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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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