Decision Support System

Hello,Choose a Decision Support System (DSS) tool for implementing proposed model (choice has to be justified)Design a simple test plan aiming at finding the best solution along with the best parameters of the model (If Applicable)Implement the proposed modelNotes:I uploaded the document to help you to complete the tasks based on it.Please don’t make the question as complete until I check the solution first.A report of 1500 words at most is to be submitted.Thank you,

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Table of Contents
1. The problem ……………………………………………………………………………………………………………………………. 2
2. Explanation of the problem ………………………………………………………………………………………………………. 2
3. A model representing the problem; variables and relationships between them………………………………. 3
4. Assumptions of the linear program solution ……………………………………………………………………………….. 5
5. A solution to the model using a different technique …………………………………………………………………….. 6
6. References ……………………………………………………………………………………………………………………………… 7
1. The problem
Companies across the world face the problem of product diversification in order to stay
competitive in the market. The market is volatile with the customer demands and preferences
changing every day and with the changing technology, more companies are joining the production
sector since technology has improved productivity, the efficiency of operations and enabled
innovation of new ways of making products. Companies, therefore, are met with the problem of
manufacturing more than one product so that they reduce the risk of being eliminated from the
market by competitors.
A single product can prove to be costly if it fails in the market and the company is forced to halt
the production process or produce other products that will have a demand in the market. The
problem with producing more than one product is the costs associated with the production since
when production increases, the factors of production such as human resources, raw materials, and
capital need to be increased also. Companies have to use the available resources to make multiple
products and assume that the factors of production will remain constant and that the required profit
will be met.
2. Explanation of the problem
When a company has limited resources for producing multiple products, for example, diesel fuel
and liquid petroleum gas, the products may not perform the same in the market with one
performing better than the other when the market conditions are constant. The products share the
same production processes but do not bring the same profits. The primary objective of
manufacturing companies is to make a profit and therefore they are faced with the problem of
determining the production runs for both multiple products so that there is profit maximization
(Rios, McConnell, and Brue, 2013).
If the products are produced differently using different production lines, there will be increased
costs and the company will operate below the accepted capacity which will lead the company not
maximizing profits. The company is therefore faced with the challenge of deciding the production
units for the products that will be economical in terms of minimizing the costs and maximizing the
profits. The costs involve inventory holding costs, therefore, the product that is not sold in the
market increases the costs of the company. Oil producing companies in the Middle East produce
a variety of products from crude oil which is a lot in the Arab region.
The companies noticed that they get more profits from selling diesel fuel than from the sale of
liquid petroleum gas. But both products have to be produced to reduce the risks that may arise
from the failure of one product in the market. The company has to employ a product mix of both
diesel fuel and liquid petroleum that will be supported by the limited resources and produce
quantities of the products that will enable it to maximize profits. Producing both diesel fuel and
liquid petroleum will enable the company to reduce costs and it will be able to maximize profits
creating a room for expansion.
3. A model representing the problem; variables and relationships
between them
Linear programming model will help the company to come up with accurate data on the production
levels of diesel fuel and liquid petroleum gas. The accurate volumes will enable the oil companies
to produce the required units that will achieve maximum profit in the market when the company’s
resources are used completely. The company takes raw oil as input and the two products are diesel
fuel and liquid petroleum gas.
The two products will be manufactured at different rates with tonnes per hour: diesel fuel, 200 and
liquid petroleum gas 140. They also have different profitability’s where: profit per ton for diesel
fuel is $ 25 and the profit per ton of liquid petroleum gas is $30. The problem is the company has
limited resources which can be employed in the production process. With the available resources,
the maximum volume of diesel fuel that can be produced is 6,000 tons while the maximum volume
of liquid petroleum gas is 4,000. The maximum production hours that the process can take is 40
hours per week (Williams, 2013).
The decision that the companies need to make is to decide what volumes of diesel fuels and what
volumes of liquid petroleum gas they should produce with the available resources and give the
best profits. We know the values of the production rates for the two products and the values the
profits they bring to the company. The quantities of the volumes of diesel fuel and liquid petroleum
gas that need to be produced at the optimal level are the unknown variables which influence the
decision of the company on how to maximize profits. This model helps to show the profits and
production functions as the formulas involving the variables that can the needed volumes at
maximum profits can be determined systematically.
Using the model, the formula, the total number hours of production and the total profit is (profit
per ton of diesel fuel) A+ (profit per ton of liquid petroleum gas produced) B. That means our aim
is to maximize 25A+30B. So adding this together will give us the linear program maximize
25A+30B which is subject to (1/200) A+ (1/140) B =4 0 0 = A = 6000 0= B = 4000. This linear
program can be solved through a number of ways but the results will give the same results. To
solve the linear program, we take the profit per ton and multiply by the tons per hour so that we
get the profit per ton of diesel fuel and liquid petroleum gas. Therefore 200×25 we have $5,000 as
the profit per hour and for the liquid petroleum gas, we have 140×130 which is $ 4,200.
Clearly, the production quantities that will give maximum profit is the production of the maximum
volume of diesel fuel which is 6,000 tins using 30 hours and then the remaining 10 hours to be
used in producing liquid petroleum gas which will be 1,400 tons. The profit is ($25×6, 000 tons)
+ ($30x1400tons) which is $192,000 (Dantzig, 2016). This is the maximum profit that the oil
companies can make if they use the model to evaluate the quantities the different products they
should produce in order simultaneously. With this model, the companies can maximize the use of
the available resources without incurring additional costs of production.
The dependent variables are the quantities or volumes of the diesel fuel and the liquid petroleum
gas that are required to be produced to achieve maximum profit. The independent variables are the
tons per hour of the diesel fuel and the liquid petroleum gas produced. The variables have a linear
relationship in that if the tons per hour produced increases, the profit per ton increases and vice
versa all factors constant. If the tons per hour of the liquid petroleum gas increase, the profit per
ton increases and vice versa all other factors constant.
4. Assumptions of the linear program solution
The assumptions are that the resources used in the production of both products remain the same
throughout the process, no additional resources will be added to the production process. The oil
from which the diesel fuel and the liquid petroleum gas are made is the same throughout the
production process. Another assumption is that the diesel fuel and the liquid petroleum gas are the
only products that are being produced by the oil companies. If the companies produce another
product, the products variables can be included in the linear program and the solution will provide
the combined quantities of three products that can be produced to achieve maximum profits with
the available resources. The third assumption is that the production technology that is used in the
production of both products remains the same throughout the production process (Fuss, and
McFadden, 2014). No special equipment is used to produce the diesel fuel and the liquid
petroleum gas. The last assumption is that the resources available are used in an efficient way to
achieve maximum profit. This means that the factors of production are used in the best costeffective way.
5. A solution to the model using a different technique
The graphical representation can also be used to solve the linear program that can be used to get
the units that will give the maximum profits for the products. The vertical axis represents the
volume of the liquid petroleum gas produced while the horizontal axis represents the volume of
the diesel fuel produced. The available production hours are constant at 40 hours
If the quantities are presented in a graph as shown, the vertical line represents that production limit
for diesel fuel while the horizontal axis represents the production limit for production of liquid
petroleum gas. Any point in the feasible region provides a solution for the variables. The diagonal
line represents the limitation of the number of hours available. The solution is the lower corner
where the lines intersex and corresponds to the production of 6,000 tons of diesel fuel and 1,400
tons of liquid petroleum gas at a profit of $192,000 which is the same as in the first techniques.
6. References
Williams, H. P. (2013). Model building in mathematical programming. John Wiley & Sons.
Dantzig, G. (2016). Linear programming and extensions. Princeton university press.
Rios, M. C., McConnell, C. R., & Brue, S. L. (2013). Economics: Principles, problems, and
policies. McGraw-Hill.
Fuss, M., & McFadden, D. (Eds.). (2014). Production Economics: A Dual Approach to Theory
and Applications: Applications of the Theory of Production (Vol. 2). Elsevier.

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