A Continuous-Time MILP Formulation for the Multi-Mode Resource-Constrained Project Scheduling Problem

The well-known multi-mode resource-constrained project scheduling problem aims at selecting for each project task a start time and an execution mode to obtain a precedence- and resource-feasible schedule with minimal project duration. The available execution modes for the tasks differ in their durations and demands for some scarce resources. Numerous problem-specific solution methods and several mixed-integer linear programming (MILP) formulations have been described in the literature. We introduce a new continuous-time MILP formulation that employs continuous start-time variables and three types of binary variables: mode-selection, resource-assignment and sequencing variables. The results of our computational analysis indicate that the proposed formulation achieves superior performance than two formulations from the literature when the range of the tasks' durations is relatively high.