Exam 5: Network Modeling

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 Pittsburg 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. 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 Pittsburg 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?

Consider the equipment replacement problem presented in the chapter. Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j. How could the network model below be modified to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window?

The equipment replacement problem is an example of which network problem?

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

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

Joe Fix plans the repair schedules each day for the Freeway Airline. Joe has 3 planes in need of repair and 5 repair personnel at his disposal. Each plane requires a single repairperson, except plane 3, which needs 2 personnel. Anyone not assigned to maintaining an airplane works in the maintenance shop for the day (not modeled). Each repairperson has different likes and dislikes regarding the types of repairs they prefer. For each plane, Joe has pulled the expected maintenance and determined the total preference matrix for his repair personnel. The preference matrix is: Plane 1 Plane 2 Plane 3 Repair Person 1 11 9 21 Repair Person 2 17 7 13 Repair Person 3 9 12 17 Repair Person 4 14 8 28 Repair Person 5 12 5 12 Draw the network flow for this assignment problem assuming Joe would like to maximize the total preference in his worker-to-aircraft schedule.

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.

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.

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

The arcs in a network indicate all of the following except?

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 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.

Maximal flow problems are converted to transshipment problems by

The constraint X₁₃ + X₂₃-X₃₄ $\ge$ 50 indicates that

A factory which ships items through the network would be represented by which type of node?

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

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

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

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. Draw the network flow model that captures this problem.

A trucking company wants to find the quickest route from Seattle to Denver. What values should be placed in cells L6:L10 of the following Excel spreadsheet?