Exam 5: Network Modeling

What is the interpretation of units "shipped" along arcs from dummy supply nodes to demand nodes?

Decision variables in network flow problems are represented by

For a network with n nodes,a spanning tree is

Which method is preferred for solving minimal spanning tree problems?

An oil company wants to create lube oil,gasoline and diesel fuel at two refineries.There are two sources of crude oil.The following Excel spreadsheet shows this problem.What formula should be entered in cell E6 and copied to cells E7:E15)in this spreadsheet?

Draw the network and solution for the maximal flow problem represented by the following Excel spreadsheet.

Solve the following minimal spanning tree problem starting at node 1.

What is the objective function for the following shortest path problem?

The demand nodes in the graphical representation of the transshipment problem:

In a transshipment problem,which of the following statements is a correct representation of the balance-of-flow rule if Total Supply < Total Demand?

What is the constraint for node 2 in the following maximal flow problem?

In the shortest route model,the originating and terminating network nodes are called:

A company wants to manage its distribution network which is depicted below.Identify the supply,demand and transshipment nodes in this problem.

Draw the network representation of the following network flow problem. MIN: ^{5 X}₁₂ ^{+ 3 X}₁₃ ^{+ 2 X}₁₄ ^{+ 3 X}₂₄ ^{+ 2 X}₃₄ Subject to: ^−X₁₂ ^{− X}₁₃ ^{− X}₁₄ ^{= −10} X₁₂ − X₂₄ = 2 X₁₃ − X₃₄ = 3 X₁₄ + X₂₄ + X₃₄ = 5 X_ij ≥ 0 for all i and j

Project 5.1 ? Recruit Training You are a military training analyst in charge of initial training for the XXX career field and must decide how to best train the new recruits to satisfy the requirements for skilled recruits.There are six different courses A,B,C,D,E, F)used for training in the XXX career field and four different sequences of courses that can be taken to achieve the required skill level.These sequences are A-E,B,C-F,and A-D-F.The table below provides information on the six courses. Caurse Cost Per Student Min. Num. af Trainees Mar. Num. af Trainees A 25 15 40 B 55 10 50 30 15 50 D 10 15 50 E 20 10 50 F 15 10 50 There are 100 recruits available for training and a demand for 100 skilled recruits.Assume all recruits pass each course and that you are trying to put students in classes in order to minimize the total cost of training.Assume non- integer solutions are acceptable.Further,assume each course will be held. a.Draw a network flow diagram describing the problem. b.Formulate the associated network flow linear program. c.Implement a spreadsheet model and use Risk Solver Platform RSP)to obtain a solution to the problem.Use your model to answer the following questions. What is the expected student load for each course? Should any course be expanded? Should any course or sequence be considered for elimination? Next,assume that not all students pass each course.In fact only 90% of the students pass courses A,E,and F and only 95% of the students pass courses B,C,and D.Each course is considered independent.The requirement for 100 skilled recruits remains.Your job is now to determine the number of recruits to place into the training program to obtain the 100 trained recruits while continuing to minimize the total cost of training. d.Re-draw the network flow diagram describing the problem to accommodate the above changes. e.Formulate the associated generalized network flow linear program. Implement a spreadsheet model of this changed model and use Risk Solver Platform RSP) f.to obtain a solution to the expanded problem.How many recruits are needed and what is the change in total training cost?

Almost all network problems can be viewed as special cases of the

Which method is preferred for solving fully connected transportation problems?

Maximal flow problems are converted to transshipment problems by

What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?

The assignment problem is equivalent to a transportation problem with