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Full-Text Articles in Other Mathematics
Logistics Planning: Putting Math To Work In A Business Setting, Michael C. Hannan
Logistics Planning: Putting Math To Work In A Business Setting, Michael C. Hannan
Senior Projects Spring 2023
The optimization of business procedures benefits all aspects of the product. Maximizing efficiency can lead to more profits for the business, cheaper products for the consumer, and less fuel consumption for the environment. Tracing the history of optimization, we can see that people have always strived for the most efficient way to allocate scarce resources. However, the field of optimization did not blossom until innovations in mathematics allowed us to solve a majority of real world problems. The discovery of linear and nonlinear programming in the 1940s allowed us to optimize problems that were unsolvable before. This paper introduces how …
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Envy-Free Fair Division With Two Players And Multiple Cakes, Justin J. Shin
Senior Projects Fall 2016
When dividing a valuable resource amongst a group of players, it is desirable to have each player believe that their allocation is at least as valuable as everyone else's allocation. This condition, where nobody is envious of anybody else's share in a division, is called envy-freeness. Fair division problems over continuous pools of resources are affectionately known as cake-cutting problems, as they resemble attempts to slice and distribute cake amongst guests as fairly as possible. Previous work in multi-cake fair division problems have attempted to prove that certain conditions do not allow for guaranteed envy-free divisions. In this paper, we …