Multi-Mode Double Resource-Constrained Time/Cost Trade-Offs Project Scheduling Problems

The discrete time/cost trade-offs problem (DTCTP) is a widely concerned subject in project scheduling. However, in traditional research, it only treat cost as a non-renewable resource constraint, the availability of renewable resources per period has been neglected. Therefore, when renewable resources are considered, the traditional DTCTP is extended to a new multi-mode double resource-constrained time/cost trade-offs problem (MDRCTCTP), which involves both renewable and non-renewable resources constraints simultaneously. The required amount of renewable resources is added to the execution mode for each activity and by predefining the resource price, and the activity costs are related to the renewable resources. The objective of MDRCTCTP is to minimizing the project makespan with respect to the renewable resource limitation and the project total cost budget. Finally, we validate the MDRCTCTP by adopting a numerical example, the results show that the optimizing project duration is longer than the traditional DTCTP.