Simulated annealing for centralised resource-constrained multiproject scheduling to minimise the maximal cash flow gap under different payment patterns

This paper involves a centralised resource-constrained multiproject scheduling problem with four different payment patterns. In the problem, renewable resources can be shared by all the individual projects, and the task is to arrange activities’ start times to minimise the contractor’s maximal cash flow gap. First, based on the problem formulation, we construct an optimisation model for the problem, and through the analysis of the constructed model, we propose some properties of the problem. Then, due to the NP-hardness of the problem, we develop a simulated annealing algorithm and, according to the proposed properties, design a measure to enhance its searching efficiency of the algorithm. Finally, we conduct a computational experiment on an existing dataset to evaluate the performance of the developed algorithm and analyse the effects of key parameters on the objective function value. From the research results, we draw the following conclusions: The improved simulated annealing algorithm is the most promising algorithm for solving the problem being studied, and the effect of the improvement measure varies as the project parameters change. The maximal cash flow gap increases along with the network complexity, modified average utilisation factor of renewable resources, or discount rate per period while it decreases with the increase in the normalised average resource loading factor, variance in modified average utilisation factors, number of milestone activities, advance payment proportion, progress payment proportion, or deadline of projects. Among the four payment patterns, the expense-based and milestone activity-based payment patterns may be the best and worst, respectively, for the contractor to reduce the maximal cash flow gap.