Preemptive scheduling with variable profile, precedence constraints and due dates

This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an earliest due date first algorithm provides an optimal nonpreemptive schedule for unit execution time tasks, then the preemptive priority scheduling algorithm, referred to as smallest laxity first, provides an optimal preemptive schedule for real-execution-time tasks. When the objective is to minimize the makespan, we get the same kind of result between highest level first schedules solving nonpremptive tasks with unit execution time and the longest remaining path first schedule for the corresponding preemptive scheduling problem with real-execution-time tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained

Multi-project scheduling with 2-stage decomposition

A non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources is considered. A 2-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. At stage one, each project is reduced to a macro-activity with macro-modes resulting in a single project network where the objective is the maximization of the net present value and the cash flows are positive. For setting the time horizon three different methods are developed and tested. A genetic algorithm approach is designed for this problem, which is also employed to generate a starting solution for the exact solution procedure. Using the starting times and the resource profiles obtained in stage one each project is scheduled at stage two for minimum makespan. The result of the first stage is subjected to a post-processing procedure to distribute the remaining resource capacities. Three new test problem sets are generated with 81, 84 and 27 problems each and three different configurations of solution procedures are tested

Railway scheduling reduces the expected project makespan.

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.Railway scheduling; Roadrunner scheduling; Feeding buffer; Priority list; Resource availability;

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations.

We present an optimal procedure for the resource-constrained project scheduling problem (RCPSP) with generalized precedence relations (further denoted as RCPSP-GPR) with the objective of minimizing the project makespan. The RCPSP-GPR extends the RCPSP to arbitrary minimal and maximal time lags between the starting and completion times of activities. The procedure is a depth-first branch-and-bound algorithm in which the nodes in the search tree represent the original project network extended with extra precedence relations which resolve a resource conflict present in the parent node. Resource conflicts are resolved using the concept of minimal delaying alternatives, i.e. minimal sets of activities which, when delayed, release enough resources to resolve the conflict. Precedence and resource-based lower bounds as well as dominance rules are used to fathom large portions of the search tree. The procedure can be extended to other regular measures of performance by some minor modifications. Even non-regular measures of performance, such as the maximinization of the net present value of the project or resource levelling objectives, can be handled. The procedure has been programmed in Microsoft* Visual C++ for use on a personal computer. Extensive computational experience is obtained.Scheduling;

Beyond C<i>max</i>: an optimization-oriented framework for constraint-based scheduling

This paper presents a framework taking advantage of both the flexibility of constraint programming and the efficiency of operations research algorithms for solving scheduling problems under various objectives and constraints. Built upon a constraint programming engine, the framework allows the use of scheduling global constraints, and it offers, in addition, a modular and simplified way to perform optimality reasoning based on well-known scheduling relaxations. We present a first instantiation on the single machine problem with release dates and lateness minimization. Beyond the simplicity of use, the ptimizationoriented framework appears to be, from the experiments, effective for dealing with such a pure problem even without any ad-hoc heuristics

Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

A graph based process model measurement framework using scheduling theory

Software development processes, as a means of ensuring software quality and productivity, have been widely accepted within the software development community; software process modeling, on the other hand, continues to be a subject of interest in the research community. Even with organizations that have achieved higher SEI maturity levels, processes are by and large described in documents and reinforced as guidelines or laws governing software development activities. The lack of industry-wide adaptation of software process modeling as part of development activities can be attributed to two major reasons: lack of forecast power in the (software) process modeling and lack of integration mechanism for the described process to seamlessly interact with daily development activities. This dissertation describes a research through which a framework has been established where processes can be manipulated, measured, and dynamically modified by interacting with project management techniques and activities in an integrated process modeling environment, thus closing the gap between process modeling and software development. In this research, processes are described using directed graphs, similar to the techniques with CPM. This way, the graphs can be manipulated visually while the properties of the graphs-can be used to check their validity. The partial ordering and the precedence relationship of the tasks in the graphs are similar to the one studied in other researches [Delcambre94] [Mills96]. Measurements of the effectiveness of the processes are added in this research. These measurements provide bases for the judgment when manipulating the graphs to produce or modify a process. Software development can be considered as activities related to three sets: a set of tasks (τ), a set of resources (ρ), and a set of constraints (y). The process, P, is then a function of all the sets interacting with each other: P = {τ, ρ, y). The interactions of these sets can be described in terms of different machine models using scheduling theory. While trying to produce an optimal solution satisfying a set of prescribed conditions using the analytical method would lead to a practically non-feasible formulation, many heuristic algorithms in scheduling theory combined with manual manipulation of the tasks can help to produce a reasonable good process, the effectiveness of which is reflected through a set of measurement criteria, in particular, the make-span, the float, and the bottlenecks. Through an integrated process modeling environment, these measurements can be obtained in real time, thus providing a feedback loop during the process execution. This feedback loop is essential for risk management and control