Exam 6: Transportation, Transshipment, and Assignment Problems

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 transshipment through the distribution center?

The cost to send a unit of product from supply source A to demand location B would be represented in the ________ of the linear programming statements.

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

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

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 demand constraints for the assembly plants?

A prohibited route in a transportation model should be assigned a value of zero.

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 -If the optimal assignments include manuscript 1 to editor B, manuscript 2 to editor E, and manuscript 3 to editor C with a total editing time of 47 minutes, what manuscripts are assigned to editors D and A?

In an unbalanced transportation problem, if demand exceeds supply, the optimal solution will be infeasible.

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 demanded by Customer B is:

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 objective function for this problem? Use the notation Xij, where i and j correspond to the node numbers indicated in the diagram.

Which of the following are assumptions or requirements of the transportation problem?

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 -The committee would like to assign three reviewers to each applicant. A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign reviewers to Applicant B and Applicant C. Applicant Reviewer 1 2 3 1 4 1 5 6 7 8 9 1

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 is the complete linear model for this scenario?

An assignment problem is a special form of transportation problem.

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. Define the decision variables for this situation.

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 would the transshipment location constraints read if it was OK to store product there on a temporary basis?

In an unbalanced transportation problem, if supply exceeds demand, the shadow price for at least one of the supply constraints will be equal to ________.

A plant has four jobs to be assigned to four machines, and each machine has different manufacturing times for each product. The production manager wants to determine the optimal assignments of four jobs to four machines to minimize total manufacturing time. This problem can be most efficiently solved using the ________ model.

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

In an assignment problem,