Interval-Valued Goal Programming Method to Solve Patrol Manpower Planning Problem for Road Traffic Management Using Genetic Algorithm

In this chapter, an interval-valued goal programming (IVGP) method is suggested for modelling and solving patrolmen deployment problem in traffic control system in the inexact environment. To formulate the model, the objectives of the problem are converted into goals by introducing target intervals to achieve objective values and incorporating interval coefficients to objective parameter sets to obtain an optimal solution in decision horizon. Again, a performance measuring function is defined to represent different kinds of objectives that are inherently fractional in form in decision premises. In the process of model formulation, the function defined for measuring various performances is transformed into linear equivalent to avoid computational difficulty with fractional objectives in course of searching solution of the problem. Then, to formulate the standard model of the problem, interval arithmetic rules are employed to convert the defined goals into goals as made in conventional GP. To design the executable model, the extended GP methodology is addressed to design priority-based IVGP model for solving traffic control problem. In the process of searching solution, a genetic algorithm (GA) computational scheme is employed to obtain the patrolmen deployment decision. In the sequel of making decision, sensitivity analysis with rearrangement of priority factors to model goals is considered, and Euclidean distance function is used to identify the best deployment strategy in traffic control horizon. The effectiveness of using the method is demonstrated via an example of metropolitan city Kolkata of West Bengal in India.