Nowadays

combinatorial optimization problems arise in many circumstances, and we need to

be able to solve optimal problems efficiently. Unfortunately many of these

problems are proven to be NP-hard i.e. it is often impossible to solve the instances

in any reasonable time. Combinatorial optimization is an emerging field at the forefront

of combinatorics and theoretical computer science that aims to use

combinatorial techniques to solve optimization problems. A discrete optimization problem seeks to

determine the best possible solution from a finite set of possibilities Combinatorial

optimization is widely applied in a number of areas now a days. However, it is

often unnecessary to have an exact solution. Minimum spanning tree and

travelling salesman problem is the example of combinatorial optimization

problem. Rural postman problem is general case of Chinese post man problem

where subset of set of link of given graph is required to traversed as minimum

cost. The Probabilistic Rural postman problem with time constraint is a problem

in which each postman/customer requires a visit only with a given probability

and independently of the others. The goal is to find an a priori tour of

minimal expected length over all customers, with the strategy of visiting a random

subset of customers in the same order as they appear in the a priori tour. The

PRPPWC is NP-hard, and only very small instances may be solved by exact

methods. There are several motivations for studying the effect of including probabilistic

elements in combinatorial optimization problems. The two most important

motivations are, firstly the desire to define and analyze models which are more

appropriate with reality where randomness is a major source of concern. For

example, for many delivery companies, only a subset of their customers requires

a delivery each day. Ideally we would like to re-optimize, i .e find an optimal

TSP tour for every day. However, we may not have the resources to do this, or

even if we have them it may be very time consuming to do that. It is therefore

necessary to adopt a model that takes into account random phenomena. Secondly the

possibility to analyze the stability of optimal solutions to deterministic

problems when the instances are disturbed by the absence of certain data. In

general, the problem is NP-hard, since the Traveling Salesman Problem can be

easily transformed into it. The Traveling Salesman Problem consist of finding a

shortest closed tour which visits all the cities in a given set. Problem: In this study the problem

is follows: The postman which are used to delivered mail to instance place.

Each postman start from main location at different time every day. The postman

pickup mail or application from start

location to the instance place in many different routes and return back the

start location in at specific time ,starting from early morning until the end

of official working hours,on following condition. (1). Every location will be

visited once in each route.(2) the capacity of each postman is enough for all

application including the each route .In this Nearest Neighbor Algorithm try to

solve optimal route.

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