# The Street Sweeping Problem.

December 1994

## Date of Award

Winter 12-12-1995

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Applied Statistics Unit (ASU-Kolkata)

## Supervisor

Roy, Bimal Kumar (ASU-Kolkata; ISI)

## Abstract (Summary of the Work)

Combinatorial techniques find widespread application in the arca of urban services. Some well-known problems are: design of rapid transit systems, location and stalfing of police stations, assignnent of shifts for municipal workers, ronting of garbage trucks to pick up garbage, routing of street sweeping vehicles, and so on.We have taken up the problem of designing the routing of street sweeping vehicles(refer Helly. W,[7) & Roberts.F.S, [1)) under the inultifarious constraints that are involved in mu nicipal street sweeping operations and the interesting graph-theoretic and combinatorial problems that are involved in the process of developing eflicient solutions.The problem has been studied in detail by L.Bodin and S.Kursh when they were developing a model for street-sweeping operations for the New York City Departanent of Sanitation in the Urban Science Program at the State University of New York at Stony Brook. The New York City Sanitation Department had a \$200, 000, 000 anual budget of which \$10, 000, 000 went to street-sweeping. The computerized sweeper routing based on this model saved about \$1,000,000. 1he model was used in a part of the District of Columbia where it cut costs by over 20%.As mentioned by Tucker and Bodin (2], the difficulties inhereut in building good mathemat- ical models for street-sweeping are indeed diverse in nature. The effort and money needed to collect proper data may be huge, changing any existing system to enhance efficiency may be next to impossible the changcover may be economically prohibitive or thete may be stiff resistance from the workers union. Morcover, it is known that more precisely one defines the problem taking carc of all the underlying coustraints, the more nwieldy the model becoines. Ou the other hand, certain idcalized assumptions made to obtain elegant mathematical analysis may make the model far from being realistic.Tucker and Bodin [2] have laid emphasis on the realization of many of the above-mentioned constraints, some of which are specific to the city under consideration. There is no analysis on the computational complexity or bounds of the algorithms presented by them. In this work, we have emphasised on the computational complexity of the problem, made a survey on the related optimization algorithnis for networks that have been used, and have presented an c-approximate algorithn for the routing in the case of a nmixed graph, which happens to be the most generalized case.

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843335

ISI-DISS-1994-17