As enterprises are led by the wave of intelligent and digital transformation, they are not only able to undertake multiple projects in parallel, but also gradually evolve to cross-disciplinary and skill-based qualifications, especially in technology-intensive enterprises. Enterprise staff often have multiple skills and they can be shared in multiple projects, which is known as multi-skilled staff Distributed Resource Constrained Multi-Project Scheduling Problem (MS-DRCMPSP). This type of problem is called Multi-skilled Distributed Resource Constrained Multi-Project Scheduling Problem (MS-DRCMPSP), i.e., the information asymmetry of multiple projects presents the form of distributed independent management. The only link between projects is the sharing of multi-skilled resources in the enterprise, so the key to solving MS-DRCMPSP is to achieve the rational allocation of multi-skilled resources and to arrange the starting time of project activities. However, in practice, skilled staff are usually the main resources and scarce resources, once such personnel take leave, it will not only lead to a decline in the availability of resources in the project execution process, but also lead to the destruction of the pre-established baseline scheduling plan. If not coordinated properly,  the staff leave will lead to project delays, as well as to cause serious losses to the management of the enterprise.

Aiming at the multi-skilled distributed resource-constrained multi-project scheduling problem (MS-DRCMPSP) in the case of staff leave, a dynamic reactive scheduling methodology is designed to study the problem. A three-stage decision-making model is established, which includes initial local scheduling, global coordination decision-making and repair scheduling. The initial local scheduling model and the global coordination decision-making model are used to formulate the initial baseline scheduling plan, and the repair scheduling model is constructed based on the manager's decision-making preference for activities and projects when the baseline scheduling plan is disrupted by the staff leave. When the baseline scheduling plan is damaged due to staff leave, the repair scheduling model is constructed based on the manager's preferences for activities and projects, and the repair scheduling plan is developed by designing a "dynamic" strategy that includes "wait" and "adjust" strategies. Considering that the scale of the problem affects the difficulty of coordinating the global resource conflict, we design coordination mechanisms to adapt to different problem scales: for small-scale instances, we design a conflict activity-based ranking mechanism; for large-scale instances, we design a conflict activity-based Softmax scoring mechanism that takes into account the characteristics of the activities that are affected by the staff leave. The Softmax scoring mechanism includes a series of evaluation factors: activity duration, slack time, resource demand, and several immediate activities.

Based on the RANGEN and MSPLIB adaptations, we obtain examples of multi-skilled scheduling problems of different scales, and then conduct a study, which shows that:

(1)  The results of decision piece good analysis

(a) For small-scale instances, the "dynamic" strategy can be adopted when the preference is based on the deviation of the activity start time; the "adjust" or "dynamic" strategy can be adopted when the decision preference is based on the deviation of the average project extension, and when the rehabilitation objectives of both projects and activities are considered together. For large-scale instances, the "adjust" or "dynamic" strategy can be used for both increasing demand and supply of resources when considering the rehabilitation objectives of both projects and activities.

(b) For large-scale instances, when considering one aspect of decision preference alone, the "adjust" strategy is more suitable; when considering both activity and project restoration goals, the "dynamic" strategy can be used directly to develop restoration scheduling plans, showing that the "adjust" and "dynamic" strategies are more suitable for the large-scale instances.

(2) The results of algorithm comparison

The optimisation algorithms designed for different scaled instances are better than the other 8 restoration algorithms compared, and the two mechanisms are compared under the same scale (e.g., large-scale instances). In addition, comparing the two mechanisms for the same scale (e.g., large-scale instances), it is found that the repair algorithm based on the Softmax scoring mechanism of conflicting activities is better than the sequential game algorithm. The optimisation result can be improved by a maximum of 18.29%, which has no advantage over the heuristic algorithm LST, and it is only lower than 1.87%. However, the Softmax method can be improved by a maximum of 8.89% compared with the other six heuristic algorithms.



This paper makes up for the vacancy of the multi-skilled scheduling problem in the distributed decision-making environment, especially in the case of uncertain resource availability. In addition, it provides a suitable repaired strategy for managers' different preferences and the related reference for subsequent relevant literature.