Exam 6: Transportation, Transshipment, and Assignment Problems

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 the quantity shipped from Madison is:

In the linear programming formulation of a transportation network,

For most real-world applications, an unbalanced transportation model is a more likely occurrence than a balanced transportation model.

An example of a ________ point is a distribution center or warehouse located between plants and stores.

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 are the supply constraints for the factories?

In a linear programming formulation of a transportation model, each of the possible combinations of supply and demand locations is a(n) ________

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

In a ________ problem, items are allocated from sources to destinations at a minimum cost.

In an unbalanced transportation model, all constraints are equalities.

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 constraints are required to model this as a linear program?

The assignment problem constraint x31 + x32 + x33 + x34 ≤ 2 means

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 -If 120 units are shipped from Factory C to Assembly Plant 1, 60 units from Factory C to Assembly Plant 3, and 400 units from Factory B to Assembly Plant 2, what are the remaining shipments?

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 are the total monthly transportation costs for the optimal solution?

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. -Write every constraint that involves Company A.

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 -Which of the following constraints represents the assignment for student A?

If the optimal solution includes x11 = 100 and x22 = 200, determine the remaining shipments that will result in a minimum cost of $1700.

Assignment problems are always balanced.

In a transshipment problem, items may be transported from sources through transshipment points on to destinations.

Due to increased sales, a company is considering building three new distribution centers (DCs) to serve four regional sales areas. The annual cost to operate DC 1 is $500 (in thousands of dollars). The cost to operate DC 2 is $600 (in thousands of dollars.). The cost to operate DC 3 is $525 (in thousands of dollars). Assume that the variable cost of operating at each location is the same, and therefore not a consideration in making the location decision. The table below shows the cost ($ per item) for shipping from each DC to each region. Region 1 1 3 3 2 2 2 4 1 3 3 3 2 2 3 The demand for region A is 70,000 units; for region B, 100,000 units; for region C, 50,000 units; and for region D, 80,000 units. Assume that the minimum capacity for the distribution center will be 500,000 units. Write the objective function for this problem.

In most real-world cases, the supply capacity and demanded amounts result in a(n) ________ transportation model.