Abstract
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.
The work of the first author on this chapter was partially supported by National Science Foundation Grant GP-PO33568-X00.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
O. Ore, Graphs and Their Uses. New York: Random House, 1963. A short, introduction to graph theory written for able high school students (and lower division undergraduates); of the many interesting applications, the logical puzzles (Sections 2.4 and 6.1) are especially enjoyable.
R. Wilson, Introduction to Graph Theory. New York: Academic Press, 1972. A concise, well-written undergraduate text.
F. Hillier and G. Lieberman, Introduction to Operations Research. San Francisco:Holden-Day, 1967. The classic undergraduate operations research text; the algorithms used in this module are discussed in greater detail in Chapters 6 and 7.
H. Wagner, Principles of Operations Research. Englewood Cliffs, NJ: Prentice- Hall, 1969. The other standard operations research text; is a bit more advanced than [4]; algorithms used in this module are in Chapter 6.
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.
E. Beltrami and L. Bodin, “Networks and vehicle routing for municipal waste collection,” Networks, vol. 4, pp. 65–94, 1973. This paper describes two other garbage routing problems as well as a primitive version of the procedure presented in this module.
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tucker, A.C., Bodin, L. (1983). A Model for Municipal Street Sweeping Operations. In: Lucas, W.F., Roberts, F.S., Thrall, R.M. (eds) Discrete and System Models. Modules in Applied Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5443-0_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5443-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5445-4
Online ISBN: 978-1-4612-5443-0
eBook Packages: Springer Book Archive