| Course | BU 407 Quantitative Decision-Making |
|---|---|
| Unit | Unit 6 |
| Paper type | Transportation model record |
| Length | About 950 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Analytics |
| Updated | September 2026 |
Free sample paper for BU 407 Unit 6
Three Plants, Four Markets and a Dummy Region: A Transportation Model Record for a Composite Dairy Cooperative's Weekly Truckloads, Including the Lanes Left Empty
Student Name
Business, Herzing University
BU 407: Quantitative Decision-Making
Instructor Name
April 1, 2026
Three Plants, Four Markets and a Dummy Region: A Transportation Model Record for a Composite Dairy Cooperative's Weekly Truckloads, Including the Lanes Left Empty
Supply and Demand
Northwoods, the invented cooperative in this course, ships finished dairy products from three plants to four regional distribution points each week. This record builds the transportation model for that shipping plan, solves it and explains the result. Supply is measured in refrigerated truckloads per week: the Eau Claire plant can ship 40, Wausau 55 and Green Bay 35, a total of 130. Demand is measured the same way: the Twin Cities distribution point needs 30 truckloads, Madison 45, Milwaukee 25 and Chicago 20, a total of 120. All figures come from the cooperative's logistics records and belong to the composite case.
Supply exceeds demand by 10 truckloads. To balance the model, a dummy region with a demand of 10 is added, with a shipping cost of zero from every plant. The dummy is fictitious; a shipment to it means the plant leaves that capacity unused. Render et al. (2018) explain that balancing with a dummy lets the standard transportation method work on an unbalanced problem, and that the dummy's allocation shows where spare capacity sits in the optimal plan.
The Unit Cost Tableau
Each cell gives the cost, in dollars, of one refrigerated truckload from a plant to a distribution point, based on mileage, driver time and tolls. Costs to the dummy region are zero.
| From / To | Twin Cities | Madison | Milwaukee | Chicago | Dummy (unused) | Supply |
|---|---|---|---|---|---|---|
| Eau Claire | $210 | $330 | $420 | $560 | $0 | 40 |
| Wausau | $360 | $260 | $330 | $470 | $0 | 55 |
| Green Bay | $520 | $290 | $210 | $340 | $0 | 35 |
| Demand | 30 | 45 | 25 | 20 | 10 | 130 |
The Solution
The model was solved as a linear program, minimizing total weekly shipping cost subject to each plant shipping no more than its supply and each region receiving exactly its demand. Hillier and Lieberman (2015) note that transportation problems are a special case of linear programming whose structure guarantees whole-number solutions when supplies and demands are whole numbers, which matters here because a truckload cannot be split. The optimal plan costs $31,250 a week.
| From / To | Twin Cities | Madison | Milwaukee | Chicago | Dummy (unused) | Shipped |
|---|---|---|---|---|---|---|
| Eau Claire | 30 | 10 | 30 of 40 | |||
| Wausau | 45 | 10 | 55 of 55 | |||
| Green Bay | 15 | 20 | 35 of 35 |
Reading the Plan
Eau Claire ships 30 truckloads to the Twin Cities, its cheapest lane at $210, and leaves 10 truckloads of capacity unused, which is the dummy's allocation. Wausau ships its full 55: 45 to Madison, its cheapest lane at $260, and 10 to Milwaukee. Green Bay ships its full 35: 15 to Milwaukee, its cheapest lane at $210, and 20 to Chicago, the only plant for which Chicago is reasonably close. The total checks: 30 times $210, plus 45 times $260, plus 10 times $330, plus 15 times $210, plus 20 times $340, equals $6,300 plus $11,700 plus $3,300 plus $3,150 plus $6,800, or $31,250.
The spare capacity lands at Eau Claire because Eau Claire is far from Madison, Milwaukee and Chicago; its only efficient market is the Twin Cities, which needs just 30 truckloads. If the cooperative ever needed to reduce production at one plant, this plan suggests Eau Claire is where shipping costs would least suffer.
Three features of the plan make it practical. It uses only five of the twelve real lanes, which keeps dispatching simple. Each plant serves at most two destinations, so drivers learn a small number of routes. And every destination is served from its cheapest or second-cheapest plant, so no region is supplied from an obviously distant source that customers or drivers would question. The dispatch team can therefore adopt the plan largely as written, adjusting week by week for actual order volumes.
Why the Empty Lanes Stay Empty
Seven lanes carry nothing, and each would need a cost reduction before it would enter the plan. The reduced cost of an empty lane is the amount total cost would rise for each truckload forced onto it; equivalently, it is how much that lane's cost would have to fall before using it would pay. Wausau to Chicago is the closest to entering: it would add only $10 per truckload, so a toll change or a backhaul arrangement worth more than $10 a load would bring it into use, shifting Chicago volume from Green Bay. Eau Claire to Madison would add $70 per load, Eau Claire to Milwaukee $90 and Eau Claire to Chicago $100. Green Bay to Madison would add $150, Wausau to the Twin Cities $220 and Green Bay to the Twin Cities $500, the last effectively ruled out by distance.
The Wausau to Chicago lane deserves attention because a $10 difference is within the error of the cost estimates. Two plans are therefore almost equally good, and the cooperative could choose between them on grounds the model does not capture, such as driver schedules or the reliability of the Wausau fleet.
The reduced costs also serve as a guide for negotiation. If a carrier offered Eau Claire to Madison at $250 a truckload instead of $330, a reduction of $80, the lane would enter the plan because its reduced cost is only $70, and some of Eau Claire's idle capacity would displace Wausau shipments to Madison. Before signing any new rate, the logistics team can compare the discount with the lane's reduced cost to see whether the change would actually alter the plan.
Assignment Problems and Spreadsheets
An assignment problem, such as matching drivers to routes, is a special case of the transportation model in which every supply and demand equals one. The same method applies, and so does the same caution about whole numbers. This model was solved in Python; Excel Solver produces the same plan when the problem is set up with a cell for each lane, supply and demand constraints and the minimize option. Solving by hand with the northwest corner rule followed by the stepping-stone method would reach the same answer through more steps (Winston, 2004). Northwoods Dairy Cooperative, its plants, costs and volumes are composites created for this course.
References
Hillier, F. S., & Lieberman, G. J. (2015). Introduction to operations research (10th ed.). McGraw-Hill Education.
Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2018). Quantitative analysis for management (13th ed.). Pearson.
Winston, W. L. (2004). Operations research: Applications and algorithms (4th ed.). Thomson Brooks/Cole.
Reading the BU 407 Unit 6 instructions
For Unit 6, students set up and solve a transportation problem. Most versions want supply by source and demand by destination stated with units, a check of whether totals balance, a dummy source or destination added where they do not, a unit cost tableau, a solved shipping plan and an explanation of the result. Many rubrics ask why some lanes carry nothing and what would have to change for them to be used. Instructors look for clearly labeled dummy rows or columns and a total cost that can be checked. The problem may be solved by hand, with a spreadsheet solver or with software. Expect a few pages with grids, citing optimization sources in APA 7, and verify the total cost with a line of arithmetic.
Inside the BU 407 Unit 6 example
The sample states supply and demand with units, finds a 10-truckload surplus and adds a labeled dummy region at zero cost. The cost tableau gives a cost for every lane. The solution section explains the method and why whole-number answers are guaranteed, then presents the shipping grid and total cost. A reading section explains each plant's shipments, checks the total with arithmetic and notes practical features of the plan. The empty lanes section gives each unused lane's reduced cost, flags a near tie and explains how reduced costs can guide rate negotiations. A final section links the model to assignment problems and alternative solution methods.
BU 407 Unit 6 rubric: what full points look like
The rubric for the transportation unit generally assesses the setup, the solution, the interpretation of the plan and the analysis of unused lanes. Setup earns full points when supply and demand are stated with units and any imbalance is handled with a labeled dummy. The solution is judged by a correct, feasible plan with a verified total cost. Interpretation scores highest when the plan is explained in practical terms, including where spare capacity sits. Analysis of unused lanes rewards reduced costs interpreted as the cost change needed to use each lane, as the sample does. Instructors also credit noticing near ties, since two almost equal plans give the manager a real choice. Clear grids and citations complete the grade.
BU 407 Unit 6 help: mistakes that cost points
A common Unit 6 mistake is forgetting to balance supply and demand, which makes the model infeasible or wrong. Another is placing a dummy without labeling it, so readers think a real destination exists. Students often report a total cost that does not match the grid. Some papers show the solution without explaining why certain lanes are empty. Others miss alternative optimal plans when reduced costs are near zero. Finally, remember that transportation solutions should be whole numbers when supplies and demands are; a fractional truckload is a sign something went wrong.
Get a BU 407 Unit 6 example written to your instructions
Give us the Unit 6 instructions from the BU 407 classroom, the rubric, and the supply, demand and cost figures your assignment sets. We write a custom example that checks the balance first, labels any dummy, keeps rates apart from quantities and turns the final grid into shipping instructions. First custom sample free, returned in 24 to 48 hours.
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BU 407 Unit 6 questions, answered
What do I do when supply and demand do not match?
Add a dummy row or column for the difference and give every cell in it a zero cost. Excess supply needs a dummy destination that absorbs it, excess demand needs a dummy source that is never actually shipped. Label the addition and say what it represents, since an unlabeled dummy looks like an invented plant and reads as an error to a marker.
Is an assignment problem the same model?
It is a special case, with supply and demand of one at every point, so the same tableau and the same logic apply. What changes is the interpretation: the answer is a pairing of people or machines to work rather than a set of shipment volumes. If your unit covers both, keep the two write-ups distinct in their closing sections.
Can I solve it with a spreadsheet instead of by hand?
Follow the instructions, since sections differ on whether a manual initial solution and optimality check are required. Where either method is allowed, use the spreadsheet and show the layout, then verify the total cost by hand from the grids. That check costs a minute and catches the range errors that make a confident answer wrong.
Where can I find a free BU 407 Unit 6 sample paper?
Everything in the BU 407 Unit 6 record, from the cost tableau to the empty lane analysis, is open above to read free. If your transportation problem has different sources or costs, send the prompt with your supply, demand and cost figures, and a free custom record will be built for you, usually within about two days.
What do I do when supply and demand do not match in BU 407 Unit 6?
Add a dummy source or destination with zero cost to absorb the difference, and label it clearly. The sample adds a dummy region for 10 truckloads of surplus supply, and the dummy's allocation shows which plant holds the spare capacity.