Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap

This paper addresses a project scheduling problem (PSP) where the activities can be performed with several discrete modes and with four different payment patterns. Cash outflows depend on the activities' execution modes, while cash inflows are determined by the payment pattern. Under project deadline constraints, the objective is to minimize the maximal cash flow gap, which is defined as the greatest gap between the accumulative cash inflows and outflows over the course of the project. Based on the definition of the problem, the optimization models are constructed using the activity-based method. Due to the NP-hardness of the problem, the mixed and nested versions of variable neighbourhood search (VNS), tabu search (TS), and variable neighbourhood search with tabu search (VNS-TS) are developed. Based on the characteristics of the problem, two improvement measures are proposed and embedded into the algorithms. Through a computational experiment conducted on a data set generated randomly, the performance of the developed algorithms, the contributions of the improvement measures, and the effects of the key parameters on the objective function are analysed. Based on the computational results, the following conclusions are drawn: Among the algorithms developed, the nested version of the VNS-TS is the most promising algorithm, especially for larger problems. The maximal cash flow gap decreases with the increase of the advance payment proportion, payment number, payment proportion, or project deadline. Among the four payment patterns, the expense based and progress based payment patterns may be more favourable for contractors to decrease the gap. The research in this paper has practical implications for contractors to smooth their cash flows and academic implications for project scheduling research due to the introduction of a new objective.