Metaheuristics for multi-mode cash flow balanced project scheduling with stochastic duration of activities

- A multi-mode CFBPSP with stochastic activity durations is proposed.
- Metaheuristics with different structures are developed for solving the problem.
- A computational experiment is conducted to evaluate performances of metaheuristics.
- The impacts of project parameters on the objective function are analyzed.

This study investigates the multi-mode cash flow balanced project scheduling problem with stochastic duration of activities. The objective is to generate a robust baseline schedule to minimize the contractor's maximal cumulative gap between cash outflows and cash inflows. Owing to the NP-hardness of the problem, we develop two metaheuristics, i.e. simulated annealing (SA) and tabu search (TS), which have different search structures and are equipped with an improvement measure, to solve the problem. An extensive computational experiment is conducted on a data set generated by ProGen to evaluate the performance of the metaheuristics. The results demonstrate the effects of the improvement measure and indicate that the efficiency of TS decreases, whereas that of SA tends to increase with increasing problem scale. The influence of the key parameters on the objective function is analyzed and the following conclusions are drawn: The contractor's maximal gap of cumulative cash flows decreases with an increase in the expected project deadline, times of attenuation coefficient, payment number, compensation proportion, advanced payment proportion, whereas it increases with an increase in the times of marginal cost and the retention proportion.