| Course | SOP-7200 Strategic Operations Management |
|---|---|
| Module | Module 4 |
| Paper type | Written assignment 4: location, capacity and forecasting problems |
| Length | About 1,048 words, 6 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | Master of Business Administration |
| Updated | October 2026 |
Free sample paper for SOP 7200 Module 4
Where, How Big and How Many: Location, Capacity and Forecasting Problems
Student Name
Master of Business Administration, Thomas Edison State University
SOP-7200: Strategic Operations Management
Mentor Name
Month Day, Year
Where, How Big and How Many: Location, Capacity and Forecasting Problems
The last set of problems takes Port Newark Fulfillment, the composite center in Elizabeth, New Jersey, used throughout the course, to a decision its growth has forced. Volume has risen, a later shipping cutoff is drawing new clients, and the general manager is weighing a second building to serve the household goods brand's store replenishment in the Philadelphia and Trenton area. Using the Module 4 methods in Krajewski et al. (2016), the problems ask where the building should go, how much capacity the company needs and whether to commit to it in one step, and how many orders to plan for. Each answer gives the formula, the inputs and the decision.
Problem 1: Center of Gravity
The building would ship to four regional distribution points, placed on a grid in miles, with annual loads in truckloads: A at (20, 60) with 300, B at (10, 20) with 500, C at (30, 35) with 200 and D at (0, 0) with 250. The center of gravity weights each coordinate by its load. The x coordinate is (300 x 20 + 500 x 10 + 200 x 30 + 250 x 0) / 1,250 = 13.6, and the y coordinate is (300 x 60 + 500 x 20 + 200 x 35 + 250 x 0) / 1,250 = 28.0. The point (13.6, 28.0) is a starting place for the search, not an answer, since roads, zoning and available buildings decide what can actually be leased.
Problem 2: Load-Distance and Factor Rating
Two buildings are available, Site 1 at (15, 30) and Site 2 at (25, 40). With rectilinear distance, which suits a road grid, the load-distance score sums each load times its distance from the site. Site 1 scores 35 x 300 + 15 x 500 + 20 x 200 + 45 x 250 = 33,250, and Site 2 scores 25 x 300 + 35 x 500 + 10 x 200 + 65 x 250 = 43,250. Site 1, near the center of gravity, cuts transport effort by about 23 percent.
Cost of movement is not the only factor. A weighted factor rating scores each site from 1 to 10 on four factors the management team agreed on.
| Factor | Weight | Site 1 score | Site 2 score | Site 1 weighted | Site 2 weighted |
|---|---|---|---|---|---|
| Labor availability | 0.30 | 8 | 7 | 2.40 | 2.10 |
| Highway access | 0.25 | 9 | 7 | 2.25 | 1.75 |
| Lease cost | 0.25 | 6 | 8 | 1.50 | 2.00 |
| Local incentives | 0.20 | 7 | 6 | 1.40 | 1.20 |
| Total | 1.00 | 7.55 | 7.05 |
Site 2 is cheaper to lease, but Site 1 leads on labor and access and wins 7.55 to 7.05. Because both methods favor Site 1, the choice is robust; a sensitivity check shows lease cost would need a weight above about 0.40, with the other weights scaled down in proportion, before Site 2 came out ahead.
Problem 3: Capacity Cushion and Gap
Peak demand next year is forecast at 13,800 orders a day, and the current building's effective capacity is 12,500. Krajewski et al. (2016) recommend a capacity cushion, capacity held above expected demand, to absorb surges and keep service fast. With a 15 percent cushion, required capacity is 13,800 / 0.85, about 16,235 orders a day. The gap is about 3,735 orders a day. A large cushion fits here because the center competes on a same-day cutoff, and in fulfillment, unlike in a capital-intensive plant, idle capacity is relatively inexpensive while missed cutoffs lose clients.
Problem 4: Expansion Decision Tree
Management can build out Site 1 fully now or lease half of it now with an option on the rest. Demand growth will be high with probability 0.6 or low with probability 0.4. Payoffs below are five-year net present values in millions of dollars from the finance team.
| Alternative | High demand (0.6) | Low demand (0.4) | Expected value |
|---|---|---|---|
| Small expansion, no option | 2.1 | 1.2 | 1.74 |
| Large expansion now | 3.4 | -0.3 | 1.92 |
| Small now, expand if demand is high | 2.9 | 1.2 | 2.22 |
The large expansion beats a small one without an option, $1.92 million against $1.74 million, but it loses money if growth stalls. The staged plan, a smaller lease with the right to take the remaining space after a year, has the highest expected value at $2.22 million and no losing branch, because the company commits the second half only once demand is known. The recommendation is the staged expansion, with the option exercised if weekly orders sustain the trend found in Problem 5.
Problem 5: Forecast Comparison
Weekly orders in thousands over the last eight periods were 61, 64, 60, 66, 68, 65, 70 and 72. A three-period moving average forecast periods 4 through 8 as 61.67, 63.33, 64.67, 66.33 and 67.67, with errors of 4.33, 4.67, 0.33, 3.67 and 4.33. The mean absolute deviation, or MAD, is 3.47. Every error is positive, so the method is biased low. The tracking signal, cumulative error divided by MAD, is 17.33 / 3.47 = 5.0, beyond the common limit of plus or minus 4, which says the forecast is consistently missing in one direction.
Exponential smoothing with alpha of 0.3, started at the first actual value, did worse, with a MAD of about 4.39, because simple smoothing also lags a trend (Gardner, 1985). A linear trend fitted to the eight periods gives forecast = 59.11 + 1.476 x period, so the forecast for the next period is about 72.4 thousand orders, and its fitted errors for periods 4 through 8 have a MAD of about 1.42. That figure flatters the trend line, since it was fitted to the same data, so it should be confirmed on new periods. Hyndman and Koehler (2006) caution that error measures depend on scale and should be compared on the same series, which is the case here. The trend method should be used, with its tracking signal reviewed every period.
Conclusion
Both location methods favor Site 1. The center needs about 3,735 more orders a day of capacity to keep a 15 percent cushion, and the staged lease gives the best expected value without risking a loss. Demand is trending up by about 1,500 weekly orders each period, so a trend forecast, not a moving average, should drive the decision on when to take the second half of the building.
References
Gardner, E. S. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4(1), 1-28. https://doi.org/10.1002/for.3980040103
Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688. https://doi.org/10.1016/j.ijforecast.2006.03.001
Krajewski, L. J., Malhotra, M. K., & Ritzman, L. P. (2016). Operations management: Processes and supply chains (11th ed.). Pearson.
Reading the SOP 7200 Module 4 assignment instructions
The fourth SOP-7200 written assignment closes the set of problem assignments that together carry 22 percent of the grade, and its chapters on location, capacity and forecasting also feed the group final project. Expect problems that locate a facility, compare sites, size capacity, weigh an expansion under uncertainty and compare forecasting methods. Show each formula with the inputs, and label distances, loads and units. For decision trees, state the probabilities and payoffs, compute expected values and say what risk each branch carries. For forecasts, report the error of each method, check bias with a tracking signal and recommend one method. Explain what any formula leaves out. Keep the same periods when comparing errors across methods.
Inside the SOP 7200 Module 4 example
The paper treats a single business question, a second building, through three lenses: where to put it, how big to make it and how much demand to plan for. Two location methods are applied and compared, and the paper tests how sensitive the factor rating is to a weight. The capacity problem explains why a large cushion fits a service that competes on speed. The decision tree adds an option, showing that flexibility has value, and the forecasting problem compares three methods by error before choosing one. Notice the cross-references: the forecast trend decides when to exercise the expansion option, so the problems form one plan. The conclusion restates each decision in a sentence.
Reading the SOP 7200 Module 4 grading rubric
As with the earlier problem sets, the fourth is graded on a 100-point scale. Mentors reward correct calculations with units, sound choices between methods and interpretations that lead to a decision. Location answers earn more when they note what the math ignores, such as available buildings. Capacity answers should justify the size of the cushion from the firm's priorities. Decision trees need expected values and attention to downside risk, and forecast comparisons need an error measure and a bias check, not just a forecast. Linking the problems together, as when a forecast drives an expansion trigger, shows integration that strong papers display. Tables and APA citations finish the grade. A clear conclusion adds polish.
Common SOP 7200 Module 4 mistakes, and how to avoid them
Typical errors include using straight-line distance when the problem specifies rectilinear distance, forgetting to divide by total load in the center of gravity, and stopping a decision tree at expected value without mentioning a branch that loses money. In forecasting, students often report a forecast with no error measure, or compare MAD values computed on different periods. Our writers can work SOP 7200 location, capacity and forecasting problems from the chapters your module assigns. Draw the decision tree before computing, list the periods each forecast covers, and keep a running tally of cumulative error for the tracking signal. End each problem with one sentence naming the choice. Then check that the decisions agree with each other.
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SOP 7200 Module 4 questions, answered
Where can I find a free SOP 7200 Module 4 sample paper?
The fourth Strategic Operations Management problem set appears in full above, covering center of gravity, load-distance, factor rating, capacity cushion, a decision tree and forecast comparison for a second fulfillment building.
How is a center of gravity calculated?
Multiply each location's x and y coordinates by its load, sum each, and divide by the total load to get the weighted average coordinates.
What is a capacity cushion?
Spare capacity, stated as a percent of the total, kept for surges; the capacity needed is expected demand divided by one minus that percent.
What does a tracking signal show?
Cumulative forecast error divided by MAD; values beyond about plus or minus 4 indicate a forecast that is biased in one direction.
Why can a staged expansion have a higher expected value?
Keeping an option to add capacity later avoids the loss in low-demand outcomes while still capturing much of the gain if demand is high.