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Exam 5: Network Models

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Question 1

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A typical shortest path problem is a special case of the general network flow model.

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B) False

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Question 2

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The flow balance constraint for each transshipment node in a network flow model has the form Flow in = Flow out.

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In a typical network model representation of the transportation problem,the nodes indicate

Exhibit 5-2 A small engineering firm employs one civil engineer, two engineering technicians, and one summer intern. The types of projects the firm does includes surveys (typically 7 per month), designs (5 per month), and construction project plans (four per month). The times, in hours, required for each employee to complete teach type of project are shown below. Based on their capabilities and time spent on travel and administrative tasks, the engineer, tech 1, tech 2, and intern can handle 5, 4, 4, and 3 projects per month, respectively.  ​ -Refer to Exhibit 5-2.Based on their salaries,the engineer,tech 1,tech 2,and intern earn $90,$65,$65,and $45 per hourly,respectively.Change the firm's objective function to minimize staff costs and find the optimal assignment plan.Does it change from the base case

In an assignment model of machines to jobs,the machines are analogous to which of the following in a transportation problem

In a general logistics model that minimizes the cost of network flow,the flow balance constraint for each supply node has the form

It is useful to model network problems by listing all of the arcs and their corresponding flows in one long,comprehensive list.

In transportation problems,shipments between supply points or between demand points are possible.

Problems which deal with the direct distribution of products from supply locations to demand locations are called:

Exhibit 5-3 Steve the auto parts salesman is trying to navigate his way between the rural west Texas towns of Jonestown and Upland. The possible routes for this trip are shown below, along with the mileage along each route. $\begin{array}{lrcc}\text { Origin } & & \text { Destination } & \text { Distance (miles) } \\\text { Jonestown } & \text { to } & \text { Haleyville } & 25 \\\text { Jonestown } & \text { to } & \text { Krickburg } & 55 \\\text { Jonestown } & \text { to } & \text { Karn City } & 35 \\\text { Haleyville } & \text { to } & \text { Mart } & 50 \\\text { Haleyville } & \text { to } & \text { Krickburg } & 25 \\\text { Haleyville } & \text { to } & \text { Karn City } & 30 \\\text { Karn City } & \text { to } & \text { Mart } & 50 \\\text { Karn City } & \text { to } & \text { Baker } & 65 \\\text { Krickburg } & \text { to } & \text { Karn City } & 20 \\\text { Krickburg } & \text { to } & \text { Baker } & 30 \\\text { Krickburg } & \text { to } & \text { Mart } & 45 \\\text { Mart } & \text { to } & \text { Baker } & 20 \\\text { Mart } & \text { to } & \text { Upland } & 40 \\\text { Baker } & \text { to } & \text { Upland } & 30\end{array}$ -Refer to Exhibit 5-3.What general type of LP model can be applied to this problem What modifications to the general type are required for this problem

Exhibit 5-1 Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: $\begin{array} { | l | l | l | l | } \hline & \text { Grand Rapids } & \text { Blue Ridge } & \text { Sunset } \\\hline \text { Ohio Valley } & 50 & 40 & 100 \\\hline \text { Lakeview } & 60 & 50 & 75 \\\hline\end{array}$ -Refer to Exhibit 5-1.Suppose the Lakeview plant was required to run at capacity.How much more would the shipping plan cost Sinclair

The network model representation of the transportation problem has the following advantage relative to the special case of a simple transportation model:

The decision variables in transportation problems are:

A particularly useful Excel function in the formulation of transportation problems is the:

In network models of transportation problems,arcs represent the routes for getting a product from one node to another.

Which of the following is not an example of a condition that a more complex logistics model might include

The objective in transportation problems is typically to:

Exhibit 5-1 Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant which can produce up to 10,000 tons per month and the Lakeview plant which can produce up to 7,000 tons per month. Sinclair sells its polyethylene to three different auto manufacturing plants, Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: $\begin{array} { | l | l | l | l | } \hline & \text { Grand Rapids } & \text { Blue Ridge } & \text { Sunset } \\\hline \text { Ohio Valley } & 50 & 40 & 100 \\\hline \text { Lakeview } & 60 & 50 & 75 \\\hline\end{array}$ -Refer to Exhibit 5-1.Implement the LP model in Solver and obtain the optimal shipping plan.What is the optimized cost

In an optimized shipping plan,most of the shipments occur on the low-cost routes,but this is not always the case.

Transshipment points are locations where goods neither originate nor end up,but goods are allowed to enter such points to be shipped out to their eventual destinations.