## Abstract

Operation research can be defined as the process of using advanced analytical methods in aiding towards better decision-making. Operation research will always involve application of various mathematical modeling techniques, mathematical optimization and statistical modeling and analysis. Some scientists consider operation research as being a sub-branch of mathematics.

Operation research is mainly concerned with the determination of an optimal or a maximum solution that will minimize costs and increase profits. Such complex solutions have found their application in the transportation sector, manufacturing sector and procurement sectors.

Information technology can be defined as the field of technology which handles data and information. Data is raw facts and figures, while information is processed data which can be used to make conclusions. Information technology involves the process of data acquisition, processing and storage. It also encompasses the process of data dissemination.

Operation research has found its application in various fields, including the education sector, manufacturing sector and engineering sector. Operation research in information technology can be defined as application of various operations researches in the information technology filed. It encompasses activities like application of mathematical modeling in handling data for decision-making processes. Operation research is sometimes interchangeably used with the term management science.

This essay is going to look at the various application of operation research in the information technology sector, as well as integration of operation research in the information technology sector.

## Discussion

Application of operation research in information technology.

Initially, operational research was done manually and traditionally. These manual and traditional ways proved to be hectic and prone to various errors. But with the advent of information technology, the process has been made easy and almost instant. Information technology has largely boosted the manner in which operational research is done. As earlier stated, operation research involves various activities which include but not limited to the following: problem formalization, model validation and construction, solutions analysis and solution implementation.

Computer networks and the concept of databases have made it easier for information to be available. Also, data integrity software and database tools ensure that the right data is available. This has also increased the validity and reliability of the solutions obtained from the operations research problems. For example, the SIMNET II and the TORA software’s are the examples of operational research software.

The following are the various areas where the application of information technology can be applied in operations research.

### Simulation

A computer reproduction can be termed as a computational model or a computer model which can simulate some kind of an abstract model. Many mathematical models will involve the use of computer simulations. For example, computer simulations are used in the following scientific fields: biology, chemistry, human systems and astrophysics. Also, computer simulation is applied in the various humanities fields which include psychology, economics and social sciences.

The following are some of the practical examples of computer simulations:

- Training of pilots using Flight simulators
- Weather forecasting
- Noise barriers design in order to reduce noise on the road side
- Price predictions in various financial markets using adaptive models
- Organizational and management studies
- Understanding the behavior of structures, especially in building of structures
- Design of industrial process.

### Network Flow Programming

Network flow program is a type of linear programming model which involves the solving of linear models to minimize costs or maximize profits. Examples of linear programming models include assignment problems, transportation problems, maximum flow problems, optimization and minimization problems. Linear programming models can be solved using some software, such as Excel solver, Jensen Network solver and Jensen IP/LP solver.

The following example is a sample of a linear programming model. It is a transportation model that needs to be solved linearly.

#### Problem

A company makes and distributes fuel additives (in oil drums) for marine engines. It makes the additives at three ports (Alpha, Beta and Charlie). It has contracts to supply three other ports with additives (Delta, Echo and Foxtrot). The monthly supply and demand situation together with the relevant transportation costs between ports (per oil drum) are summarized below.

Using the Transportation Method, find the least cost solution to supply the three ports with additive. State solution and overall least cost. Show all working.

The main methods used to solve transportation and assignment problems are the Vogel approximation method and the North corner method. In this assignment, we are going to employ the North corner method of linear programming.

The main step is to identify which routes can be used to ship equipment, considering the warehouse requirements, and which combination of routes will reduce costs. This step involves various iteration processes. In order to achieve an optimal solution, we also need to find an improvement index. An improvement index is a measure of how an unused route will improve the cost of transportation.

The North West corner rule consists of the following major steps:

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**Step 1**. Select the top-left corner cell of the transportation table and assign the maximum number of units to equal the minimum between the demand and supply

**Step 2**. Adjust the demand and supply numbers in the respective columns, and rows.

**Step3**. Providing the demand in the first cell is met, proceed to the next cell in the second column.

**Step 4**. When the supply for the first row is finalized, move to the next first cell in the second row.

**Step 5**. If at any point, the supply and demand is the same, then the next allocation can be moved in the next row or column.

**Step 6**. Continue repeating the process until all demand and supply values are exhausted.

After creating an initial solution, we need to check whether the initial solution is feasible, calculating the cost incurred by taking this shipment route.

From the above model, the total transportation cost using the above routes amounts to £ 2382.5. This is the initial solution and it does not represent the optimal values.

The next stage will involve moving from the initial feasible solution to an optimal feasible solution.

As a guiding rule

Occupied shipping routes (used square) ≥ [number of rows + number of columns] – 1.

If occupied shipping routes (used square) < [number of rows + number of columns] – 1, then the solution is referred to as degenerate or collapse.

We then have to test for possible improvement by testing out what the results would be if we have to ship the goods via an unused route. The process involves the following key major steps:

- We select unused square to evaluate, such as G – KO
- Now starting from G- KO we then draw a closed path using the current occupied squares, placing a minus and a plus sign in the corners of the path.
- We then compute the improvement index from the source G to destination KO.

I _{GKO} = +GKO – GU +ZU –ZKO

= £ (+1.5-3+1.0-2.50) = - 3

= Which is a negative improvement index.

This indicates that, for every oil tank transported via the source G to destination KO, the total transportation cost will reduce by £3 per unit over the current level costs.

Since we are looking for a route that has the highest negative number, we continue evaluating the other unused routes. A negative improvement index indicates that there will be a reduction of transportation costs by the value obtained.

Now, by evaluating the unused route G-KI we obtain the following:

= +GKI –GU +ZU-ZKO+KKO-KKI

I_{GKI }= £(+3.5 -3+1.0 -2.50+4-2.10) = +£ 1.4 Hence, it will increase the shipping cost. This indicates that, the cost of transporting a an oil will increase by £ 1.4 per unit.

When evaluating the unused route ZKI, the improvement index would be:

= +ZKI –ZKO+KKO-KKI

= £(+8-2.50+4-2.10) = + £ 7.4 Hence, opening up the route ZKI increases the shipping cost.

The above improvement index implies that the cost of transportation is going to be increased by £ 7.4 per unit; hence, it is not an optimal solution.

Evaluating the unused square KU, the improvement index will be:

=+KU-KKO+ZKO-ZU

= £(+7-4+2.50-1.0) = + £ 4.5. This indicates that opening up the route KU will increase the shipping costs. The total transportation costs will =be increased by £ 4.5 per unit over the initial value, if goods were to be shipped through KU route.

To obtain an improved solution, we have to add 125 to the KO and ZU squares, while at the same time, subtracting 125 units from the GU and the ZKO squares. This will eventually create balanced rows and columns known as an improved solution.

From the above table, we realize that the total cost of transportation using the above model reduces the transportation cost by £ 375. i.e. £( 2382.5- 2007.5). There is a noticeable improvement, but yet it is not an optimal solution. We still have to get a more optimal solution by performing further iteration.

Performing the second iteration to obtain a more improved solution we use the following unused squares:

Improvement index on route GKI will be = +GKI-GKO+KKO-KKI.

£(3.5-1.50+4-2.1) = +£3.9. This indicates that the transportation cost is going to increase by £3 per oil drum shipped; hence, this is not an optimal solution. We have then to calculate the improvement index of the next unused square.

Improvement index on route ZKI

= +ZKI - ZKO+KKO-KKI

= £(+8-2.50+4-2.1) = + £ 7.4

The improvement index indicates that the cost of shipment will increase by £ 7.4 per oil drum shipped; hence, this is not an optimal solution for transportation. We have to continue calculating the improvement index further on unused squares.

Improvement index on route KU will be £(+7-4+2.50-1) = +£4.5.Since it is a positive improvement, it indicates that the shipment cost per oil drum will increase by £4.5.

After the second iteration, there is no negative improvement index. This indicates that to optimize on the transportation costs, then maximum number of oil drum should be transported using the GKO route.

i.e I _{GKO} = +GKO – GU +ZU –ZKO

= £ (+1.5-3+1.0-2.50) = - 3

This negative index indicates that the shipping cost is going to reduce by £ 3 per oil drum shipped. Hence it is shipping more oil drums through this route will provide the least cost of transportations.

### Conclusion

In conclusion, operational research is an area that is useful in determining trends and solving complex problems. The area of operation research can also be used in decision and prediction processes hence helping a company make informed decisions. Through the various analyses of problems involving application of operational research, an organization is able to make informed decision about a plan of action and a remedy to a problem.