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4: Case Problem Stateline Shipping and Transport Company - Assignment Example

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The scope is to study to create two models; one will show how to minimize the shipping cost of transportation of waste from six plants to three disposal sites, the other one will illustrate how to organize the same work using transshipment concept. The objects for…
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Assignment 4: Case Problem Stateline Shipping and Transport Company
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Download file to see previous pages The solution is approached by creating a 6 x3 matrix illustrated in Table 1. Each cell of transportation expressed through Xij depicts quantity from the supply source to waste disposal site. The matrix also shows that total supply quantity is 223 bbls per week and the total demand quantity is 250 bbls per week. Supply and demand are not balanced; the solution requires to implement a dummy supply source of 27 bbls. Decision variable, in this case, is the quantity for a site, and objective function is cost minimization. The model is represented through the following linear equations (“Linear programing”, n.d).
The solution was obtained using the “Transportation” module of POM - OM software (“The Transportation model”, n.d.) The shipment from the supply source to waste the side is illustrated in Table 3. The POM – OM solution includes a dummy supply source for 27 bbls. The minimum cost is $2,832; it does not include dummy supply source quantity.
The idea is based on the concept that shipping line will use an intermediary supply center, which could be either a plant or waste disposal site. This concept gives a 9 x 9 matrix where supply plus disposal sources together act as supply sources and disposal sources (Rajendran & Pandian, 2012). Table 5 displays the feed matrix to achieve a solution. The values for supply and demand quantities of the matrix are based on the following assumptions:
The solution is achieved by solving the 9x9 matrix for cost minimization. Each Xij of the matrix depicts the quantity it may contain in determining the minimum transportation cost. The supply and demand constraints are obtained, in the same way as shown in the previous example. The summation of each row of the matrix presents a supply constraint equation. The summation of each column of the matrix presents a demand constraint. The minimization solution is ...Download file to see next pagesRead More
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