Heuristic branch-and-price for building long term trainee schedules.

Branch-and-price is an increasingly important technique for solving large integer programming models. Staff scheduling has been a particularly fruitful area since these problems typically exhibit a decomposable structure. Beside computational efficiency branch-and-price produces two other important advantages in comparison with pure integer programming. Firstly, it often allows for a more accurate problem statement since many constraints which are hard to formulate in the integer program could be easily incorporated in the column generator. Secondly, a branch-and-price algorithm can easily be turned into an effective heuristic when optimality is no major concern. We illustrate these advantages for a medical trainee scheduling problem encountered at Oogziekenhuis Gasthuisberg Leuven and present some computational results together with implementation issues.Advantages; Area; Branch-and-price; Constraint; Efficiency; Heuristic; Integer programming; Model; Models; Problems; Research; Scheduling; Staff scheduling; Structure;

Models for robust resource allocation in project scheduling.

The vast majority of resource-constrained project scheduling efforts assumes complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. In reality, however, project activities are subject to considerable uncertainty which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects the makespan of a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed robust resource allocation problem in exact and approximate formulations. The procedure relies on constraint propagation during its search. We report on computational results obtained on a set of benchmark problems.Model; Resource allocation; Scheduling;

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

A branch-and-bound algorithm for stable scheduling in single-machine production systems.

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that will change little when variations in the input parameters arise. This paper proposes a branch-and-bound algorithm for optimally solving a single-machine scheduling problem with stability objective, when a single job is anticipated to be disrupted.Branch-and-bound; Construction; Event; Job; Robust scheduling; Robustness; Scheduling; Single-machine scheduling; Stability; Systems; Uncertainty;

Project scheduling with modular project completion on a bottleneck resource.

In this paper, we model a research-and-development project as consisting of several modules, with each module containing one or more activities. We examine how to schedule the activities of such a project in order to maximize the expected profit when the activities have a probability of failure and when an activity’s failure can cause its module and thereby the overall project to fail. A module succeeds when at least one of its constituent activities is successfully executed. All activities are scheduled on a scarce resource that is modeled as a single machine. We describe various policy classes, establish the relationship between the classes, develop exact algorithms to optimize over two different classes (one dynamic program and one branch-and-bound algorithm), and examine the computational performance of the algorithms on two randomly generated instance sets.Scheduling; Uncertainty; Research and development; Activity failures; Modular precedence network;