The Resource-Constrained Project Scheduling Problem (RCPSP) is concerned with single-item or small batch production where limited resources have to be allocated to dependent activities over time. Over the past few decades, a lot of work has been made with the use of optimal solution procedures for this basic problem type and its extensions. Brucker and Knust[1] discuss, how timetabling problems...

For many problems in Scheduling and Timetabling the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using “supernodes”. In the definition of George and McIntyre [SIAM J. Numer. Anal. 15 (1978), no. 1, 90–...

Abstract The optimization of periodic timetables is an indispensable planning task in public transport. Although the event scheduling problem (PESP) provides elegant mathematical formulation timetabling that led to many insights for primal heuristics, it notoriously hard solve optimality. One reason standard mixed-integer linear programming formulations, relaxations are weak, and integer variab...

We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve minimum cost problems, as...

This paper considers a timetabling problem and describes a mathematical programming model for solving it. The proposed model combines both teacher assignment and course scheduling problems simultaneously, which causes the entire model to be more complex. However, we are able to solve the model for several randomly generated data sets of sizes comparable to that encountered in an institution. Th...

background operating room (or) planning involves the creation of a “master surgical schedule” in which surgeons are assigned to specific operating rooms (ors) on specific days of a week. the master schedule is typically one or two weeks long repeatable for several months. objectives the purpose of this study was to recommend using a mathematical program to generate a rotation in a way that the ...

This paper elaborates the different operations research methods used to solve container terminal operational decisions including terminal design, berth allocation, quay crane assignment, quay crane scheduling, container storage space allocation, container location assignment, retrieval, and premarshalling, as well as resource scheduling and terminal logistics in general. Solution methods includ...

Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixed-integer programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance is achieved by introducing an integer v...

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. T...