Sigrid Knust

A branch and bound algorithm for the resource-constrained project scheduling problem

A branch and bound algorithm is presented for the resource-constrained project scheduling problem (RCPSP). Given are n activities which have to be processed without preemptions. During the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited. Furthermore, finish–start precedence relations between the activities are given. The objective is to determine a schedule with minimal makespan. The branching scheme starts from a graph representing a set of conjunctions (the classical finish–start precedence constraints) and disjunctions (induced by the resource constraints). Then it either introduces disjunctive constraints between pairs of activities or places these activities in parallel. Concepts of immediate selection are developed in connection with this branching scheme. Immediate Selection allows to add conjunctions as well as further disjunctions and parallelity relations. Computational results based on the test data of Kolisch et al. (Kolisch, R., Sprecher, A., Drexl, A., 1995. Management Science 41, 1693–1703.) and Kolisch and Sprecher (Kolisch, R., Sprecher, A., 1997. PSPLIB – A project scheduling problem library, EJOR 96, pp. 205–216.) are reported.

Invited Review: Scheduling in sports: An annotated bibliography

Sports have worldwide appeal. Professional sport leagues involve significant investments in players. Events such as the Olympics Games, the Football World Cup and the major golf and tennis tournaments generate huge worldwide television audiences and many sports are multi-million dollar industries. A key aspect of sporting events is the ability to generate schedules that optimize logistic issues and that are seen as fair to all those who have an interest. This is not just restricted to generating the fixtures, but also to other areas such as assigning officials to the games in the competitions. This paper provides an annotated bibliography for sports scheduling articles. This area can be traced back over 40 years. It is noticeable that the number of papers has risen in recent years, demonstrating that scientific interest is increasing in this area.

A linear programming and constraint propagation-based lower bound for the RCPSP

Abstract A new destructive lower bound for the resource-constrained project scheduling problem (RCPSP) is presented. Given are n activities which have to be processed without preemptions. During the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited. Furthermore, finish–start precedence relations between the activities are given. The objective is to determine a schedule with minimal makespan. The lower bound calculations are based on two methods for proving infeasibility of a given threshold value T for the makespan. The first uses constraint propagation techniques, while the second is based on a linear programming formulation. A column generation procedure is presented for the linear programming formulation and computational results are reported for an algorithm combining both concepts.

Tabu Search Algorithms and Lower Bounds for the Resource-Constrained Project Scheduling Problem

We present two tabu search algorithms for the resource-constrained project scheduling problem. Given are n activities which have to be processed without preemptions. During the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited. Furthermore, finish-start precedence relations between the activities are given. The objective is to determine a schedule with minimal makespan. The first tabu search approach relies on elimination of critical arcs and list-scheduling techniques. The second neighborhood is based on schedule schemes, where neighbors are generated by placing activities in parallel or deleting a parallelity relation. Furthermore, a column-generation approach for a linear programming-based lower bound is presented and computational results are reported.

Makespan minimization for flow-shop problems with transportation times and a single robot

In a flow-shop problem with transportation times and a single robot n jobs consisting of m operations have to be processed in the same order on m machines. Additionally, transportation times are considered if a job changes from one machine to another. We assume that unlimited buffer space exists between the machines and all transportations have to be done by a single robot. The objective is to determine a feasible schedule with minimal makespan. New complexity results are derived for special cases where the processing or transportation times are constant values. Some of these may also be interpreted as new results for special cases of the classical 3-machine flow-shop F3||Cmax with constant processing times at certain stages.

Lower bounds for resource-constrained project scheduling problems

Abstract A destructive lower bound for the multi-mode resource-constrained project scheduling problem with minimal and maximal time-lags is presented. Given are n activities which may be processed in different modes without preemptions. During processing certain amounts of renewable and non-renewable resources are needed where the available capacity of each resource type is limited. Furthermore, minimal and maximal time-lags between the activities are given. The objective is to determine a schedule with minimal makespan. The lower bound calculations are based on two methods for proving infeasibility of a given threshold value T for the makespan. The first uses constraint propagation techniques, while the second is based on a linear programming formulation which is solved by a column generation procedure. Computational results are reported for several test instances of the multi-mode problem with and without time-lags and the single-mode version with time-lags.

Loading, unloading and premarshalling of stacks in storage areas: Survey and classification

Problems of loading, unloading and premarshalling of stacks as well as combinations thereof appear in several practical applications, e.g. container terminals, container ship stowage planning, tram depots or steel industry. Although these problems seem to be different at first sight, they hold plenty of similarities. To precisely unite all aspects, we suggest a classification scheme and show how problems existing in literature can be described with it. Furthermore, we give an overview of known complexity results and solution approaches.

List scheduling in a parallel machine environment with precedence constraints and setup times

We present complexity results which have influence on the strength of list scheduling in a parallel machine environment where additional precedence constraints and sequence-dependent setup times are given and the makespan has to be minimized. We show that contrary to various other scheduling problems, in this environment a set of dominant schedules cannot be calculated efficiently with list scheduling techniques.

Optimized load planning of trains in intermodal transportation

In this paper the problem of load planning for trains in intermodal container terminals is studied. The objective is to assign load units to wagons of a train such that the utilization of the train is maximized, and setup and transportation costs in the terminal are minimized. Contrary to previous approaches additionally weight restrictions for the wagons are integrated into our model. We present three different integer linear programming formulations and test them on some real-world instances. It is shown that even non-commercial MIP-solvers can solve our models to optimality in reasonable time.

Integrated production and distribution scheduling with lifespan constraints

We consider an integrated production and distribution scheduling problem in a make-to-order business scenario. A product with a short lifespan (e.g., perishable or seasonal) is produced at a single production facility with a limited production rate. This means that the product expires in a constant time after its production is finished. Orders are received from a set of geographically dispersed customers, where a demand for the product and a time window for the delivery is associated with each customer for the planning period. A single vehicle with non-negligible traveling times between the locations is responsible for the deliveries. Due to the limited production and distribution resources, possibly not all customers may be supplied within their time windows or the lifespan. The problem consists in finding a selection of customers to be supplied such that the total satisfied demand is maximized. We extend the work by Armstrong et al. (Annals of Operations Research 159(1):395–414, 2008) on the problem for fixed delivery sequences by pointing out an error in their branch and bound algorithm and presenting a corrected variant. Furthermore, we introduce model extensions for handling delays of the production start as well as for variable production and distribution sequences. Efficient heuristic solution algorithms and computational results for randomly generated instances are presented.