Christoph Schwindt

Project Scheduling with Time Windows and Scarce Resources

1 Temporal Project Scheduling.- 1.1 Minimum and maximum time lags.- 1.2 Activity-on-node project networks.- 1.3 Temporal project scheduling computations.- 1.4 Orders in the set of activities.- 2 Resource-Constrained Project Scheduling - Minimization of Project Duration.- 2.1 Formulation of the problem.- 2.2 Cycle structures in activity-on-node project networks.- 2.3 Properties of the feasible region.- 2.3.1 Strict orders and order polyhedra.- 2.3.2 Forbidden sets and resolution of resource conflicts.- 2.4 Different types of shifts and sets of schedules.- 2.5 Branch-and-bound and truncated branch-and-bound methods.- 2.5.1 Enumeration scheme.- 2.5.2 Preprocessing.- 2.5.3 Lower bounds.- 2.5.4 Branch-and-bound algorithm.- 2.5.5 Truncated branch-and-bound methods.- 2.5.6 Alternative enumeration schemes.- 2.5.7 Alternative preprocessing and constraint propagation.- 2.5.8 Alternative lower bounds.- 2.6 Priority-rule methods.- 2.6.1 Direct method.- 2.6.2 Decomposition methods.- 2.6.3 Priority rules.- 2.6.4 Serial generation scheme.- 2.6.5 Parallel generation scheme.- 2.7 Schedule-improvement procedures.- 2.7.1 Genetic algorithm.- 2.7.2 Tabu search.- 2.8 Experimental performance analysis.- 2.8.1 Random generation of projects.- 2.8.2 Computational experience.- 2.9 Application to make-to-order production in manufacturing industry.- 2.10 Regular objective functions different from project duration.- 2.11 Calendarization.- 2.12 Project scheduling with cumulative resources.- 2.12.1 Discrete cumulative resources.- 2.12.2 Continuous cumulative resources.- 2.13 Project scheduling with synchronizing resources.- 2.14 Project scheduling with sequence-dependent changeover times.- 2.15 Multi-mode project scheduling problems.- 2.15.1 Problem formulation and basic properties.- 2.15.2 Solution methods.- 2.16 Application to batch production in process industries.- 2.16.1 Case study.- 2.16.2 Batching problem.- 2.16.3 Project scheduling model for batch scheduling.- 2.16.4 Solution procedure for batch scheduling.- 3 Resource-Constrained Project Scheduling - Minimization of General Objective Functions.- 3.1 Different objective functions.- 3.2 Additional types of shifts and sets of schedules.- 3.3 Classification of objective functions.- 3.3.1 Separable and resource-utilization dependent objective functions.- 3.3.2 Class 1 of regular objective functions.- 3.3.3 Class 2 of antiregular objective functions.- 3.3.4 Class 3 of convex objective functions.- 3.3.5 Class 4 of binary-monotone objective functions.- 3.3.6 Class 5 of quasiconcave objective functions.- 3.3.7 Class 6 of locally regular objective functions.- 3.3.8 Class 7 of locally quasiconcave objective functions.- 3.4 Time complexity of time-constrained project scheduling.- 3.5 Relaxation-based approach for function classes 1 to 5.- 3.5.1 General enumeration scheme.- 3.5.2 Branch-and-bound algorithm for the net present value problem.- 3.5.3 Branch-and-bound algorithm for the earliness-tardiness problem.- 3.6 Tree-based approach for function classes 6 and 7.- 3.6.1 General enumeration scheme.- 3.6.2 Branch-and-bound algorithms for resource investment, resource levelling, and resource renting problems.- 3.6.3 Experimental performance analysis.- 3.6.4 Alternative lower bounds.- 3.7 Priority-rule methods.- 3.7.1 Time-constrained project scheduling.- 3.7.2 Resource-constrained project scheduling.- 3.7.3 Experimental performance analysis.- 3.8 Schedule-improvement procedures.- 3.8.1 Neighborhoods for project scheduling problems.- 3.8.2 A tabu search procedure.- 3.9 Application to investment projects.- 3.9.1 Computation of the net present value function.- 3.9.2 Decision support.- 3.10 Hierarchical project planning.- References.- List of Symbols.- Three-Field Classification for Resource-Constrained Project Scheduling.

Benchmark instances for project scheduling problems

With the development of project scheduling models and methods arose the need for data instances in order to benchmark the solution procedures. Generally, benchmark instances can be distinguished by their origin into real world problems and artificial problems. The analysis of algorithmic performance on real world problem instances is of a high practical relevance, but at the same time it is only an analysis of individual cases. Consequently, general conclusions about the algorithms cannot be drawn. A solution procedure which shows very good performance on one real world instance might produce poor results on another. In order to allow a systematic evaluation of the performance of algorithms, characteristics of the projects have to be identified. The characteristics can then serve as the parameters for the systematic generation of artificial instances. The variation of the levels of these problem parameters in a full factorial design study allows to produce a set of well-balanced instances (cf. Montgomery 1976).

Advanced production scheduling for batch plants in process industries

Abstract. An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.

Truncated branch-and-bound, schedule-construction, and schedule-improvement procedures for resource-constrained project scheduling

Abstract. We present heuristic procedures for approximately solving large project scheduling problems with general temporal and resource constraints. In particular, we propose several truncated branch-and-bound techniques, priority-rule methods, and schedule-improvement procedures of types tabu search and genetic algorithm. A detailed experimental performance analysis compares the different heuristics devised and shows that large problem instances with up to 1000 activities and several resources can efficiently be solved with sufficient accuracy.

Batch scheduling in process industries: an application of resource–constrained project scheduling

Abstract. The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time.Zusammenfassung. Die Arbeit behandelt Batch–Scheduling–Probleme in der Prozeßindustrie. In mehreren aufeinanderfolgenden chemischen oder physikalischen Transformationsschritten werden aus Rohstoffen auf Mehrzweckanlagen Endprodukte hergestellt. Wird die Anlage im Batch–Modus betrieben, so werden die Gesamtbedarfe an Zwischen- und Endprodukten in Chargen unterteilt. Der Produktionsbeginn einer Charge auf einer Stufe erfordert die Verfügbarkeit aller Eingangsstoffe. Wir betrachten das Problem der Ablaufplanung für die Chargenproduktion mit dem Ziel der Zykluszeitminimierung. Nebenbedingungen wie zeitliche Mindest- und Höchstabstände zwischen aufeinanderfolgenden Produktionsstufen, reihenfolgeabhängige Umrüstzeiten von Betriebsmitteln, kapazitiv begrenzte Zwischenlager, Produktionspausen und die zeitlich schwankende Personalverfügbarkeit tragen zur Komplexität dieses Problems bei. Wir schlagen einen neuen Lösungsansatz auf der Grundlage von Modellen und Methoden der ressourcenbeschränkten Projektplanung vor, mit dessen Hilfe Probleminstanzen industrieller Größe in angemessener Rechenzeit näherungsweise gelöst werden können.

Project scheduling with inventory constraints

Abstract. Inventory constraints refer to so-called cumulative resources, which can store a single or several different products and have a prescribed minimum and maximum inventory, where the inventory is depleted and replenished over time. Some additional applications of cumulative resources, e.g. to investment projects, are also discussed in this paper. We study some properties of the feasible region of the project scheduling problem with inventory constraints and general temporal constraints and especially show how to resolve so-called resource conflicts. The feasible region represents the intersection of a union of polyhedral cones with the polyhedron of time-feasible solutions. These results can be exploited for constructing an efficient branch-and-bound algorithm which enumerates alternatives to avoid stock shortage and surplus by introducing precedence constraints between disjoint sets of events. Finally, we sketch how the procedure can be truncated to a filtered beam search heuristic. An experimental performance analysis shows that problem instances with 100 events and five cumulative resources can be solved in less than one minute.

Activity-on-node networks with minimal and maximal time lags and their application to make-to-order production

Maximal time lags between activities of a project play an important role in practice in addition to minimal ones. However, maximal time lags have been discussed very rarely in literature thus far. This paper shows how to model projects with minimal and maximal time lags by cyclic activity-on-node networks. As an important application, the production process for make-to-order production with limited resources is studied, which can be represented by a multi-project network where the individual operations of the jobs correspond to the nodes of the network. For different product structures, careful consideration is given to the modelling of a nondelay performance of overlapping operations by appropriately establishing minimal and maximal time lags.ZusammenfassungZeitliche Maximalabstände zwischen den Vorgängen eines Projektes spielen neben zeitlichen Minimalabständen in der Praxis eine wesentliche Rolle. Bis heute sind zeitliche Maximalabstände jedoch in der Literatur kaum behandelt worden. Die vorliegende Arbeit zeigt, wie Projekte mit zeitlichen Minimal- und Maximalabständen als zyklische Vorgangsknotennetzwerke modelliert werden können. Als wichtige Anwendung wird der Produktionsprozeß in der Auftragsfertigung mit Kapazitätsbeschränkungen behandelt, der als Multi-Projekt-Netzwerk dargestellt werden kann, wobei die einzelnen Arbeitsgänge den Knoten des Netzwerks entsprechen. Für verschiedene Produktionsstrukturen wird die Modellierung einer unterbrechungsfreien offenen Fertigung durch die Bestimmung geeigneter zeitlicher Minimal- und Maximalabstände beschrieben.

Scheduling of continuous and discontinuous material flows with intermediate storage restrictions

This paper deals with scheduling batch (i.e., discontinuous), continuous, and semicontinuous production in process industries (e.g., chemical, pharmaceutical, or metal casting industries) where intermediate storage facilities and renewable resources (processing units and manpower) of limited capacity have to be observed. First, different storage configurations typical of process industries are discussed. Second, a basic scheduling problem covering the three above production modes is presented. Third, (exact and truncated) branch-and-bound methods for the basic scheduling problem and the special case of batch scheduling are proposed and subjected to an experimental performance analysis. The solution approach presented is flexible and in principle simple, and it can (approximately) solve relatively large problem instances with sufficient accuracy.

Project scheduling with calendars

Abstract. For many applications of project scheduling to real-life problems, it is necessary to take into account calendars specifying time intervals during which some resources such as manpower or machines are not available. Whereas the execution of certain activities like packaging may be suspended during breaks, other activities cannot be interrupted due to technical reasons. Minimum and maximum time lags between activities may depend on calendars, too. In this paper, we address the problem of scheduling the activities of a project subject to calendar constraints. We devise efficient algorithms for computing earliest and latest start and completion times of activities. Moreover, we sketch how to use these algorithms for developing priority-rule methods coping with renewable-resource constraints and calendars.

A steepest ascent approach to maximizing the net present value of projects

Abstract. We study the scheduling of projects subject to general temporal constraints between activities such that the project net present value is maximized. The proposed algorithm is based on a first-order steepest ascent approach, where the steepest ascent directions are normalized by the supremum norm. In each iteration, the procedure ascends from a vertex of the feasible region to some non-adjacent vertex, which leads to a considerable speed-up compared to standard line-search. In an experimental performance analysis, we compare previous solution methods from literature to the algorithm presented in this paper. On the basis of two randomly generated test sets, the efficiency of the steepest ascent approach is demonstrated. Problem instances with up to 1000 activities can be solved in less than one second on a personal computer.