Exam 5: Network Modeling

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?

The supply nodes in the graphical representation of the transshipment 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 network representation depicts this problem. Write out the LP formulation for this problem.

Which formula should be used to determine the Net Flow values in cell K6 in the following spreadsheet model?

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

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. 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. cost per clock shipped)Cost to Ship to Distribution Center Plant St Louis Pittsburgh Toledo \ 2 \ 4 Centerville \ 3 \ 2 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?

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

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: Distance Center 1 Center 2 Center 3 Center 4 Supply Plant A 45 60 53 75 500 Plant B 81 27 49 62 70 Plant C 55 40 35 60 650 Demant 350 325 400 375 Draw the transportation network for Clifton's distribution problem.

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

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.

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)?

Draw the network and indicate how many units are flowing along each arc based on the following Analytic Solver Platform solution.

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?

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

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?

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.

Draw the network representation of this LP model.What type of problem is it? MAX ^X₄₁ Subject to: ^X₄₁ ^{− X}₁₂ ^{− X}₁₃ ^{= 0} X₁₂ − X₂₄ = 0 X₁₃ − X₃₄ = 0 X₂₄ + X₃₄ − X₄₁ = 0 0 ≤ X₁₂ ≤ 5, 0 ≤ X₁₃ ≤ 4, 0 ≤ X₂₄ ≤ 3, 0 ≤ X₃₄ ≤ 2, 0 ≤ X₄₁ ≤ ∞

The constraint X₁₃ + X₂₃ − X₃₄ ≥ 50 indicates that

The equipment replacement problem is an example of which network 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: