The Decision Making Problem Economics Essay

Published: 2021-06-27 09:40:04
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The decision making problem which the plastic manufacturer faces for the industrial use worldwide is significant (Ananda and Herath, 2009, Cagman and Enginoglu, 2010, Yoon et al., 2009, Yu et al., 2009). One of the main aspects of the problem which is being researched is that the capacity between the different components of the organization is such that the economics of scale needs to be achieved. One of the issues which have been highlighted in the literatures with regards to the decision making issues is that regarding the type of product which has to be produced, and the relevant nature of the problem solving. In this case, one of the classical economic problems which the organization faces relates to the use of the best possible resources and exploitation of the economies of scale. One of the key challenge for the organizational actors is that they need to ensure that they have to ensure that they have the ability to deal with the differ issues. One of the key to the development of the differ problems is to have a wider view of the problems of transportation, which is much higher to Europe from Americans and much lower from South Asia. In such conditions, one of the ways in which facilities should be built which can ensure that the production of the products can be in South Asia, and then moves to Europe to reduce the costs (Porcelli and Delgado, 2009, Xu, 2009, Yeh and Chang, 2009).
The economies scale are also possible as they allow the differ stakeholders to not only develop and understand the nature of the scale, but also allows an insight into the problem solving of the decision making (Porcelli and Delgado, 2009, Turskis et al., 2009, Yu et al., 2009). One of the problems is that the size of the plants cannot be increased in the local vicinity, therefore there is a need to reduce the fixed costs at the local level, while also allowing the differ organizations to not only reduce their operations in the international scale, but also helps the organization in managing the transportation costs (Porcelli and Delgado, 2009, Turskis et al., 2009, Yu et al., 2009). The cost of production and transportation is significantly lower in South Asia, and therefore it would be appropriate to use the a model which can depict the appropriate costs in order to deliver the objectives (Costa et al., 2011, Fisher et al., 2009, Hahn et al., 2009).
Indicate the problem type, and determine the criteria and objective which are important to the company’s manager.
The problem type is one of optimization. This requires the tradeoffs between the different options in order to examine the most appropriate way of modeling the problem. In this case, one of the key problems for the use of the most appropriate plant sizes (Ye, 2010, Yeh and Chang, 2009, Zavadskas et al., 2010). The size of the plant is based on a number of criteria. The first is the relative transportation costs to other regions. For example, the transportation costs between Europe and South Asia and between South America and North America are less. This could mean that the company can choose to have plans in different locations and transport locations which are more feasible for the transportation of the goods. The choice of putting in 10 million unit plan would also be based on the cost of the plant, and the relative cost of transportation, which would be one of the key determining criteria for a manager. The managers would also need to take into account the way in which the larger capacity, of the 10 million unit plant can be used to effectively transport the products to other regions from either Europe or South Asia, This modeling will help the different managers in a number of ways (Ye, 2010, Yeh and Chang, 2009, Zavadskas et al., 2010).
Firstly, the managers need to set out the major criteria for their decision making. The decision making in this approach is to ensure the most optimum production levels, which can be transported to other areas without difficultly. The optimum levels of accuracy need to be assured in order to ensure that the efficacy of the different sectors can be ensured (Yoon et al., 2009, Yu et al., 2009). One of the key issues for the organization is that they need to ensure that they have the ability to deal with the transportation requirements of the organization, which can lead to long term benefits for the managers,. The objectives which are important for the company's managers are also based on a number of factors. Firstly, the local factory managers need to ensure that they have the most appropriate systems put into place, which can enable them to avoid the duties and high transportation costs. One of the key determinants for the company is to ensure that they have the ability to deal with the wider requirements of the company, and therefore any transportation and factory size also needs to be based on the demand. The demand in the European region is the highest, and therefore the objective of the manager should be to fulfill this demand from a combination of factories which can help in achieving the best possible economies of scale in the case of the model (Yoon et al., 2009, Yu et al., 2009).
The preferred modeling technique for solving this problem is optimization. Optimization has a number of advantages for the managers. Optimization helps in analyzing the problem, and supports the best fit between the need for transportation and the local production, and can sometimes also support the use of a multilayered approach where a mix of different actions can be undertaken. The solution of the problems would therefore be to ensure that the European region can receive the best possible optimized figure for dealing with the problem (Yoon et al., 2009, Yu et al., 2009).
Indicate the problem type, and determine the criteria and objective which are important to the company’s manager.
The transportation model is formulated for a kind of problems with the following unique characteristics: firstly, a product is transported from a number of sources to a number of destinations at the minimum possible cost, in a transportation problem, items are allocated from sources to destinations at a minimum cost; secondly, each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product (Bernard W. Taylor III). In this case, This Company is just consistent with these two characteristics so I decide to use the linear programming transportation model to formulate the problem.
Formulate the problem using your proposed model.
The linear programming model for this problem is formulated as follows:
Minimize=40X11+45X12+51X13+65X14+51X21+57X22+47X23+60X24+58X31+63X32+45X33+31X34+71X41+50X42+51X43+53X44+3000Y11+4500Y12+3200Y21+4800Y22+2000Y31+3000Y32+1800Y41+2700Y42
Subject to
X11+X12+X13+X14<=5Y15+10Y12
X21+X22+X23+X24<=5Y25+10Y22
X31+X32+X33+X34<=5Y35+10Y32
X41+X42+X43+X44<=5Y45+10Y42
X11+X21+X31+X41=6
X12+X22+X32+X42=4
X13+X23+X33+X43=7
X14+X24+X34+X44=8
Y11+Y12<=1
0<=Y11<=1
0<=Y12<=1
Y21+Y22<=1
0<=Y21<=1
0<=Y22<=1
Y31+Y32<=1
0<=Y31<=1
0<=Y32<=1
Y41+Y42<=1
0<=Y41<=1
0<=Y42<=0
e.f) please see appendix
Appendix
Solve the problem using an appropriate approach e.g. the simplex method or any available software.
Figure 1
There are two possible plant types: low capacity that can produce up to 5 million units a year at a fixed cost that depends on the region and is given in cells G5:G8 of Fig. 1, and high
capacity that can produce up to 10 million units a year at a 50% higher fixed cost (thus exhibiting
economies of scale). The associated cost and maximum capacity are given in cells H5:H8 of Figure 1.
Total demand in each region (in millions of units) is given in cells B9:E9
Need to decide:
 How many, and what type of plants we should build in each region
 How to allocate production between them
 What markets should each plant supply.
Figure 2
The highlighted cells (G15:I18) in Figure 2 indicate how many plants of each type we build in each region. In this case, i suggest three small plants in North America and two large plants in South America and one large in Europe and South Asia.
Now, how much should i produce and where should i transport the goods? Let me distribute the output from each location:
In cells (B15:E18) we specify that we would like to produce 10 units in North America and sell them locally. We would like the South Asia facilities to supply 1 unit locally, 5 more to Europe and 1 to North America. We would also like the Europe to produce 3 units supply to South America, 2 units to South Asia and 3 units to locally. South America supply 20 units to north America and 5units to Europe and locally.
Now compute the excess capacity that we have in each region, in millions of units. It is equal to the amount produced:
[Number of Small Plants] x [Low Capacity] + [Number of Large Plants] x [High Capacity]
Minus the amount transported from the region: e.g. excess capacity for North America (cell B23) is equal to [G15*G5+I15*I5-SUM (B15:E15)] (Figure 3). By using the solver add-in in Excel.
Figure 3
Here, the excess capacity is equal to 5, meaning that we produce 5 units fewer in North America than our capacity allows. Similarly we can compute the excess capacity for other regions and see that we allocated 30 units to be transported from South America whereas we can produce only 20 there, resulting in negative excess capacity. This discrepancy will be fixed when we have Excel solves the problem for us.
I can also compute the unmet demand in each region, equal to the initial demand minus the total amount of units transported there (Figure 4):
Figure 4
It shows that we have excess supply in some regions and unmet demand in others.
The total cost of production is equal to the sum of variable costs (equal to the sum of cell-bycell product of unit costs and amounts produced) and fixed costs.
Figure 5
Figure 6
Figure 7
The solution calls for one small plant in North America, one large in Europe and one large in Africa. The Asia plant will supply North America, Europe and Asia itself, North America will supply itself and the Europe plant will supply South America and South Asia.
Update the solution with a new constraint as follows:
The constraint will ensure that either a low capacity or a high facility capacity facility is built in the European supply region.
Update the original solution from part ‘e’ as well as the solution derived from part ‘i’ with a new constraint as follows:
The constraint will ensure that a low capacity facility is not built in South America.
The first constraint can be formulated as Y41 + Y42 = 1, transfer into excel is cell I18 = F18 + H18 = 1. And then, using the same methods to solve this question. 
The second constraint is Y21 + Y22 = 0, and put the second constraint and first constraint together, which is shown in the excel I16 = F16 + G16 = 0

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