Planning and Scheduling of Complex Operations: Models, Methods and Applications

Scheduling is about planning the timing of activities subject to scarce resources such as machines in order to fulfill an objective such as minimizing the flow time in the best possible way. Many scheduling problems in manufacturing and services are complex in the sense that there are precedence constraints enforcing minimum or maximum time lags between activities, more than one unit or type of scarce resource is required for processing an activity, capacity of resources is changing over time and complicated objective functions such as net present value have to be taken into account. The theory of resource-constrained project scheduling offers powerful modeling and solution techniques in order to address these kind of problems. The module empowers students to apply the main modeling and solutions concepts in order to successfully addressing real-world scheduling problems. The module is divided into four main parts which relate to different modelling concepts. Within each part the modelling concept, a linear programming formulations, heuristic and metaheuristic approaches as well as applications will be addressed. Next to its practical relevance, the module serves as a good starting point in order to undertake a master- thesis or a PhD-thesis. • Scheduling activities with general precedence constraints o Linear Program formulation o Network flow algorithms for scheduling activities with general precedence constraints: Label correcting algorithm and Floyd-Warshall algorithm o Applications • Scheduling activities with renewable resource constraints: The Resource-constrained project scheduling problem o Linear program formulations o Special cases o Heuristics and Metaheuristics o Applications • Scheduling activities with multiple modes, renewable and nonrenewable resource constraints: The Multi-mode resource-constrained project scheduling problem o Linear program formulation o Special cases o Heuristics and metaheuristics o Applications • Scheduling activities with renewable resource constraints and stochastic durations: The stochastic resource-constrained project scheduling problem o Heuristics and metaheuristics o Applications

Upon completion of the module students are empowered to analyze and optimize scheduling problems in services and manufacturing. In particular they 1) know the prevalent models and methods available in the literature. 2) They are capable of coding and implementing relevant algorithms. 3) They know how to model and solve linear programs in the field with off-the-shelf software. And 4) they understand and are able to present new approaches available in the scientific literature.

Grading of the module will be based on the following four assessments: 1) At the end of the module the students have to take an open book written test of 60 minutes length. Through the course students have to hand in two assignments and have to make a 15 minute presentation followed by a 5 minute discussion. Taking the test the students show that they have understood the problems, models, methods and applications treated in the module. By undertaking the two assignments students demonstrate that they have acquired the capability of i) coding and implementing a scheduling approach by using a computer programming language (first assignment), and ii) implementing a scheduling optimization model by using a modelling language and a solver (second assignment). With the presentation students showcase their understanding and capability of presenting a scheduling application from the scientific literature so far not treated in the module. The assessments are weighted with 50% (test), 15% (coding assignment), 20% (optimization assignment) and 15% (presentation).

Students should have knowledge in the mandatory undergraduate courses Mathematics (Linear Algebra), Statistics (probabilities, distributions), Management Science or Operations Research (Linear and Integer Programming), Production and Logistics or Operations Management, Programming, as well as a course in modelling and simulation such as in the elective undergraduate course “Modelling, Optimization and Simulation”.

The topics will be treated based on book chapters and papers in the scientific journals. Students are advised to prepare for the lecture by reading these material ahead of class. The content will be presented by the lecturer and discussed with the students. Then, students have to prepare applications of the approaches by solving small cases which will be discussed afterwards. The cases will be helping students to understand the problems addressed and the solution approaches provided. In order to empower students to implement the approaches in practice students will undertake two assignments. In the first assignment students implement an approach (exact procedure or heuristic) by using a programming language such as JAVA. In the second assignment students implement a linear programming model with the modelling language OPL and the solver CPLEX. The assignments will be provided at the beginning of the course giving students some time in order to undertake them . During the time of working at the assignments students can consult the teaching assistant in the exercise for help. In order to empower students to address problems not treated in class, students have to select and present a problem and an associated solution approach from the literature in class.