Exam 5: Network Models

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

In a typical minimum cost network flow model,the nodes indicate

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: -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 transportation model is a special case of the minimum cost network flow model (MCNFM).

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.Suppose Tech 2 will not be available during the next month.Keeping the same number of design and construction plan projects,how many survey projects would the firm be able to do? What would be the revised assignment plan in that case?

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

In transportation problems,the three sets of input numbers that are required are capacities,demands and flows.

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

The flow balance constraint for each transshipment node in a general minimum cost network flow model (MCNFM)has the form Flow in = Flow out.

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: -Refer to Exhibit 5-1.Implement the LP model in Solver and obtain the optimal shipping plan.What is the optimized cost?

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: -Refer to Exhibit 5-1.Suppose the shipping capacity between any two plants was limited to 2500 tons per month.Implement a minimum cost flow network model in Solver and obtain the optimal shipping plan.How much more would the shipping plan cost Sinclair in that case?

The graphical representation of a network in an optimization problem can be an aid in the development of a spreadsheet model.

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: -Refer to Exhibit 5-1.Formulate (write out algebraically)an LP transportation model to help Sinclair minimize its shipping costs.

In a minimum cost network flow model,the flow balance constraint for each supply node has the form

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. -Refer to Exhibit 5-3.Suppose the roads leading into and out of Krickburg are unpaved,so Steve would only be able to travel half of his usual 60 mile/hour speed on those routes.Modify the model to account for this condition.Would the shortest path change from the base case solution?

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

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

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. -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?