Seminario 21/12: Francisco Saldanha (University of Lisbon): Project Scheduling with Flexible Resources: Is there a good optimization model?
- Ponente: Francisco Saldanha,
- Fecha: 10/may/2021 - 12:00 horas
- Lugar: Seminarios online CIO: http://cio.edu.umh.es/seminariosonline/
A project scheduling problem is defined by a set of activities, their precedence relations, and the corresponding execution times. The goal is to sequence and schedule the activities so that some performance measure of interest is optimized. Often, specific resources that exist in a limited amount are required to execute the activities. This extension of the problem is called the Resource-Constrained Project Scheduling Problem (RCPSP). One assumption in the RCPSP is that each resource has one specific function. However, in many situations (e.g. when human resources are involved), a resource masters several skills and thus can contribute in different ways to the execution of an activity. This extension leads to the so-called multi-skill resource constrained project scheduling problem (MS-RCPSP). This is a problem emerging for instance in consulting companies that have to allocate multi-skilled teams to different projects. Software development companies also face this problem when people with different capabilities are to be combined in different teams to contribute to the development of several products. The organization of evaluation teams is another example in which one may face a MS-RCPSP. In this case, multi-skilled teams are to be organized to visit departments, organizations or institutions and write an assessment report.
In the simplest setting of the MS-RCPSP, each activity requires several units of each skill. Additionally, each resource has several skills but can contribute with at most one skill-unit to each activity. Moreover, the allocation of each resource to some activity should last for the entire duration of the activity. The resources are assumed to be renewable, which means that after being used in some activity they can be assigned to another one (without overlap). The goal is to find a sequence and scheduling for the activities together with allocation of the resources to them so that the makespan is minimized.
In this seminar the state-of-the-art in the topic is discussed namely, the possibility of modeling mathematically this class of problems. Different modeling frameworks are discussed highlighting their advantages and disadvantages. In particular, the models are compared theoretically in terms of the linear programming relaxation since the use of such bounds is often the only way to assess the quality of heuristic solutions developed for the problem.