Exam 6: Transportation, Transshipment, and Assignment Problems

A logistics specialist for Wiethoff Inc. must distribute cases of parts from three factories to three assembly plants. The monthly supplies and demands, along with the per-case transportation costs are: $~~~~~~~~~~\text { Destination Assembly Plant }$ Supply A 5 9 16 200 Factory 1 2 6 400 2 8 7 200 Demand 120 620 60 -What is the objective function for the linear programming formulation of this problem?

In a transshipment problem, items may be transported

In a transportation problem, items are allocated from sources to destinations at a maximum value.

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 -What are the linear programming constraints for manuscript 1 and editor C?

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 -How many tasks will be assigned to the students?

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. -How many decision variables are in this problem?

In a balanced transportation model where supply equals demand,

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, assume that no travel is possible between source nodes, between intermediate nodes, and between destination nodes, and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. -State the constraint for intermediate node 4.

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. In addition, assume that no travel is possible between source nodes, between intermediate nodes, and between destination nodes, and no direct travel from source nodes to destination nodes. Let the source nodes be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination nodes be labeled as 6 and 7. -If there are 175 units demanded at destination 6, state the constraint for destination 6.

A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient.

If the number of sources is greater than the number of destinations, then we have a(n) ________ assignment problem.

In a transshipment problem, items may be transported from one source to another.

In order to model a "prohibited route" in a transportation or transshipment problem, the cost assigned to the route should be ________.

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

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. -What are the objective function terms that involve the demand locations?

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. -In an assignment problem all supply and demand values equal are:

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 constraint for Philadelphia is

A form of the transportation problem in which all supply and demand values equal 1 is the ________ problem.

In a ________ transportation model where supply equals demand, all constraints are equalities.

In the process of evaluating location alternatives, the transportation model method minimizes the