SOP 7200 Module 2 Midterm Operations Problems Example

72 Orders an Hour, 1,050 Orders in the Building and a Cpk of 1.17: Four Midterm Problems for a Fulfillment Center

Student Name

Master of Business Administration, Thomas Edison State University

SOP-7200: Strategic Operations Management

Mentor Name

Month Day, Year

72 Orders an Hour, 1,050 Orders in the Building and a Cpk of 1.17: Four Midterm Problems for a Fulfillment Center

The four problems below cover Modules 1 and 2 of Krajewski et al. (2016), process analysis and quality systems, using data from Port Newark Fulfillment, the composite e-commerce fulfillment center in Elizabeth, New Jersey, analyzed in the first written assignment. Each answer shows the method, the calculation and its operational meaning.

Problem 1: Finding the Bottleneck

An order passes through four stations on a packing line: picking (40 seconds per order), sorting (25 seconds), packing (50 seconds) and labeling (20 seconds). A process's capacity is set by its bottleneck, the step with the lowest capacity (Krajewski et al., 2016). The packing station, at 50 seconds per order, can handle 3,600 divided by 50, or 72 orders an hour, so the line's capacity is 72 orders an hour no matter how fast the other stations work.

Adding a second packer cuts the effective packing time to 25 seconds per order, raising that station's capacity to 144 an hour. The bottleneck then moves to picking, at 40 seconds, so line capacity rises to 3,600 divided by 40, or 90 orders an hour, an increase of 25 percent. Adding a third packer would add nothing until picking is improved. The general manager should add the second packer and then look at picking.

Problem 2: Little's Law

By Little's law, the average inventory in a process equals the rate at which work flows through it times how long each unit stays (Little, 1961). During the afternoon peak the center ships about 1,400 orders an hour, and an order takes on average 45 minutes, or 0.75 hours, from release to the dock. The average number of orders in process is therefore 1,400 multiplied by 0.75, or 1,050 orders.

The result matters for the later shipping cutoff the center wants. If it moves the cutoff from 1 p.m. to 3 p.m. and must ship everything before carrier pickup, it can reduce the time orders spend in the building, for example through zone batch picking, rather than holding more orders in process. Cutting flow time to 30 minutes at the same throughput would lower work in process to 700 orders, freeing space at packing stations.

Problem 3: Controlling Shipping Errors

The center audits a sample of 400 orders each day for errors such as wrong items or quantities. Over 20 days, the average error proportion was 0.6 percent. A p-chart, a tool that grew out of early work on statistical control (Shewhart, 1931), sets limits at the average proportion plus and minus three standard deviations, with the standard deviation found by multiplying the average proportion by one minus that average, dividing by the sample size and taking the square root.

On one day the audit found 9 errors in 400 orders, a proportion of 2.25 percent, above the upper limit. That point signals an assignable cause, something different about that day, rather than ordinary variation. Investigation found that two temporary pickers had started without the usual training. The appropriate response is to correct the cause, here a training gap, rather than to adjust the whole process. The textbook stresses that control charts help managers avoid both overreacting to normal variation and missing real problems.

Problem 4: Process Capability

Client contracts require that each order leave the dock within four hours of release. Measured dock-to-ship time averages 2.6 hours with a standard deviation of 0.4 hours. Because only an upper limit applies, capability is measured with the upper capability index, the upper specification minus the mean, divided by three standard deviations: (4.0 minus 2.6) divided by 1.2, or about 1.17.

A value above 1.0 means the process can meet the four-hour requirement most of the time, but it falls short of the 1.33 that the textbook notes many firms use as a target, leaving little room for the longer afternoon peaks a later cutoff would bring. Reducing the standard deviation to 0.3 hours, through steadier staffing at the peak, would raise the index to about 1.56.

Conclusion

The four problems show how process analysis and quality tools work together: the pack station limits capacity until a second packer moves the bottleneck to picking; Little's law links flow time to orders in process; a p-chart flags a day with an assignable cause; and the capability index shows that the four-hour promise is met but without enough margin for a later cutoff. Each result points to a specific improvement, and together they give the general manager an order of work: add the packer, investigate the error spike, then reduce variation in fulfillment time.

References

Krajewski, L. J., Malhotra, M. K., & Ritzman, L. P. (2016). Operations management: Processes and supply chains (11th ed.). Pearson.

Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387. https://doi.org/10.1287/opre.9.3.383

Shewhart, W. A. (1931). Economic control of quality of manufactured product. Van Nostrand.