Exam 6: Transportation, Transshipment, and Assignment Problems

In a transshipment problem, items may be transported from destination to destination and from source to source.

Which of the following assumptions is not an assumption of the transportation model?

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 300 units available at source 2, state the constraint for source node 2.

In a transportation problem, items are allocated from sources to destinations

In an assignment problem, all demand and supply values are equal to ________.

The transshipment model includes intermediate points between the sources and destinations.

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 objective function is:

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 constraints for the 3 distribution centers.

The ________ model is an extension of the transportation model in which intermediate points are added between the sources and destinations.

In order to prevent the accumulation of inventory at transshipment points, they should be modeled as being ________ nodes.

In order to model a "prohibited route" in a transportation or transshipment problem, the route should be omitted from the linear program.

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 constraints allows for some inventory to be held at one of the crossdock facilities?

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 task 2, scanning?

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 -Formulate this as an assignment problem in which two reviewers are assigned to review each applicant's material.

In a transshipment model, the supply at each source and demand at each destination are limited to one unit.

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 demand-side constraints are there? Write the demand-side constraints.

In a transshipment problem, items may be transported directly from sources to destinations.

The problem that deals with the distribution of goods from several sources to several destinations is the

Assignment linear programs always result in integer solutions.

The following table represents the cost to ship from Distribution Center 1, 2, or 3 to Customer A, B, or C. \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace Customer DC A B C Supply 4 6 8 500 5 2 7 400 3 5 9 300 Demand 200 350 400 -The constraint that represents the quantity supplied by DC 1 is: