A large number of business processes involve assignment: matching scarce resources to jobs, tasks, regions, or choosing to hold them in reserve.

Without optimization, businesses use rules that are of the form: “Given conditions X, Y, and Z, assign A to B.”  Sometimes these rules are programmed; sometimes they are in people’s heads.  Neither is optimization.  In virtually all cases, optimization can provide not only a better assignment, but a significantly better set of assignments.

• For the airline, crew are assigned to a plane and crew/planes are assigned to a series of pickup and delivery stops that form “a flight line."  As with most transportation carriers, the airline also decides which flights to assign to its own fleet and which flights to assign to its vendors.  Key to the assignment is minimizing empty air miles and wasted jet fuel, as well as maximizing crew utilization and jet utilization.

• For the business publication, advertisements are assigned to sections, and blank pages are assigned to these sections to carry the ads.  Key to the assignment is providing customers with their placements of choice.  This requires juggling the many combinations that arise when a customer expresses multiple choices to accommodate as many customers as possible.

• For the regional agribusiness, assignment in a dynamic level includes which railcars should be used to transport which waiting crop loads.  Key to the optimization is maximizing asset utilization while minimizing the time between the time the crops are harvested and milled.

• For the pharmaceutical company, assigning blood serum samples to different tests and test equipment is used to maximize diagnostic power and minimize costs and wasted slots in the machines.

• For the printing company, pockets in the complex binding line are assigned to batches of similar pages to create magazines in a way that maximizes the throughput of the binding line and minimizes costly change-outs.
• For the biotech manufacturer, high-value machines and personnel are assigned through a production scheduling optimization solution that maximizes throughput, minimizes cycle time, minimizes operator overtime, and balances resource utilization.
• For the e-commerce trailblazer, a custom optimization model groups products and assigns subscribers according to proprietary objectives and constraints tied to subscriber profiles, history, and activity, product and vendor attributes.
• For the 2020 U.S. Census, automation enables significant changes as to how cases are assigned and how the field staff is supervised. By making it easier for supervisors to monitor and manage their workers, the ratio of workers to supervisor can be increased, reducing the number of supervisors required.