New formulations for multiple traveler minimum latency problem with time windows

Abstract

In this paper, new mathematical models for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows (kLPTW), named as M2 and M4 are developed. These models are computationally compared with existing models named as M1 and M3 for kLPTW in terms of CPU times and percentage deviation from linear programming relaxation values. A short summary of the computational analysis is given in table A below. In Table A, k is the number of travelers. The first column under the number of traveler cell shows the average CPU times of problems solved in time limit and the second column shows the average percentage deviations. We observed that, our formulations are superior than the existing formulations for all the problems for both kLPTW types with respect to each performance criteria. Purpose: The aim of this study is to develop new mathematical formulations for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows. Theory and Methods: Based on the mixed integer linear programming, mathematical models with polynomial number of decision variables and constraints are developed. Benchmark instances from the literature are solved with existing formulations and proposed new formulations by using CPLEX 12.5.0.1. CPU times and percentage deviation from linear programming relaxation values are considered as performance criteria. Results: We solved 125 problems with varying number of nodes and time windows. In all the problem solved proposed formulations are better than the existing formulations in terms of both of the performance criteria. Conclusion: The proposed formulations for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows are superior than the existing formulations and able to solve the problems up to 100 nodes with narrow time windows. Proposed formulations may be used to solve small and moderate real-life problems very easily. They may also be used for testing the performance of the heuristics constructed for kLPTW.