Frank Salewski

ProGen/πx – An instance generator for resource-constrained project scheduling problems with partially renewable resources and further extensions

Abstract Project scheduling has long been an area of intensive research, but until recently most efforts have been dedicated to developing solution procedures and generalizing models, with little work done on generating problem instances. Additionally, if labor time regulations have to be taken into consideration, the classical resource-constrained project scheduling problem (RCPSP) cannot be used for many problems in manpower scheduling. This paper introduces several extensions to the RCPSP aimed at modeling such problems, and a problem instance generator based on the project generator ProGen incorporating these extensions. Thus, it becomes possible to thoroughly test solution procedures for, e.g., audit-staff scheduling, crew scheduling and timetabling problems. Preliminary computational results are given that were obtained with a greedy randomized solution method using priority rules specifically tailored to the generalized model.

Project scheduling under resource and mode identity constraints: Model, complexity, methods, and application

Abstract A recurring problem in project management involves the allocation of scarce resources to the individual jobs comprising the project. In many situations such as audit-staff scheduling, timetabling, and course scheduling, the resources correspond to individuals (skilled labour). This naturally leads to an assignment-type project scheduling problem, i.e. a project has to be performed by assigning one or more of several individuals (resources) to each job. In this paper we consider the nonpreemptive variant of a resource-constrained project scheduling problem with mode identity. Mode identity refers to a generalization of the multi-mode case where the set of all jobs is partitioned into disjoint subsets while all jobs forming one subset have to be processed in the same mode. Both time and cost incurred by processing a subset of jobs depend on the resources assigned to it. This problem is a substantial and nontrivial generalization of the well-known multi-mode case. Regarding precedence and temporal relations as well as release dates and deadlines, the question arises to which jobs resources should be assigned in order to minimize overall costs. For solving this time-resource-cost-tradeoff problem we present a tailored parallel randomized solution approach called ramses into which both static and dynamic priority rules can be incorporated. The results of an extensive computational study on a practical application from the field of audit-staff scheduling indicate that ramses is capable of producing “good” solutions in neglectable amounts of time.

Distribution requirements and compactness constraints in school timetabling

This paper provides the following contributions: First, distribution requirements for lessons of different lengths are modelled in a novel way by the use of the so-called multiple mode concept with mode identity constraints. Second, we show that several types of constraints may be modelled using the unifying framework of partially renewable resources. Among these constraints are: No class, subject, room, and teacher overlaps; class, subject, room, and teacher unavailabilities; compactness constraints; preassignment constraints; lectures to be given simultaneously; lunch breaks, etc. Third, we present two-phase parallel greedy randomized and genetic methods. Fourth, we provide an instance generator for the generation of a representative set of instances. Fifth, the generator along with a statistical model is used for a thorough experimental evaluation of the methods. Computational results show that the methods solve the instances investigated close to optimality.

New Modelling Concepts and Their Impact on Resource-Constrained Project Scheduling

A recurring problem in project management involves the allocation of scarce resources to the individual activities comprising the project. In many situations such as audit-staff scheduling or timetabling, the resources correspond to individuals (skilled labour). This naturally leads to an assignment-type project scheduling problem, i.e. a project has to be performed by assigning one or more of several individuals (resources) to each activity.

Audit-Staff Scheduling by Column Generation

When scheduling its audit-staff, the management of an auditing firm encompasses a number of decisions. These may be grouped into several categories which differ markedly in terms of organizational echelon involved, length of the planning horizon and the planning periods, degree of aggregation of the audit tasks, degree of detail of the required information, and decision objective. However, traditional audit-staff scheduling models (Balachandran and Zoltners 1981, Chan and Dodin 1986, Gardner et al. 1990, Dodin and Chan 1991, Drexl 1991, Dodin and Elimam 1997, Dodin et al. 1998, Brucker and Schumacher 1999, Rolland et al. 2005) are single-level models which try to construct a direct assignment of auditors to tasks and periods. To facilitate algorithmic treatment, all these models are more or less gross simplifications of practical planning situations.

Prüffeldorientierte Zuordnung von Prüfern für die operative Personaleinsatzplanung in Wirtschaftsprüfungsgesellschaften

ZusammenfassungBasierend auf den Ergebnissen einer empirischen Untersuchung wurde ein hierarchischer Ansatz zur Personaleinsatzplanung in Wirtschaftsprüfungsgesellschaften entwickelt, der die Teilprobleme der taktischen, der taktisch-operativen und der operativen Planung umfaßt. Der vorliegende Beitrag setzt sich mit der operativen Planung auseinander. Das Problem wird zunächst als binäres Optimierungsproblem formuliert. Anschließend wird ein speziell an die Problemstruktur angepaßtes heuristisches Verfahrensschema vorgestellt, das unter Verwendung von Prioritätswerten randomisierte Auswahlentscheidungen trifft. Die Eignung des Verfahrensschemas wird in einer umfangreichen experimentellen Untersuchung nachgewiesen.AbstractBased upon an empirical survey, an hierarchical framework for audit-staff scheduling has been developed which distinguishes between a tactical, a tacticaloperational and an operational level. In our paper we investigate the operational level. A binary optimization model is formulated, which adequately represents the problem. Afterwards, a randomized heuristic scheme specifically tailored to the problem structure is described which uses priority values to base randomized selection decisions upon. Its suitability is demonstrated in an extensive computational study.

Audit-Staff Scheduling: An Hierarchical Approach

Traditional audit-staff scheduling models are single-level models which try to construct a direct assignment of auditors to audit tasks and periods. By contrast, an empirical investigation among 200 of the biggest audit companies in Germany shows that the process of audit-staff scheduling usually is divided into three different levels [3]. While the names of these levels, viz. medium-term, medium-to-short Herrn, and short-term planning, refer to their differing planning horizons, also clear distinctions can be made in terms of organizational echelon involved, length of planning periods, degree of aggregation of the audit tasks, degree of detail of the required information, and decision objectives. Furthermore, the results of a more aggregated level are used as input to a more disaggregated level.

Audit-Staff Scheduling: Methods for the Medium-to-Short-Term Level

The medium-to-short-term model is a component of an hierarchical approach with three levels, which is suitable to represent the problem of audit-staff scheduling from the user’s point of view [2]. The formulation of the model is based on the results of an empirical study conducted among 200 of the biggest German audit companies. The medium-to-short-term planning disaggregates the results of the first level, the medium-term planning, for one week and all auditors [1]. The outcome is a schedule that specifies for each auditor — on the basis of periods of four hours — all the phases in which the auditor is involved in the considered week. The objective function minimizes the total costs of the resulting schedule.

Audit-Staff Scheduling: Methods for the Medium-Term Level

A survey conducted among 200 of the biggest German CPA firms shows that the process of audit-staff scheduling is usually divided into three distinct levels [1]. The first of these levels, the medium-term planning [2], assigns teams of auditors to audit engagements; then it constructs a schedule covering all the engagements’ phases, e.g. preliminary, intermediate, and final audit, and determines the workload per auditor and week — on the basis of forty-hours-periods — over a planning horizon of between three and twelve months.

Audit-Staff Scheduling: Methods for the Short-Term Level

A survey conducted among 200 of the biggest German CPA firms indicates that the process of audit-staff scheduling is usually divided into three different levels, viz. medium-term, medium-to-short-term, and short-term planning [2]. This paper addresses the short-term planning level of the corresponding hierarchical approach. The short-term planning is based upon the results of the medium-to-short-term level for one week and one phase [1]. It assigns the auditors involved in auditing that phase in the considered week to the corresponding audit tasks and schedules them on the basis of periods of one hour. Decision objective is the balancing of the auditors’ workload.