Exam 5: Network Modeling

The number of constraints in network flow problems is determined by the number of

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

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following flowchart depicts this problem. What is the balance of flow constraint for node 7 (Diesel)? ​ ​

The following network depicts a balanced transportation/distribution problem for Clifton Distributing. Formulate the LP for Clifton assuming they wish to minimize the total product-miles incurred. ​

In a network flow problem, the value +80 next to a node indicates that the number of units needs to decrease by 80.

A railroad needs to move the maximum amount of material through its rail network. The numbers on arcs represent maximum flow. Formulate the LP model to determine this maximum amount based on the following network diagram. ​

If a side constraint for a network flow model cannot be avoided, and non-integer solutions result, how can the solution be expressed as an integer solution?

How many arcs are required to make a spanning tree in a network with n nodes and m arcs?

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 balanced transportation network for Clifton's distribution problem.

In the generalized network flow problem solver could not find a feasible solution. This means that:

Project 5.2 − Small Production Planning Project (Fixed Charge Problem via Network Flow with Side Constraints) Jack Small Enterprises runs two factories in Ohio, one in Toledo and one in Centerville. His factories produce a variety of products. Two of his product lines are polished wood clocks which he adorns with a regional theme. Naturally, clocks popular in the southwest are not as popular in the northeast, and vice versa. Each plant makes both of the clocks. These clocks are shipped to St Louis for distribution to the southeast and western states and to Pittsburgh for distribution to the south and northeast. Jack is considering streamlining his plants by removing certain production lines from certain plants. Among his options is potentially eliminating the clock production line at either the Toledo or the Centerville plant. Each plant carries a fixed operating cost for setting up the line and a unit production cost, both in terms of money and factory worker hours. This information is summarized in the table below. Production Cost Clocks Produced per Clock per Hour Available Plant Fixed Cost for Southwest Northeast Southwest Northwest Hours per Line Clock Clock Clock Clock Month Toledo $20,000 $10 $12 5 6 500 Centerville $24,000 $9 $13 5.5 6.2 675 ​ The Southwest clocks are sold for $23 each and the Northwest clocks are sold for $25 each. Demand rates used for production planning are 1875 Southwest clocks for sale out of the St Louis distribution center and 2000 Northeast clocks for sale out of the Pittsburgh distribution center. Assume all these units are sold. The per clock transportation costs from plant to distribution center is given in the following table. Develop a generalized network flow model for this problem and implement this model in solver. Use the model to answer the following questions. a. Should any of the production lines be shut down? b. How should worker hours be allocated to produce the clocks to meet the demand forecasts? Are there any excess hours, and if so how many? c. What is the expected monthly profit? d. If a plant is closed, what are the estimated monthly savings?

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

What formula would be entered in cell G18 in this Excel model?

The street intersections in a city road network represent

The right hand side value for the ending node in a shortest path problem has a value of

What is the objective function in the following maximal flow problem? ​ ​

A network flow problem that allows gains or losses along the arcs is called a

What is missing from transportation problems compared to transshipment problems?

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. The following network flow model captures this problem. ​ ​ Write out the LP formulation for this problem.

The minimal spanning tree solution algorithm works by defining a subnetwork and