This article demonstrates a fuzzy goal programming (FGP) procedure with the use of genetic algorithm (GA) solution approach for proper allocation and deployment of patrol manpower to various road-segment areas in different shifting times to deter violation of traffic laws and thereby reducing the accident rate in the traffic control planning horizon. In the proposed approach, the different structural constraints and various relationships of deployment of patrol units and measuring the performance of traffic operations are fuzzily described. In the model formulation, the membership functions of the defined fuzzy goals are characterized first to measure the degree of achievement of the aspiration level of the goals in the decision making context. Then, the achievement function for minimizing the regret with under-deviations from the highest membership value (unity) of the defined membership goals to the extent possible on the basis of priorities is constructed for smooth functioning of the traffic control system.
[...] Data description of cij (cost in Rs.) for deployment of patrol unit Shift Road segment Now, regarding traffic operations, it is to be followed that there is no additional effect for deployment of more than 5 patrolmen in any road-segment area during any shift. As such, the range of xij is considered as 1 xij i = m ; j = n. The different parameters involved with the traffic operations are estimated by using the conventional two point estimates and presented in the Table 5. [...]
[...] Now, the FGP formulation of the problem by defining the membership functions of the fuzzy goals and thereby solving the problem by using the proposed GA is demonstrated via the case example presented in the Section A demonstrative case example The manpower deployment problem of the department of Traffic Police of the Eastern Metropolitan City Kolkata of India is considered to illustrate the potential use of the proposed model. The required data were collected from the Annual Review Bulletin (2007) published by the Kolkata Traffic Police Department. [...]
[...] Then, the goal expressions can be defined as follows : Segment-wise physical contact goals Since the physical-contact operations are made in terms of number contacts and on the basis of traffic density, segment-wise physical-contact goal expression appears as n P j ij pij & pi , xij i = m Total physical-contact goal To measure the overall performance against deployment of patrol units, the goal expression for total physical-contact takes the form P i j m n ij pij & PC xij Sight-contact goals: Beyond physical-contact, sight-contact should be an integral and vital part to smoothing the vehicle speed, preventing against violation of general traffic rules etc. [...]
[...] However, the study on management science models for patrol manpower deployment problems is still very thin and not widely circulated in the literature. In this article, a FGP formulation of a patrol unit deployment problem with the various performance achievements in fractional form is considered. A solution scheme based on GA is introduced to reach a satisfactory decision on the basis of priorities of achieving the defined objectives in the decision making environment. An illustrative case example of the metropolitan city Kolkata of India is presented to expound the potential use of the proposed approach FGP problem formulation In a fuzzy decision making environment, instead of crisp description of objectives and structural resource constraints, fuzzification of them depends on the needs and desires of the decision maker in the decision situation. [...]
[...] Larson, C.Richard, “Models for the Allocation of Urban Police Patrol Forces”, MIT Operations Research Center Technical Report No Isaacs, Herbert, Study of Communications, Crimes, and Arrests in a Metropolitan Police Department”, Task Force Report : Science and Technology : A Report to the Presidents Commission on Law Enforcement and Administration of Justice, U.S.Government Prininting Office, Washington, D.C D.G.Hanna and W.D.Gentel, guide to Primary police Management Concepts”, Charles Thomas Publisher, Spring-field, III R.C.Larson, ”Urban Police Patrol Analysis”, MIT Press, Cambridge, Massachusetts Keeney, L.Ralph, “Utility Functions for Multiattributed Consequences,” Management Science, Vol pp. [...]
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