Exam 5: Network Modeling

A minimum or maximum flow restriction in the network flow problem can be modeled by

The idea that the total flow into a node must be consumed at a node and the remainder must flow out of a node is referred to as:

The constraint X₁₃ + X₂₃ − X₃₄ ≥ 50 indicates that

Which method is preferred for solving minimal spanning tree problems?

In generalized network flow problems

The following network depicts a balanced assignment/transportation problem for Joe Fix's repair scheduling problem. Formulate the LP for Joe assuming he wishes to maximize the total repairperson to plane assignment preferences. ​

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

The following network depicts an assignment/transportation problem for Joe Fix's repair scheduling problem. Formulate the LP for Joe assuming he wishes to maximize the total repairperson to plane assignment preferences. ​

For minimum cost network flow problems where Total Supply > Total Demand, the balance of flow rule to use at each node is Inflow - Outflow >= Supply or Demand.

How many constraints are there in a transshipment problem which has n nodes and m arcs?

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

A manufacturing company has a pool of 50 labor hours. A customer has requested two products, Product A and Product B, and has requested 15 and 20 of each respectively. It requires 2 hours of labor to produce Product A and 3 hours of labor to produce Product B. The company can obtain up to 50 additional hours of labor if required. In-house labor costs $25 per hour while contracted labor costs $45 per hour. It requires 2 hours of labor to produce Product A and 3 hours of labor to produce Product B. Draw the network flow model that captures this 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?

A company wants to determine the optimal replacement policy for its photocopier. The company does not keep photocopiers longer than 4 years. The company has estimated the annual costs for photocopiers during each of the 4 years and developed the following network representation of the problem. ​ Write out the LP formulation for this problem. ​

Clifton Distributing has three plants and four distribution centers. The plants, their supply, the distribution centers, their demands, and the distance between each location is summarized in the following table: Draw the transportation network for Clifton's distribution problem.

A company needs to ship 100 units from Seattle to Denver at the lowest possible cost. The costs associated with shipping between the cities are: ​ ​ What values would you enter in the Analytic Solver Platform task pane for the following Excel spreadsheet? Objective Cell: Variables Cells: Constraints Cells:

A company needs to ship 100 units from Roanoke to Washington at the lowest possible cost. The costs associated with shipping between the cities are: ​ Draw the network representation of this problem.

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 values would you enter in the Analytic Solver Platform task pane for the following Excel spreadsheet? Objective Cell: Variables Cells: Constraints Cells:

In the assignment problem:

When the lines connecting the nodes in a network are arrows that indicate a direction, the arcs in the network are called directed arcs.