Exam 6: Transportation, Transshipment, and Assignment Problems

An appropriate choice of a model for analyzing the best shipping routes for a supply chain consisting of a manufacturer, warehouse, and retailer would be the ________ model.

Networks may be used to represent assignment problems.

An assignment problem is a special form of transportation problem where all supply and demand values equal 1.

Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Dayton, Bloomington, or Albany. Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively. The network representing the shipping routs is shown below. The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. -What is the constraint for Bloomington?

Awards committees need to be formed to review potential award recipients. In the past, three people have been assigned to review each applicant. The only stipulation is that a reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains an "X", then that specific reviewer is ineligible to review an applicant's material. For example, reviewer 1 cannot review materials submitted by candidate B. It is possible that some reviewers may not receive an assignment. Applicant Reviewer A B C 1 2 3 4 5 6 7 8 9 -A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign two reviewers to Applicant B and 1 additional reviewer to Applicant C. Applicant Reviewer 1 X 2 X 1 3 X 4 1 5 X 6 X 7 X 8 1 X 9 X Demand 2 2 2 Assigned 2

The difference between the assignment and the transportation problem is that

A professor needs help from three student helpers to complete four tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below. Student A 90 50 40 20 120 60 30 50 110 60 50 70 -Based on the information in the table, which tasks are least likely to be assigned to a student?

Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to $2. Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. -Which constraint represents the quantity shipped to retail outlet 6?

Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Dayton, Bloomington, or Albany. Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively. The network representing the shipping routs is shown below. The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. -What is the constraint for the transshipment node in Knoxville?

For an assignment model, all the supply and demand values are ________.

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work, however their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does what manuscript. Estimates of editing times (in hours) for each manuscript by each editor is: Editor Manuscript A B C D E 12 8 10 16 13 9 10 14 13 9 17 14 9 18 12 15 7 11 9 18 12 18 22 11 27 -a) How many supply-side constraints are needed? b) How many demand-side constraints are needed? c) How many variables are involved in this assignment method?

Consider the following transportation problem: Source Supply 1 5 6 100 2 4 2 200 3 3 6 150 4 9 7 50 Demand 250 250 -How many supply-side constraints are there? Write the supply-side constraints.

The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

Sketch the network for this problem and label all nodes and arrows with the appropriate information.

The assignment problem constraint x41 + x42 + x43 + x44 ≤ 3 means

Write the assignment problem matrix below as a network flow problem. Assume that the numbers in each cell represent the travel distance required between nodes. The dash indicates that there is not a route between nodes. A B C 1 4 6 - 2 - 2 1 3 3 5 9

Companies A, B, and C supply components to three plants (F, G, and H) via two crossdocking facilities (D and E). It costs $4 to ship from D regardless of final destination and $3 to ship to E regardless of supplier. Shipping to D from A, B, and C costs $3, $4, and $5, respectively, and shipping from E to F, G, and H costs $10, $9, and $8, respectively. Suppliers A, B, and C can provide 200, 300 and 500 units respectively and plants F, G, and H need 350, 450, and 200 units respectively. Crossdock facilities D and E can handle 600 and 700 units, respectively. Logistics Manager, Aretha Franklin, had previously used "Chain of Fools" as her supply chain consulting company, but now turns to you for some solid advice. -Which of these is not an element of the objective function?

Madlantic Devices designs and manufactures high-end medical devices. The facilities in Madison and Atlanta serve as design and component manufacturing facilities. Components are then shipped to warehouses in Philadelphia or Knoxville, where they are held until final assembly is completed at either Dayton, Bloomington, or Albany. Manufacturing capacity in Madison and Atlanta is 1000 units. Demand at Dayton, Bloomington, and Albany is 450, 500, and 610, respectively. The network representing the shipping routs is shown below. The costs for shipping between each facility is shown below. A blank cell indicates that shipping between two facilities is not permitted. -The transshipment locations are