Metaheuristic Algorithms for Multimode Multiproject Scheduling with the Objective of Positive Cash Flow Balance

This paper investigates the problem of how to achieve a positive cash flow balance by multimode multiproject scheduling, in which a contractor must implement multiple projects concurrently, and activities can be performed with one of several alternative modes. First, based on formulating cash flows for the projects, we construct an optimization model that can minimize the maximum gap between accumulative cash outflow and cash inflow, thus balancing cash flow positively by arranging optimal execution modes and start times for activities. Then, we prove the NP-hardness of the studied problem and design two metaheuristic algorithms, namely, tabu search (TS) and simulated annealing (SA), which search the desirable solutions in nested and mixed ways, respectively. Finally, taking the multistart iterative improvement (MSII) as comparison algorithm, the performance of the two algorithms developed is evaluated through a computational experiment performed on a data set generated randomly. From the research results, the following conclusions are drawn. The TS and SA are more suitable for solving the smaller and larger problems, respectively, while the nested searching structure could enhance the algorithm's efficiency. With increases in the advance payment proportion, the number of milestone activities, the client's payment proportion, or the project deadline, the contractor's maximal cash flow gap decreases.