Vehicle Root Optimization for simultaneous pick up and delivery: A mixed integer formulation

Location of the customers in the map of Brooklyn, USA

Formulation of the problem into mixed integer programming

The objective function is given by

Decision Variables

Rij: amount of delivery goods on board between nodes i and j

Constraints

Constraints 1:

Costs of travel between nodes

The costs of travel between nodes are given by the following table. Here node 0 represents depot and nodes 1 to 11 represents customers

Results

Optimum number of vehicle is 3. The total optimum cost for vehicle 1 is $ 19144.484. The optimum path for each vehicles is given by the following figures

Conclusion

The problem is successfully implemented in mixed integer programming. The model can be useful in public transport in which vehicles deliver and pick passenger simultaneously. Also it can be used to optimize the delivery logistics of a firm or factory.

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