A hyper-heuristic with two guidance indicators for bi-objective mixed-shift vehicle routing problem with time windows

In this paper, a Mixed-Shift Vehicle Routing Problem is proposed based on a real-life container transportation problem. In a long planning horizon of multiple shifts, transport tasks are completed satisfying the time constraints. Due to the different travel distances and time of tasks, there are two types of shifts (long shift and short shift) in this problem. The unit driver cost for long shifts is higher than that of short shifts. A mathematical model of this Mixed-Shift Vehicle Routing Problem with Time Windows (MS-VRPTW) is established in this paper, with two objectives of minimizing the total driver payment and the total travel distance. Due to the large scale and nonlinear constraints, the exact search showed is not suitable to MS-VRPTW. An initial solution construction heuristic (EBIH) and a selective perturbation Hyper-Heuristic (GIHH) are thus developed. In GIHH, five heuristics with different extents of perturbation at the low level are adaptively selected by a high level selection scheme with the Hill Climbing acceptance criterion. Two guidance indicators are devised at the high level to adaptively adjust the selection of the low level heuristics for this bi-objective problem. The two indicators estimate the objective value improvement and the improvement direction over the Pareto Front, respectively. To evaluate the generality of the proposed algorithms, a set of benchmark instances with various features is extracted from real-life historical datasets. The experiment results show that GIHH significantly improves the quality of the final Pareto Solution Set, outperforming the state-of-the-art algorithms for similar problems. Its application on VRPTW also obtains promising results

Effect of Member Income on Additional Voluntary Contributions to Pension Funds in Kenya: Case of Universities in South Eastern

The focus of this study was to investigate the determinats of additional voluntary contributions to pension funds in Kenya with Specific aim of finding out the effect of member’s income to additional voluntary contributions. The population for this study consisted of 859 members of four Universities pension funds in South Eastern Kenya. Questionnaire was used to collect primary data which was analyzed using descriptive statistics. The study found out that Member income affected participation on additional voluntary contributions to pension schemes. The study recommends that the Government should proved incentives in form of tax exemptions on income earned by additional voluntary contributions to pension funds and increase exemption rate of pension contributions from the current maximum of Ksh 20,000 per month to encourage members of the pension schemes to make additional voluntary contributions