There are many other types of linear programming applications. One particular application was first developed and used by American Airlines in the early 1990s, and it is called revenue management. This was designed to use differential pricing for seats so that additional revenue could be obtained. Some customers who were willing to book with certain restrictions, such as 14-day advance purchase or with a stay over a Saturday night, would receive lower fares. However, if all seats are sold at this reduced cost, then higher-paying passengers, often business travelers who might try to book seats at the last minute, would not be able to do so. The extra revenue generated from these passengers is then lost. A revenue management system was developed to determine how many seats to make available to each type of passenger. Linear programs would have an objective of maximizing the total revenue, while constraints would be based on the total number of seats available on the plane and the total number of seats allocated to each category. Companies have reported dramatic increases in revenues as a result of this.

Given the success of revenue management systems in the airlines industry, similar systems were also adopted by many hotel chains. The airline industry and the hotel industry have products with similar characteristics—a limited inventory of a very perishable product. A plane has a limited number of seats, and when the plane takes off, any empty seats can no longer be sold and the revenue is lost. A hotel has a limited number of rooms, and once a particular date has passed, an empty room on that date cannot be sold and the revenue is lost.

Another common type of application is data envelopment analysis (DEA). This is sometimes used to measure the efficiency of several similar operating units such as hospitals or schools. It is often used with nonprofit entities where measuring the success of a particular unit is difficult, as there is no single objective, such as profit, that is to be optimized. In developing the LP, the inputs and outputs of the particular system must be identified. For a hospital system, the inputs might be the number of doctors working, the number of nurses working, the number of bed-days available per year, and the total payroll. The outputs might be the number of patient-days in the hospital, the number of nurses trained, the number of surgeries performed, the number of outpatient procedures performed, and the number of doctors trained. Constraints are developed for each of these inputs and outputs for each unit in the system. The objective is basically to minimize the resources needed to generate specific levels of output. The results indicate whether fewer resources could have been used to generate the same level of outputs when compared to a typical unit in the system. Efforts can then be made to identify specific areas that are deemed to be potentially inefficient, and improvements can be targeted for these areas.

Transportation problems, transshipment problems, and assignment problems are very widely used in business. These are so common that special purpose algorithms have been developed to solve these more quickly than the current procedures used for other types of linear programming problems. These applications will be presented in the next chapter.