Modeling and solving multi‑skilled resource‑constrained project scheduling problem with calendars in fuzzy condition

In this study, we aim to present a new model for the resource-constrained project scheduling problem (RCPSP) considering a working calendar for project members and determined the skill factor of any member using the efficiency concept. For this purpose, the recyclable resources are staff resources where any person with multiple skills can meet the required skills of activities in a given time. Then, considering uncertainty condition for parameters, it provided a fuzzy scheduling model and validated models by solving different examples. The proposed mathematical programming model optimizes the allocation of limited resources to project activities for scheduling purposes in an essential activity in the real condition of scheduling problems. Moreover, the proposed model can decrease the risk of deviation from scheduling by allocating members with higher skill factors to critical activities. Then, considering uncertainty condition for parameters, it provided a fuzzy scheduling model and validated models by solving different examples. Considering fuzzy conditions for the calendar of the project and multi-skill operators are firstly considered in this paper. Also, the recyclable resources are staff resources which are being considered for the model concurrently in response to the risks of availability to resources and delay in completing the project under uncertainty. The results derived from the model solved by CPLEX indicated a decreased need for employment and shortened project completion duration. Assuming the uncertainty of available resource capacity at any time, the results obtained from the fuzzy model for the value of objective function were evaluated under the influence of the resource calendar and showed the benefits. Effect of the multi-skill members with calendar constraints on the model is tested, and the advantages are determined.