QUESTIONS on TRANSPORTATION ( University Papers)

QUESTIONS ON TRANSPORTATION ( University Papers)

Oct.2010

A company has three plants & four warehouses. The supply & demand in units & corresponding transportation costs in rupees are given below. On the basis of past experience, following dispatch schedule has been finalized.

Plants / Warehouses / Supply in units
Transportation cost per unit
1 2 3 4
A / 3
1000 / 2
4000 / 7 / 6 / 5000
B / 7
2500 / 5 / 2
2000 / 3
1500 / 6000
C / 2
2500 / 5 / 4 / 5 / 2500
Demand in units / 6000 / 4000 / 2000 / 1500

Answer the following questions with justifications.

1. Is the above solution optimal? find the optimal solution & total minimum transportation cost.
2. If transport carrier offers to drop the cost on route B to 2 from Rs.5 to Rs.3, will there any change in the optimal solution?

April 2010

A company has 3 plants & 4 warehouses. The supply & demand in units & corresponding transportation costs in rupees are given below. On the basis of past experience, following dispatch schedule has been finalized.

Plants / Warehouses / Supply in units
Transportation cost per unit
1 2 3 4
A / 10 / 8
5000 / 7 / 12 / 5000
B / 12 / 13 / 6
4500 / 10
1500 / 6000
C / 8
7000 / 10
500 / 12 / 14
1500 / 9000
Demand in units / 7000 / 5500 / 4500 / 3000

Answer the following questions with justifications.

1. Is the above solution optimal? find the optimal solution & total minimum transportation cost.
2. If transport carrier offers 10% discount on route C to 3,should the management accept the offer? Analyse the optimal solution to find answer.

Oct 2009

a\ A product is manufactured in 3 factories and sold through 4 warehouses. The following table shows relevant details of capacities of factories, requirement of warehouses and transportation cost in rupees per unit for every distribution route

W 1 / W 2 / W 3 / W 4 / CAPACITY
FACTORY 1 / 3 / 2 / 7 / 6 / 5000
FACTORY 2 / 7 / 5 / 2 / 3 / 6000
FACTORY 3 / 2 / 5 / 4 / 5 / 2500
REQUIREMENT / 6000 / 4000 / 2000 / 1500

1. Suggest optimal allocation schedule so that total transportation cost is minimized
2. Is your optimal solution unique?
3. If F 3 – W 2 route contractor offers 20 % discount on quoted price, if minimum 500 units are given to him transportation, do you agree on this proposal? Justify your answer.

April 2009

A company is spending Rs.1200 on transportation of finished goods from 3 plants to 4 distribution centers every month. The supply and demand for finished goods every month with unit cost of transportation are as given below.

Factories / Transportation cost per unit in rupees
D1 / D 2 / D 3 / D 4 / Monthly capacity in units
F 1 / 20 / 30 / 50 / 15 / 7
F 2 / 70 / 35 / 40 / 60 / 10
F 3 / 40 / 12 / 60 / 25 / 18
Monthly demand in units / 5 / 8 / 7 / 15 / 35

1. Find the optimal solution to give minimum cost schedule to transport finished goods to market
2. What can be the maximum savings every month by optimal scheduling?

Oct 2008

A company has 3 plants and 4 warehouses. The supply and demand in units and corresponding transportation costs per unit in rupees,, are as given below:

PLANTS / / WAREHOUSES / / SUPPLIES IN UNITS
1 / 2 / 3 / 4
A / 5 / 10 / 4
10 / 5 / 10
B / 6
20 / 8 / 7 / 2
5 / 25
C / 4
5 / 2
10 / 5
5 / 7 / 20
REQUIREMENT / 25 / 10 / 15 / 5

Answer the following questions with justifications

1. Is the above solution feasible?
2. Is this solution degenerate?
3. Is this solution optimal?
4. Is this solution unique ?
5. If the cost of transportation from B to 3 is reduced from rs.7 to rs.6 per unit what will be the optimal solution?

April 2008

The following data relating to production capacities of plant, order from warehouses and transport costs for the company manufacturing products is given below

PLANT / UNIT PRODUCTION COST IN RUPEES / PRODUCTION CAPACITY (000 UNITS)
X / 12 / 20
Y / 10 / 16
Z / 15 / 25
WAREHOUSE / ORDER SIZE( 000 UNITS )
P / 15
Q / 18
R / 12
S / 14

Freight cost rupees per unit

P / Q / R / S
X / 3 / 1 / 2 / 4
Y / 6 / 4 / 3 / 2
Z / 4 / 5 / 7 / 3

From the above information determine the optimal shipping schedule

Oct 2007

A company has 3 plants and 4 warehouses. The supply and demand in units and corresponding transportation costs per unit in rupees, are as given below:

PLANTS / / WAREHOUSES / / SUPPLIES IN UNITS
1 / 2 / 3 / 4
A / 10 / 8
5 / 7 / 12 / 5
B / 12 / 13 / 6
4.5 / 10
1.5 / 6
C / 8
7 / 10
0.5 / 12 / 7
1.5 / 9
REQUIREMENT / 7 / 5.5 / 4.5 / 3 / 20

Answer the following questions with justifications

1. Is the above solution feasible?
2. Is this solution degenerate?
3. Is this solution optimal? Find the optimal solution
4. Is this solution unique?
5. If the cost of transportation from B to 2 is reduced from rs.13 to rs.10 per unit will the optimality of the solution change?

APRIL 2007

The following data relating to production capacities of plant, order from warehouses and transport costs for the company manufacturing products is given below Find a transportation schedule to minimize transportation time

PLANTS / / WAREHOUSES / / SUPPLY
A / B / C / D
1 / 6 / 3 / 9 / 4 / 22
2 / 5 / 9 / 2 / 7 / 15
3 / 5 / 7 / 8 / 6 / 8
REQUIREMENT / 7 / 12 / 17 / 9

Oct 2006

A company has 3 warehouses & 4 markets. The supply and demand in units and corresponding transportation costs per unit in rupees, are as given below:

WAREHOUSES / / MARKETS / SUPPLIES IN UNITS
1 / 2 / 3 / 4
W 1 / 10
300 / 10 / 16 / 20 / 300
W 2 / 16 / 6
175 / 17
25 / 25 / 200
W 3 / 8
25 / 21 / 10
75 / 15
150 / 250
REQUIREMENT / 325 / 175 / 100 / 150

Answer the following questions with justifications

1. Is the above solution feasible?Is this solution degenerate? Is this solution unique ?
2. Is this solution optimal? Find the optimal solution. Calculate the opportunity cost Opportunity cost of transporting 1 unit from W 1 to M 4
3. The manger is forced to transport 1 unit from W 2 to M 4 find the rate of increase in the cost per unit.
4. If the transport carrier offers 20 % discount on route W 2 to M 4 provided at least 20 units are transported ,should the ,management accept that offer?
5. Due to some problems at W 1 its supply is reduced by 2 units. To compensate for the loss it was decided to increase the supply by 2 units from W 2.will such decision lead to increase the cost? If yes what will be the increase?
6. To improve the condition of the market, it is decided to undertake advertising campaign however due to budget constraints only one market can be chosen at present. Decide which market the advertising campaign should be undertaken.

Oct 2004

The following table gives the data regarding the transportation timing from 4 different origins to 4 different destinations

ORIGINS / / DESTINATIONS / / SUPPLIES
D 1 / D 2 / D 3 / D 4
01 / 6 / 7 / 3 / 4 / 5
02 / 7 / 9 / 1 / 2 / 7
03 / 6 / 5 / 16 / 7 / 8
04 / 18 / 9 / 10 / 2 / 10
REQUIREMENTS / 10 / 5 / 10 / 5

Using appropriate method, find the basic feasible solution to this transportation problem and also obtain the optimum solution so as to minimize transportation timings.

April 2006

UNIK marketing company has 3 regional offices and 4 distribution centers. Based on the following initial feasible solution, find the transportation schedule which requires the least transportation time.

REGIONAL OFFICES / / DISTRIBUTION CENTRES / / SUPPLIES IN TONS
DC1 / DC2 / DC3 / DC4
RO 1 / 10
12 / 0
3 / 20 / 11 / 15
RO 2 / 1 / 7
5 / 9
15 / 20
5 / 25
RO 3 / 12 / 14 / 16 / 18
5 / 5
REQUIREMENT / 12 / 8 / 15 / 10

The figures in the bold indicate allocation of materials in tons from regional offices to distribution centers whereas upper left hand corner numbers indicate the number of days required to transport any volume of material from RO to DC

April 2005

The following table shows all necessary information on the availability of supply to each warehouse, the requirement of each market and unit transportation cost, in rupees, from each warehouse to each market.

WAREHOUSE / / MARKETS / / SUPPLY
P / Q / R / S
A / 6 / 3 / 5 / 4 / 22
B / 5 / 9 / 2 / 7 / 15
C / 5 / 7 / 8 / 6 / 8
REQUIREMENT / 7 / 12 / 17 / 9

The shipping clerk has worked out the following schedule from his experience.

A to Q 12 UNITS A to R 1 UNIT A to S 9 UNITS B to R 15 UNITS

C to P 7 UNITS C to R 1 UNIT

1 Check and see if the clerk has optimum schedule

2 Find the optimal schedule and minimum total cost of transportation

3 If the clerk is approached by a carrier to route C to Q who offers to reduce his rate in the hope of getting some business, by how much the rate should be reduced such that the clerk will offer him business?

APRIL 2004

Four warehouses with capacities of 85, 35, 50 and 45 tons were receiving the material from 3 factories with their supply capacities of 70, 55 and 90 tons on regular basis. The transportation costs per ton from factory to warehouse are as follows

FACTORY / WAREHOUSES
1 / 2 / 3 / 4
1 / 6 / 1 / 9 / 3
2 / 11 / 5 / 2 / 8
3 / 10 / 12 / 4 / 7

A feasible solution states that from factory 1 , 25 tons have to be transported to warehouse 3 and 45 tons to ware house 4.similarly 30 tons and 25 tons were transported from factory 2 to warehouse 1 and warehouse 3 respectively. However from factory 3, 55 tons and 35 tons were transported to warehouse 1 and 2 respectively.

1. Is the transportation schedule optimum? If not modify it and obtain optimum solution and cost thereof.

Oct 2003

Mr. Pinto is the production supervisor of a company situated in Mumbai. On arriving at work he finds the following pallet information

DEPARTMENT / PALLETS AVAILABLE / DEPARTMENTS / PALLETS REQUIRED
A / 18 / G / 14
B / 27 / H / 12
C / 21 / I / 23
J / 17

The time required for moving a pallet from one department to another is as follows

FROM / A / A / B / B / B / B / A / A / C / C / C / C
TO / G / H / G / H / I / J / I / J / G / H / I / J
Minutes required / 13 / 25 / 18 / 23 / 14 / 9 / 12 / 21 / 23 / 15 / 12 / 13

Find the distribution plan using it as a transportation problem so as to minimize the total time required for such a distribution plan.

Oct 2002

The following table shows all necessary information on the availability of supply from each plant, the requirement of each distribution center and unit transportation cost, in rupees, from each plant to each warehouse..

PLANT / / DISTRIBUTION CENTERS / / SUPPLY IN TONNES
ALLAHABAD / MUMBAI / KOLKATA / DELHI
AMETHI / 3 / 2 / 7 / 6 / 5000
BHOPAL / 7 / 5 / 2 / 3 / 6000
GWALIOR / 2 / 5 / 4 / 5 / 2500
REQUIREMENT IN TONNES / 6000 / 4000 / 2000 / 1500

Suggest an optimal transportation schedule and find minimum total cost. if transportation cost from Gwalior to Mumbai reduces to Rs 2 ,will the optimum transportation schedule change? Why?

April 2003

YOURS OWN a garment manufacturing company from Mumbai wishes to develop a monthly production schedule for the next three months. Depending on sales commitment the company can either keep up the production constant and allowing the fluctuation in inventories or maintained inventories constant with fluctuating production.

The fluctuating production necessitates working overtime the cost of which is estimated to be double the normal production cost of rs.10 per unit. Fluctuating inventories result in inventory carrying cost of rs.4 per unit. If the company fails to fulfill its sales commitment, it incurs a shortage cost of rs.5 per unit per month.

The production capacities for the next three months are shown as:

PRODUCTION CAPACITY / MONTHS
1 / 2 / 3
REGULAR / 50 / 50 / 60
OVERTIME / 30 / 00 / 50
SALES / 60 / 120 / 40

Formulate it as a transportation problem to obtain an optimal production schedule

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