A fuzzy graph multi-mode approach to modelling and solving scheduling problem with limited resources

This paper reports on a graph-based approach to modelling and solving combinatorial resource-constrained scheduling problem with respect to possibility to perform the individual activities in alternative ways (modes). These modes vary depending on processing time, time lags to other activities and resource requirements. A fuzzy scheduling problem can be formally defined by a number of activities-nodes that should be scheduled to minimize the project duration subject to generalized precedence relations, may require some units of limited in time use resources. Solution methodology is based on branch and bound procedure to operate with resource requirements and precedence constraints as well as selection of one single activity mode to construct a schedule.