| Course | BU 407 Quantitative Decision-Making |
|---|---|
| Unit | Unit 7 |
| Paper type | Simulation output brief |
| Length | About 990 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 7
Two Bays Look Like Enough on Average: A Simulation Output Brief on a Composite Dairy Plant's Truck Loading Dock, and Why the Average Answers Wrongly
Student Name
Business, Herzing University
BU 407: Quantitative Decision-Making
Instructor Name
April 15, 2026
Two Bays Look Like Enough on Average: A Simulation Output Brief on a Composite Dairy Plant's Truck Loading Dock, and Why the Average Answers Wrongly
What Is Being Modeled
Northwoods' Wausau plant loads refrigerated trucks at a dock with two loading bays during a ten-hour shift. Carriers have complained about waiting, and the plant manager must decide whether to staff a third bay. This brief describes a simulation of the dock and reports what the distribution of simulated results says about that choice.
The model represents three things. The entities are trucks, which arrive at the dock, wait if both bays are busy, are loaded and leave. The events that move them are arrivals and completions of loading. The rule that decides who is served next is first come, first served: a waiting truck takes the first bay to become free.
Inputs and Why They Were Chosen
Two inputs vary. Truck arrivals follow a Poisson process with an average of 3.6 trucks per hour, which means the time between arrivals is exponentially distributed. This distribution suits arrivals from many independent carriers, none of which coordinates with the others, and the dock's gate logs show roughly this pattern. Loading time follows a triangular distribution with a minimum of 20 minutes, a most likely value of 30 minutes and a maximum of 50 minutes, taken from the loading crew's timed records. The triangular shape was chosen because loading times cluster around a typical value but have a longer tail on the slow side, when a load is mixed or a pallet must be rewrapped. All values belong to the composite case.
Mechanics
The simulation was written in Python. For each simulated shift, arrival times were generated by drawing exponential gaps until the ten-hour shift ended, and each truck was assigned to whichever bay became free first, with a loading time drawn from the triangular distribution. Trucks that arrived before the end of the shift were loaded even if loading ran past it. The model was run for 1,000 replications, each an independent shift, for each of two configurations: two bays and three bays. Random numbers were generated with a fixed starting seed so that both configurations faced the same arrival and loading patterns, which makes the comparison between them sharper. Law (2015) recommends running enough replications that the estimates stop changing materially, and 1,000 shifts, about 36,000 trucks per configuration, is well beyond that point for averages of this kind.
Two simplifications were made and are stated so they can be questioned. The model treats the two or three bays as identical, although in practice one bay has a slower dock leveler. And it ignores breaks, assuming the crew rotates so that each bay stays staffed through the shift. Both simplifications make the dock look slightly more efficient than it is, so the waiting times reported below, if anything, understate the problem with two bays.
What an Average Would Say
A calculation based only on averages suggests two bays are enough. Trucks arrive at 3.6 an hour, and the average loading time is (20 plus 30 plus 50) divided by 3, or about 33.3 minutes. Together that is 3.6 times 33.3 minutes, or 120 minutes of loading work every hour, exactly the capacity of two bays. On average, the two bays would be fully used with nothing left over, and a manager reasoning from averages might conclude the dock is correctly sized. Savage (2009) called this the flaw of averages: plans based on average conditions are wrong on average, because variation does not cancel out when capacity is tight.
What the Simulation Shows
The simulated results tell a different story. With two bays, the average truck waited about 48 minutes before loading began, and one truck in ten waited nearly two hours or more. More than half of all trucks, 53 percent, waited longer than 30 minutes. The bays were busy about 87 percent of the time, and on a typical shift trucks spent a combined 28.8 hours waiting. With three bays, the average wait fell to about 7 minutes, one truck in ten waited 24 minutes or more and only 7 percent waited longer than 30 minutes. Bay utilization fell to about 64 percent, and combined waiting fell to about 4.3 hours a shift.
| Measure (per truck unless noted) | Two bays | Three bays |
|---|---|---|
| Average wait before loading | About 48 minutes | About 7 minutes |
| 90th percentile wait | About 118 minutes | About 24 minutes |
| Share waiting more than 30 minutes | 53% | 7% |
| Bay utilization | About 87% | About 64% |
| Combined truck waiting per shift | About 28.8 hours | About 4.3 hours |
What the Results Mean for Staffing
The difference comes from variation. Some hours bring five or six trucks and some bring two; some loads take 20 minutes and some take 50. When two bays are fully used on average, every burst of arrivals or slow load creates a queue that the dock never has spare capacity to clear. A third bay provides that spare capacity. At the carriers' typical charge for waiting time, about $65 per truck-hour in this case, two bays generate about $1,870 of waiting cost per shift, while three bays generate about $280. Staffing the third bay costs the plant about $420 per shift for a two-person crew, so three bays cost about $700 per shift in total against about $1,870 for two. The simulation supports staffing the third bay.
The model does not need to match every detail of a real dock to be useful, but its conclusion depends on the arrival rate. If carriers could be given appointment windows that spread arrivals evenly, the variation that drives the queue would shrink, and two bays might suffice; that option should be tested in the model before the third bay becomes permanent. Northwoods Dairy Cooperative, its dock and all inputs are composites created for this course (Render et al., 2018).
The distribution matters for carrier relationships as well as cost. With two bays, one truck in ten waits about two hours, which is long enough for drivers to exceed their hours on later deliveries and for carriers to add surcharges or refuse loads at peak times. With three bays, the worst waits are short enough that carriers are unlikely to notice them.
References
Law, A. M. (2015). Simulation modeling and analysis (5th ed.). McGraw-Hill Education.
Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2018). Quantitative analysis for management (13th ed.). Pearson.
Savage, S. L. (2009). The flaw of averages: Why we underestimate risk in the face of uncertainty. Wiley.
Reading the BU 407 Unit 7 instructions
The Unit 7 assignment asks students to build or describe a simulation model and interpret its output for a business decision. Most versions want the system described, including entities, events and service rules, each random input named with its distribution and justification, the mechanics of random number generation and replication explained, results reported as distributions rather than single averages and the implications for the decision discussed. Many rubrics ask how many replications were run and why. A spreadsheet simulation is usually acceptable. Instructors reward papers that compare the simulation with an average-based answer. Most briefs run a few pages built around one output table, cite simulation sources in APA 7 and state any simplifications the model makes, so a reader can judge whether they bias the result.
How the BU 407 Unit 7 example is put together
The sample describes the dock, the decision and the model's entities, events and service rule. An inputs section names the arrival and loading distributions and explains why each suits the process. A mechanics section explains how arrivals and loading times were generated, how many replications were run, why a common seed was used and which simplifications the model makes. A section on what averages would say works through the arithmetic that makes two bays look sufficient. The results section reports averages, percentiles, shares and utilization in a table. The final section explains why variation drives the queue, compares costs and discusses carrier appointments.
BU 407 Unit 7 rubric: what full points look like
Herzing's grading for the simulation brief commonly includes the model description, input justification, mechanics and interpretation of results. The description earns full points when entities, events and service rules are clear. Input justification is judged by named distributions with reasons tied to the process. Mechanics score highest when random generation, replications and any simplifications are stated, as the sample does. Interpretation carries heavy weight and rewards results reported as distributions, compared with an average-based answer and connected to the decision. Instructors also credit noting what would change the result, such as appointment windows that smooth arrivals. A brief that stops at the table loses marks even when the numbers are right. Clear tables and citations complete the grade.
Common BU 407 Unit 7 mistakes, and how to avoid them
Reporting only the average result is the Unit 7 error seen most often, and it hides the long waits that drive the decision. Another is running too few replications, so results change noticeably when the model is run again. Students often choose distributions without justification, such as a normal distribution for times that cannot be negative. Some papers describe the output without connecting it to the decision. Others leave out simplifications, making the model look more precise than it is, or skip the common seed that makes two configurations comparable. Finally, compare the simulation with the answer averages would give; that contrast is often the most persuasive part of the brief.
Get a BU 407 Unit 7 example written to your instructions
Send the Unit 7 instructions and rubric from your BU 407 classroom, with any template workbook the assignment supplies. We write a custom example that names every input distribution, describes the logic in words, reports replications, shows the spread before the mean and states the model limits. First custom sample free, back in 24 to 48 hours.
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BU 407 Unit 7 questions, answered
How many replications are enough?
Enough that the summary figure stops moving much when you run it again, and whatever number the instructions set. A practical check is to run the model twice at your chosen count and compare the means; if they differ meaningfully, raise the count. Report the number you used and the check you did, because an unstated count makes the result impossible to assess.
Can this be done in a spreadsheet?
Yes for the models most sections assign, and many classrooms expect exactly that. A random draw function, a table of replications and a summary block will carry a queue or an inventory model comfortably. Where your section supplies simulation software instead, use it and describe the settings. Either way, show enough of the build that somebody could reproduce your numbers.
Does the model have to match a real operation?
No, and claiming it does creates a problem. The composite counter only has to behave plausibly and be described honestly, with its assumptions on the page. Real arrival logs, staffing rosters and service records from an employer are not yours to feed into a coursework model, and a figure taken from one cannot be published in a submission.
Where can I find a free BU 407 Unit 7 sample paper?
The whole BU 407 Unit 7 brief, from inputs to the staffing conclusion, is free to read above. If your simulation models a different system, send the prompt and your inputs, and a free custom brief will be written, typically within 48 hours.
How many replications are enough in BU 407 Unit 7?
Enough that the results stop changing noticeably when you run more. The sample runs 1,000 shifts, about 36,000 trucks per configuration, which is well beyond that point for averages and percentiles of this kind.