A Model for Municipal Street Sweeping Operations
An enormous variety of human activities can be the subject of mathematical modeling. To optimize the performance of an auto assembly line, the process of putting two screws into an auto chassis may be broken into, say, 25 carefully defined steps and then an order and timing of these steps is determined to make the process as easy, error-free, and quick as possible. As another example, in a recent criminal trial in New York, the defense attorneys relied heavily on computer-generated profiles to pick a jury most favorably disposed towards the defendants.
KeywordsShort Path Span Tree Directed Graph Undirected Graph Minimal Span Tree
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- F. Busacker and T. Saaty, Finite Graphs and Their Applications. New York: McGraw-Hill, 1966. A good basic text in graph theory that covers a lot of ground; the second half is a survey of applications.Google Scholar
- L. Bodin, “A taxometric structure for vehicle routing and scheduling problems,” J. Computers and the Urban Society, vol. 1, pp. 11–29, 1975. This paper presents the cluster-first method and some node-covering problems (in this module we did edge covering) as well as a primitive version of the procedure presented in this module.CrossRefGoogle Scholar
- J. Meckling, “Chart day problem: A case study in successful innovation,” J. Urban Policy, vol. 2, no. 2, Nov. 1974. This paper, written by a New York City Sanitation Department administrator, describes some mathematical analysis which did not contain as interesting modeling as in this module but which resulted in an annual savings to the city of about $10,000,000. Google Scholar
- J. Edmonds and E. Johnson, “Matching, Euler tours, and the Chinese postman,” Mathematical Programming, vol. 5, pp. 88–124, 1973. This paper presents a way to build a Euler circuit in a directed graph all at once (without first getting several circuits that must be joined together as we did in Theorem 1); their method is based on a directed spanning tree and is quite intuitive.CrossRefMATHMathSciNetGoogle Scholar