An Inverse Robust Optimisation Approach for a Class of Vehicle Routing Problems under Uncertainty

Liang Sun,Bing Wang

doi:10.1155/2016/2804525

Abstract

There is a trade-off between the total penalty paid to customers (TPC) and the total transportation cost (TTC) in depot for vehicle routing problems under uncertainty (VRPU). The trade-off refers to the fact that the TTC in depot inevitably increases when the TPC decreases andvice versa. With respect to this issue, the vehicle routing problem (VRP) with uncertain customer demand and travel time was studied to optimise the TPC and the TTC in depot. In addition, an inverse robust optimisation approach was proposed to solve this kind of VRPU by combining the ideas of inverse optimisation and robust optimisation so as to improve both the TPC and the TTC in depot. The method aimed to improve the corresponding TTC of the robust optimisation solution under the minimum TPC through minimising the adjustment of benchmark road transportation cost. According to the characteristics of the inverse robust optimisation model, a genetic algorithm (GA) and column generation algorithm are combined to solve the problem. Moreover, 39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and TTC obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach.

Highlights

Vehicle routing problems (VRP) are a crucial issue in industrial and system engineering, and involve routing a fleet of vehicles from a depot to service a set of customers
39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and transportation cost (TTC) obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach
It is found that the TPC and TTC could be improved simultaneously by minimising the judgment range of benchmark road transportation cost

Summary

Introduction

Vehicle routing problems (VRP) are a crucial issue in industrial and system engineering, and involve routing a fleet of vehicles from a depot to service a set of customers. If one or both of demand and edge costs, including transportation cost and travel time are uncertain, the variant VRP becomes VRPU. The optimisation approach for solving VRPU includes stochastic [1,2,3,4,5,6] and robust optimisation approaches The former focuses on minimising the expected cost or maximising the expected revenue, but the expected values may be not the actual utility function influencing decisionmakers. A solution to robust optimisation explicitly incorporates conflicting objectives of solution robustness (the optimal solution is close to optimal for all realisation of the input data) and model robustness (the optimal solution is almost feasible for all realisation of the input data)

Objectives

Methods

Results

Conclusion