{1} Application of Seven-Step Process:

Company XYZ is a (fictitious) package delivery service that serves customers 
within the continental United States. It has several stores throughout the 
country that perform local deliveries within a given radius and which send/receive 
longer-range packages to/from other company stores.

[1: Formulate the Problem]: Because of increasing expenditures related to transportation, 
XYZ needs to revise its delivery routes and schedules to achieve a better balance between 
delivery speed and resource consumption (such as fuel consumption).

[2: Observe the System]: Several details require analysis, including: the average 
in-use capacity of delivery trucks; the routes regularly taken by trucks; the fuel 
consumption for each trip; the average time taken to deliver a given package; and 
the costs related to using air delivery for portions of a trip.

[3: Formulate a Mathematical Model of the Problem]: One possible means of modeling 
the system is by using a weighted graph(s), where one graph could have the company's 
stores as vertices and the possible delivery routes as edges. The edges will have 
varying weights depending on speed, cost, fuel efficiency, and similar factors. 
Other graphs (such as those for modeling possible routes for local deliveries) 
may also be needed to assist in spotting the best travel plans. Once the graphs 
and constraints are in place, graph-"walking" algorithms can be used to determine 
the best "walks" that yield the desired improvements.

[4: Verify the Model and Use the Model for Prediction]: After creating the models 
and finding the specific routes, some test deliveries must be performed to ensure 
that the delivery speeds, fuel efficiency, and costs are at the levels expected 
from the graph's best "walks." If the results differ by too great an amount, then 
the graphs may require revision to conform to the actual results.

[5: Select a Suitable Alternative]: The algorithms may discover several "walks" 
on each graph that have almost the same optimal delivery expenditures and speed, 
so the operations researcher will have to find the ones that follow XYZ's emphasized 
delivery practices the best.

[6: Present the Results and Conclusion of the Study to the Organization]: The best 
of the "walks" should be presented to the organization, and the operations researcher 
may mention his preferred "walks" as well to assist in providing opinions about the 
optimal choices.

[7: Implement and Evaluate Recommendations]: If the organization is satisfied with 
the results, XYZ will use the new delivery routes and practices, collecting data all 
the while to ensure that the correct choices were made.