Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems

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

Preemptive models of scheduling with controllable processing times and of scheduling with imprecise computation: A review of solution approaches

This paper provides a review of recent results on scheduling with controllable processing times. The stress is on the methodological aspects that include parametric flow techniques and methods for solving mathematical programming problems with submodular constraints. We show that the use of these methodologies yields fast algorithms for solving problems on single machine or parallel machines, with either one or several objective functions. For a wide range of problems with controllable processing times we report algorithms with the running times which match those known for the corresponding problems with fixed processing times. As a by-product, we present the best possible algorithms for a number of problems on parallel machines that are traditionally studied within the body of research on scheduling with imprecise computation

A resource allocation mechanism based on cost function synthesis in complex systems

While the management of resources in computer systems can greatly impact the usefulness and integrity of the system, finding an optimal solution to the management problem is unfortunately NP hard. Adding to the complexity, today\u27s \u27modern\u27 systems - such as in multimedia, medical, and military systems - may be, and often are, comprised of interacting real and non-real-time components. In addition, these systems can be driven by a host of non-functional objectives – often differing not only in nature, importance, and form, but also in dimensional units and range, and themselves interacting in complex ways. We refer to systems exhibiting such characteristics as Complex Systems (CS). We present a method for handling the multiple non-functional system objectives in CS, by addressing decomposition, quantification, and evaluation issues. Our method will result in better allocations, improve objective satisfaction, improve the overall performance of the system, and reduce cost -in a global sense. Moreover, we consider the problem of formulating the cost of an allocation driven by system objectives. We start by discussing issues and relationships among global objectives, their decomposition, and cost functions for evaluation of system objective. Then, as an example of objective and cost function development, we introduce the concept of deadline balancing. Next, we proceed by proving the existence of combining models and their underlying conditions. Then, we describe a hierarchical model for system objective function synthesis. This synthesis is performed solely for the purpose of measuring the level of objective satisfaction in a proposed hardware to software allocation, not for design of individual software modules. Then, Examples are given to show how the model applies to actual multi-objective problems. In addition the concept of deadline balancing is extended to a new scheduling concept, namely Inter-Completion-Time Scheduling (ICTS. Finally, experiments based on simulation have been conducted to capture various properties of the synthesis approach as well as ICTS. A prototype implementation of the cost functions synthesis and evaluation environment is described, highlighting the applicability and usefulness of the synthesis in realistic applications

Simultaneous selection and scheduling with sequence-dependent setup times, lateness penalties, and machine availability constraint : heuristic approaches

Job selection and scheduling are among the most important decisions for production planning in today's manufacturing systems. However, the studies that take into account both problems together are scarce. Given that such problems are strongly NP-hard, this paper presents an approach based on two heuristic algorithms for simultaneous job selection and scheduling. The objective is to select a subset of jobs and schedule them in such a way that the total net profit is maximized. The cost components considered include jobs' processing costs and weighted earliness/tardiness penalties. Two heuristic algorithms; namely scatter search (SS) and simulated annealing (SA), were employed to solve the problem for single machine environments. The algorithms were applied to several examples of different sizes with sequence-dependent setup times. Computational results were compared in terms of quality of solutions and convergence speed. Both algorithms were found to be efficient in solving the problem. While SS could provide solutions with slightly higher quality for large size problems, SA could achieve solutions in a more reasonable computational tim

Re-scheduling in railways: the rolling stock balancing problem

This paper addresses the Rolling Stock Balancing Problem (RSBP). This problem arises at a passenger railway operator when the rolling stock has to be re-scheduled due to changing circumstances. These problems arise both in the planning process and during operations. The RSBP has as input a timetable and a rolling stock schedule where the allocation of the rolling stock among the stations does not fit to the allocation before and after the planning period. The problem is then to correct these off-balances, leading to a modified schedule that can be implemented in practice.For practical usage of solution approaches for the RSBP, it is important to solve the problem quickly. Therefore, the focus is on heuristic approaches. In this paper, we describe two heuristics and compare them with each other on some (variants of) real-life instances of NS, the main Dutch passenger railway operator. Finally, to get some insight in the quality of the proposed heuristics, we also compare their outcomes with optimal solutions obtained by solving existing rolling stock circulation models.heuristics;railway planning;integer linear programming;rolling stock re-scheduling

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe