Constrained Renewable Resource Allocation in Fuzzy Metagraphs via Min-Slack

This paper discusses that the fuzzy metagraphs can be used as a tool for scheduling and control of fuzzy projects. Often, available resources for executing projects may be limited. It is assumed the resources required to accomplish each activity of project (metagraph edges) is renewable. One of the common methods for scheduling projects is using the min-slack. So, first, the forward and backward computations for deterministic metagraphs are described. Then, assuming that the completion time of activities are positive trapezoidal fuzzy numbers, the forward and backward computations are generalized for fuzzy metagraphs. Consequently, completion time of project, earliest and latest time of start and end of activities and floating time of them are obtained as fuzzy numbers. Also, critical activities and critical paths are defined. Then, for scheduling, by using the selected ranking method, the activities of project (metagraph edges) based on min-slack ascending were ordered. Through some numerical examples, calculation steps and the results are illustrated.