Many optimisation problems contain substructures involving constraints on sequences of decision variables. Such constraints can be very complex to express with mixed integer programming (MIP), while in constraint programming (CP), the global constraint regular easily represents this kind of substructure with deterministic finite automata (DFA). In this paper, we use DFAs and the associated laye...

In the planning stage, train operators design timetables to serve passenger trips and a circulation plan support these timetables. These designs consider not only operating costs but also convenience. this study, we developed an optimization model for new problem that focuses on timetabling train-unit scheduling while considering itinerary choices in schedule-based system. This minimizes travel...

Recently the XHSTT format for (High) School Timetabling was introduced, which provides a uniform way of modeling problem instances and corresponding solutions. The format supports a big variety of constraints, and currently 38 real-life instances from 11 di erent countries are available. Thereby the XHSTT format serves as a common ground for researchers within this area. This paper describes th...

The most complete form of academic timetabling problem is the population and course timetabling problem. In this problem, there may be multiple classes of each subject, and the decision on which students are to constitute each class is made in concert with the decision on the timetable for each class. In order to solve this problem, it is normally simplified or decomposed in some fashion. One s...

We show how to approximate in NC the problem of Scheduling Unrelated Parallel Machines, for a xed number of machines. We develop a (2 + ")-approximate parallel algorithm for the problem. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. T...

This paper presents a new mixed-integer goal programming (MIGP) model for a parallel machine scheduling problem with sequence-dependent setup times and release dates. Two objectives are considered in the model to minimize the total weighted flow time and the total weighted tardiness simultaneously. Due to the com-plexity of the above model and uncertainty involved in real-world scheduling probl...

Virtual power plant (VPP) is an effective approach to aggregate distributed generation resources under a central control. This paper introduces a mixed-integer linear programming model for optimal scheduling of the internal resources of a large scale VPP in order to maximize its profit. The proposed model studies the effect of a demand response (DR) program on the scheduling of the VPP. The pro...

This paper presents a novel, integer-linear programming (ILP) model for an identical parallel-machine scheduling problem with family setup times that minimizes the total weighted flow time (TWFT). Some researchers have addressed parallel-machine scheduling problems in the literature over the last three decades. However, the existing studies have been limited to the research of independent jobs,...