The Process of Transshipment and the Linear Programing - Paper Example

Introduction

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In our everyday life, goods need to move from source to the final consumers. The source may be a thousand miles away, or just a few kilometers away. Sometimes these goods are too bulky, or too much and as such, would require to first be store in order to meet either demand or supply conditions.

Failure to meet market conditions may lead to either wastages as is the case with overproduction or unsatisfied customers as is the case with underproduction. Therefore, it is clear that an equilibrium must be maintained in order to keep the customers satisfied.

Objective

To examine in depth the process of transshipment and the linear programing involved

Review

Transportation models are normally formulated to solve problems involving the following;

A product is transported from several sources to a number of destinations with considerations being focused on minimum cost.

a source is able to give a fixed number of units for a certain product, and a destination has a fixed demand for the product.

In a transportation or transshipment problems, goods are allocated from origin to destinations at a cost that is aimed to be most economical.

Transshipment and transportation problems are characterized by constraints that arise due to limited capacity of storage at both the supply point and the end point. This limitation enables us to look at the problem as purely a linear programming problem which can now be solved using programing methods.

In real practice, lets consider power plants 1, 2 and 3 that are used to supply electricity to four cities as indicated below. Also, lets note about the costs of making these supplies to the said cities.

plant Supply in million kW

1 35

2 50

3 40

Total 125

cities Demand in million kW

1 45

2 20

3 30

4 30

TOTAL=125

Costs in dollars

To city 1 To city 2 To city 3 To city 4

Plant 1 8 6 10 9

Plant 2 9 12 13 7

Plant 3 14 9 16 5

Realistically, we can see from the above information that the cost from plant 1 to city 1 is 8 dollars. Of importance is how much is actually supplied to city 1.

Also, the cost to city 2 from plant 1 is 6 dollars but we lack information on the exact number of watts supplied to city 2. All we know is that all power supplied from plant one must go to any of the 4 cities, but must not exceed the production capacity 35 kW (million).

What if we decide to supply equal amounts to the four cities from plant 1? What would the cost look like? Well, each city now receives 35/4 = 8.75 kW.

If we repeat this for all the other plants, we will develop a table of supply as follows,

To city 1 To city 2 To city 3 To city 4

Plant 1 8.75 8.75 8.75 8.75

Plant 2 12.5 12.5 12.5 12.5

Plant 3 10 10 10 10

Lets now look at demand city by city analysis,

Total power supplied to city 1=8.75+12.5+10=31.25 kwThis is also the power supplied to the other three cities.

From the above analysis, it can be observed that city 1 demands a total of 45 kW. So does supplying 31.25 kW really make sense? We all agree that this power is too low to meet the demands of city 1.

When we look at city 2, it has a demand of 20 kW yet it is now being supplied with 31.25 kW! This is clear wastage unless there is storage mechanism for the surplus power.

Let us now look at a different approach. What if we decide that we do not want to exceed the demand or even go lower beyond the demand of each city? What if we decide to strictly maintain the demands?

We will then have the following table,

To city 1 To city 2 To city 3 To city 4

Plant 1 15 6.7 10 10

Plant 2 15 6.7 10 10

Plant 3 15 6.7 10 10

When we look at the above table which has been developed from dividing the demand by the 3 plans, we observe many things. For the total demanded from plant say 3 now becomes,

15+6.7+10+10=41.7 kwFor plant 1 and plant 2, the total demanded is also 41.7 kW!

We know from previous information that the total supply from plant 1 is 35 kW, so how then do we get to manage 41.7kw?

Also, plant 2 can supply a total of 50 kW, but now only 41.7 kW is used, where do we take the surplus electricity supplied?

Lets now look at the cost for the first distribution,

To city 1 To city 2 To city 3 To city 4

Plant 1 8.75*8 8.75*6 8.75*10 8.75*9

Plant 2 12.5*9 12.5*12 12.5*13 12.5*7

Plant 3 10*14 10*9 10*16 10*5

Total cost = 8.758+12.59+1014+8.756+12.512+109+8.7510+12.513+1016+8.759+12.57+105This is equal to 1242 dollars.

Lets now examine the second distribution,

To city 1 To city 2 To city 3 To city 4

Plant 1 15*8 6.7*6 10*10 10*9

Plant 2 15*9 6.7*12 10*13 10*7

Plant 3 15*14 6.7*9 10*16 10*5

The total cost from the above table is 1246 dollars.

Clearly, the total cost is almost the same.

Conclusion and reflection

Therefore, we can conclude that there must be certain combinations that not only meet the demand anticipated, or the supplies made, but also one that sees that the cost is minimized. This is very ideal in every company is the chief goal is to cut costs and maximize profits.

We are then in agreement that certain methods must be employed in order to achieve the desired objectives within the provided or the unavoidable constraints. Some of the methods employed include;

-Minimum cost method

-Northwest corner method

-Vogels approximations