to buy as much as possible of what will be left over. The net profit from the 
transportation of a unit from the branch i to customer j is given in the table below. 
 
Clients 
 
Branches 
 
1 
 
2 
 
3 
 
4 
1 6 3 2 4 
2 7 5 4 6 
3 9 8 6 3 
 
The management wants to know how many units to sell to its interest to the third and 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
fourth clients and how many units should be transferred from the branches to each of 
the four clients in order to maximize the total profit. 
 
PROBLEM 19 
 
New designs must be done for the energy systems of a new building. The three 
possible sources of energy are electrical, gas and solar energy. The building needs the 
energy for electricity, water heating and heating of the interior spaces. The 
respective daily requirements are: 
 
Electricity : 20 units 
Water heating : 10 units 
Heating : 30 units 
 
The size of the roof reduces solar modules to 30 points, while there is no restriction for 
the rest. The electricity needs can be satisfied by the electricity market ($ 200 unit). The 
needs of the two other sources can be met from some source or combination of 
sources. Prices of units are: 
 
 Electricity Natural Solar 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
gas energy 
Water heating $ 450 $ 300 $ 150 
Heating $ 400 $ 250 $ 200 
(a) Design the problem as a transportation model. 
 
(b) Use the northwest corner method for finding the initial basic possible solution to the 
 problem as designed at (a). 
 
(c) Starting with the basic feasible solution of (b), use the Simplex transportation 
 method to determine the best solution. 
 
(d) Use Vogel method for finding the initial feasible solution of the problem as designed 
 at (b). 
 
e) Starting with the initial basic feasible solution of the question (d), use the 
 methodology of transposition problems to find the optimal solution. 
 Compare the numbers of steps required to determine the optimal solution using 
 the above two methods. 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
PROBLEM 20 
 
A company has two branches that produce a specific product distributed in three 
reception centers. The production of each unit has the same cost in both branches and 
the transport cost (in hundreds of U.S. dollars) per unit for the product is presented for 
each combination of branch and reception center in the table below. 
 
Reception center 
 
Branch 
 
1 
 
2 
 
3 
 Α 4 6 3 
 Β 6 5 2 
 
A total of 60 units of product are to be produced and transported per week. Each 
branch can produce and send any number of units with a maximum of 50 units 
per week, i.e. there is flexibility in how they will share the total production between 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
the two branches, in order to reduce transportation costs. 
 
 
 
The objective of the management is to determine how many should be produced at 
each branch and then what will be the total mode of transportation to minimize the 
transportation costs. 
 
Answers wanted to the following questions: 
 
(a) Suppose that each reception center must accept 20 units per week. 
 Design the problem as a transportation model. 
 
(b) Use the northwest corner method to find an initial basic feasible solution of the 
 problem, as designed in question (a). Then determine the optimal solution. 
 
(c) Suppose now that each distribution center can receive an amount between 10 and 
 30 units per week to reduce transportation costs, but the total cargo transported 
 remains at 60 points. Design the problem as a transportation model. 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
(d) Use the Vogel method to find the initial basic feasible solution for the problem as 
 designed at (c) and then determine the optimal solution. 
 
 
PROBLEM 21 
 
One of the most important products of a multinational IT company is produced in two of 
its factories and is mostly available in three main clients of the firm. The two 
factories will produce over the next period 600 and 400 units of the product, 
respectively. The company is committed with contracts for the sale of 500 units to the 
first client and at least 200 units to the second. Also the second and third clients 
both want to buy as many of the remaining units of the product. The net profit from the 
sale of each unit depends on its origin (factory) and the destination (client) and ranges 
according to the following table.Client 
Factory 
 
1 
 
2 
 
3 
1 50000 70000 60000 
2 20000 30000 50000 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
How exactly should the 1000 units of the product be allocate in order to maximize the 
total profit? 
 
 
PROBLEM 22 
 
A student who is studying abroad, decided that he needs for the next four years a car 
for his movements. Since his costs are much he wants to carry out his wish by the most 
inexpensive way. What he can’t decide is whether to buy an old car or a newer one. 
Also he does not know whether he should sell it through these four years. The following 
data are given. 
 
 Purchase 
price 
($) 
Cost of car use 
per year ($) 
Car purchase price 
per year ($) 
1st 2nd 3rd 4th 1st 2nd 3rd 4th 
Old car 1000 1900 2200 2500 2800 600 400 200 0 
New car 3800 1000 1300 1700 2300 2200 1600 1200 1000 
 
If the student changes his car within the next four years, he will do it at the end of 
that year and will take a car of one of two types. However, he plans to get in the 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
future a newer of that what he gets now. He wants to find the most appropriate solution. 
a) Describe how the problem can be expressed as a transportation model 
b) Find the initial solution using any relevant method. 
c) Determine the optimal solution by the solving transportation problems methodology 
PROBLEM 23 
 
A large construction company undertook computerization items to equip a ministry with 
the PC terminal units. It was agreed to supply 150 units next October and 225 units in 
November. Working an eight hour shift, the manufacturer can only produce 160 terminal 
units per month. Extending working hours with two hours overtime, it is possible to 
construct 30 additional units per month, with an additional unit cost of € 20. The 
terminal units can be stored at a monthly cost of € 3 per unit. The cost of producing 
each unit of PC is constant, regardless of the month of construction. 
 
Formulate the model (the initial table) in order to find out the production schedule, 
which minimizes the total cost. 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
 
PROBLEM 24 
 
A company is expected to face in the next four months monthly demands of 95, 120, 
110 and 100 units of products. The production capacity is 90 units per month at a cost 
of €20 per unit in regular employment. The overtime, which can reach 20% of normal, 
costs €30per unit. The storage cost is €1 per unit and per month, while the cost for late 
delivery of order is €3. The company is worried about the high cost of overtime 
expenses and thinks to make a limited expansion of its facilities so that the normal 
capacity to be increased to 99 units in order to reduce overtime, which seem to 
overburden the operating costs. The total production capacity will not be changed. 
 
If the company is getting expanded at the beginning of the four months, the costs will 
remain the same. If it extends at the beginning of the 3rd month, then the cost will be 
increased by €1, but according to latest legislative incentives for the extension will 
receive a subsidy by the government with €400. 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
What exactly would you suggest the company to do? 
 
 
 
 
PROBLEM 25 
 
The Build-Em-Fast Company has agreed to supply the best customers with three 
products every week for three weeks, though the production will require some overtime. 
The data involved are the following: 
 
Week Maximum production 
(normal period) 
Maximum 
production 
(overtime) 
Production cost per 
unit 
(normal period) 
1 
2 
3 
2 
2 
1 
2 
1 
2 
 $ 6000 
$ 10000 
 $ 8000 
 
The cost per unit produced in overtime for each week is $ 2000 more than in the regular 
season. The storage cost is $ 1000 per unit for each week of storage. There are already 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
two products in construction, but the administration does not want to have to 
manufacture products after the end of the three weeks. 
 
 
The administration wants to know how many units it should produce per week to 
maximize its profit. 
 
(a) Design the problem as a transportation model creating cost tables and requirement 
 tables. 
 
(b) Use the Simplex transportation method to determine the optimal solution. 
 
 
 
 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
PROBLEM 26 
 
The Metro Water District is a consulting company of environmental projects which is 
responsible for the management of the transportation of water in a large geographical 
area. The area is relatively dry so the water must be transported from other areas (from 
rivers Colombo, Sacron and Calorie) and then the company distributes it in its own turn 
throughout the area. The main customers are in the areas of Berdoo, Los Devils, San 
Goand, Hollyglass. Water can be transferred from any river in any city other than the 
river Calorie which does not communicate with the area Hollyglass. Due to the 
geographical specificity of local transportation costs depends to a large extent on the 
location of rivers and towns. The transportation cost per thousand cubic meters of 
water in dollars from all the rivers to all the cities is given in the following table. 
 
 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
 
Area 
 
River 
Berdoo Los Devils San Go Hollyglass Capacity 
supply 
Colombo 16 13 22 17 50 
Sacron 14 13 19 15 60 
Calorie 19 20 23 - 50 
Minimum requirement 30 70 0 10 
Normal requirement 50 70 30 0 
 
The charge of consumers by the company is the same for every cubic meter of water 
irrespectively of location and distance. The company is worried about how to distribute 
the water in the summer months, during which the amount of water available is limited 
(last column in table). The company must supply every city with a minimum amount of 
water to meet the minimum requirement of each city (except San Go area that has its 
own water source). The line of the normal requirement shows that Berdoo wants 20000 
cubic meters of water above the minimum requirement, the San Go wants 30000 cubic 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
meters water and Hollyglass wants as much as possible. The administration wants to 
distribute water supplies in such a way as to minimize the total transportation cost. 
 
Formulate and solve an appropriate transportation model. 
PROBLEM 27 
 
The Northern Airplane Company manufactures commercial airplanes for several airlines 
in the world. The last stage in the manufacturing process is the construction of the 
engine and its installation to the spindle of the airplane. The company works only with 
contracts with main term the delivery of a number of airplanes at certain time. There 
must be an engine production plan for the next four months. 
 
In order the company to prevent delivery days should produce engines in the way 
given in the third column of the table below. In addition all engines which must be 
produced per month are at least 10, 15, 25 and 20 respectively. But it may need some 
engines to be constructed one or more months after the initial programming due 
to production conditions. These engines however should be stored and the storage 
cost reaches the $ 15000 per month. 
 
 
 
 
TRANSPORTATION PROBLEM EXERCISES 
 
 
 
 
 
 
 
 
Month 
Scheduled facilities Maximum 
production 
Unit production 
cost 
Unit store cost 
1 10 25 1.08 0.015 
2 15 35 1.11 0.015 
3 25 30 1.10 0.015 
4 20 10 1.13 0.015 
 (The cost elements are expressed in millions of dollars) 
 
The company wants to decide which is the best way of engines production per month inorder to minimize the total cost. 
 
Formulate and solve the appropriate model.