Linear programming formulation for vehicle routing problem which is minimized idle time

Ömer Nuri Çam    
Hayrettin Kemal Sezen    


Paper is related to “What is a Vehicle Routing Problem Which Is Minimized Idle Time and how to write its Linear Programming model”. In this study, a Linear Programming (LP) model has been developed for a Vehicle Routing Problem (VRP) to minimize total idle time (MIT).  This problem has been realized according to manage the route operations of a company carrying long-distance passengers by bus in Turkey. The differences of this problem from the other VRP firstly comes from its objective function. It suggests vehicles should work more because they make profit if they work. So its objective function should be defined as to minimize the sum of idle time of those vehicles.  To the contrary of VRP problems which are examined so far, vehicles should work more and sometimes they should prefer long distance route also. Other two differences are related with constraints: Some locations should be visited more than once for different time periods and sub-tours could be allowed to occur in some situations. For presentation of the problem, 34 routes of the company which belong to one of five sub groups have been chosen as samples. For solving this kind of problems, it is very important using exact methods such as Linear programming or Branch and Bound.

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