Resource-Constrained Project Scheduling

The subject of the book is project scheduling under resource-constraints. Several well-known scheduling problems, like e.g. the job-shop-scheduling and the assembly line balancing problem, are embedded in the mathematical programming formulation used. Exact solution procedures for a broad class of performance measures, i.e. objectives, are presented. Moreover, an algorithm for the generation of problem instances (ProGen) is described. The newcomer is introduced by illustrative examples into the field of scheduling and the expert is familarized with a powerful exact solution procedure for the multi-mode resource-constrained project scheduling problem. For the more general readership the main ideas of problem generation and computational tractability are of interest.

Within a project human and non-human resources are pulled together in a tempo raray organization in order to achieve a predefined goal (d. [20], p. 187). That is, in contrast to manufacturing management, project management is directed to an end. One major function of project management is the scheduling of the project. Project scheduling is the time-based arrangement of the activities comprising the project subject to precedence-, time-and resource-constraints (d. [4], p. 170). In the 1950's the standard methods MPM (Metra Potential Method) and CPM (Cri tical Path Method) were developed. Given deterministic durations and precedence constraints the minimum project length, time windows for the start times and critical paths can be calculated. At the same time another group of researchers developed the Program Evaluation and Review Technique (PERT) (d. [19], [73] and [90]). In contrast to MPM and CPM, random variables describe the activity durations. Based on the optimistic, most likely and pessimistic estimations of the activity durations an assumed Beta distribution is derived in order to calculate the distribution of the project duration, the critical events, the distribution of earliest and latest occurence of an event, the distribution of the slack of the events and the probability of exceeding a date. By the time the estimates of the distributions have been improved (d. e.g. [52] and [56]). Nevertheless, there are some points of critique concerning the estimation of the resulting distributions and probabilities (d. e.g. [48], [49] and [50]).

Contenu
1 The Model.- 1.1 Resource Categories.- 1.2 Problem Description.- 1.3 Critical Path Analysis.- 1.4 Mathematical Programming Formulation.- 2 Special Cases.- 2.1 Flow-Shop-Problem.- 2.2 Job-Shop-Problem.- 2.3 Open-Shop-Problem.- 2.4 Assembly Line Balancing.- 3 Variants and Extensions.- 3.1 Generalized Temporal Constraints.- 3.2 Resource Requirements Varying with Time.- 3.3 Further Regular Measures of Performance.- 4 Types of Schedules.- 4.1 Introduction.- 4.2 Definitions.- 4.3 Illustrations.- 5 A Branch and Bound Algorithm.- 5.1 The Precedence Tree.- 5.2 Minimizing the Projects Makespan.- 5.3 Optimizing any Regular Measure of Performance.- 5.4 Priority Rules and Heuristic Search Strategies.- 5.5 Acceleration Schemes.- 5.6 Limitations of the Branch and Bound Procedure.- 6 Generation of Instances by ProGen.- 6.1 Introduction.- 6.2 ProGen Specific Notation and Symbols.- 6.3 Project Generation.- 6.4 Resource Demand and Availability Generation.- 7 Computational Results.- 7.1 Exact Methods.- 7.2 Truncated Exact Methods.- 8 An Artificial Intelligence Approach.- 8.1 Model Reformulations.- 8.2 A PROLOG-Based Implementationll.- 8.3 Preliminary Computational Results.- 9 Applications.- 10 Conclusions.- List of Figures.- List of Tables.