Project scheduling under undertainty – survey and research potentials.

The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;

Universal Sequencing on an Unreliable Machine

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. Our objective is to minimize ∑ wjf(Cj) for any nondecreasing, nonnegative, differentiable cost function f(Cj). We aim for a universal solution that performs well without adaptation for all cost functions for any possible machine behavior. We design a deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the machine behavior in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both performance guarantees are best possible for any unbounded cost function. Our algorithms can be adapted to run in polynomial time with slightly increased cost. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n / log log n) worse than an optimal sequence for any unbounded cost function. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a nontrivial algorithm with a small constant performance guarantee

Parallel machine scheduling subject to machine availability constraints

Cataloged from PDF version of article.Within a planning horizon, machines may become unavailable due to unexpected breakdowns or pre-scheduled activities. A realistic approach in constructing the production schedule should explicitly take into account such periods of unavailability. This study addresses the parallel machine-scheduling problem subject to availability constraints on each machine. The objectives of minimizing the total completion time and minimizing the maximum completion time are studied. The problems with both objectives are known to be NP-hard. We develop an exact branch-and-bound procedure and propose three heuristic algorithms for the total completion time problem. Similarly, we propose exact and approximation algorithms also for the maximum completion time problem. All proposed algorithms are tested through extensive computational experimentation, and several insights are provided based on computational results.Sevindik, KayaM.S

Universal Sequencing on a Single Machine

We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee. © 2010 Springer-Verlag

Minimising total flow-time on two parallel machines with planned downtimes and resumable jobs

This study considers the flow-time minimisation problem on two identical parallel machines, where the machines are subject to planned downtimes. Jobs that are interrupted due to machine downtimes may resume processing once the machine becomes available without incurring additional costs or setup times. We identify optimality properties, develop upper and lower bounding procedures, and present a branch and bound methodology based on the proposed properties and bounds. The computational efficiency is tested on problem instances with up to 35 jobs

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

Approximate Algorithms for the Combined arrival-Departure Aircraft Sequencing and Reactive Scheduling Problems on Multiple Runways

The problem addressed in this dissertation is the Aircraft Sequencing Problem (ASP) in which a schedule must be developed to determine the assignment of each aircraft to a runway, the appropriate sequence of aircraft on each runway, and their departing or landing times. The dissertation examines the ASP over multiple runways, under mixed mode operations with the objective of minimizing the total weighted tardiness of aircraft landings and departures simultaneously. To prevent the dangers associated with wake-vortex effects, separation times enforced by Aviation Administrations (e.g., FAA) are considered, adding another level of complexity given that such times are sequence-dependent. Due to the problem being NP-hard, it is computationally difficult to solve large scale instances in a reasonable amount of time. Therefore, three greedy algorithms, namely the Adapted Apparent Tardiness Cost with Separation and Ready Times (AATCSR), the Earliest Ready Time (ERT) and the Fast Priority Index (FPI) are proposed. Moreover, metaheuristics including Simulated Annealing (SA) and the Metaheuristic for Randomized Priority Search (Meta-RaPS) are introduced to improve solutions initially constructed by the proposed greedy algorithms. The performance (solution quality and computational time) of the various algorithms is compared to the optimal solutions and to each other. The dissertation also addresses the Aircraft Reactive Scheduling Problem (ARSP) as air traffic systems frequently encounter various disruptions due to unexpected events such as inclement weather, aircraft failures or personnel shortages rendering the initial plan suboptimal or even obsolete in some cases. This research considers disruptions including the arrival of new aircraft, flight cancellations and aircraft delays. ARSP is formulated as a multi-objective optimization problem in which both the schedule\u27s quality and stability are of interest. The objectives consist of the total weighted start times (solution quality), total weighted start time deviation, and total weighted runway deviation (instability measures). Repair and complete regeneration approximate algorithms are developed for each type of disruptive events. The algorithms are tested against difficult benchmark problems and the solutions are compared to optimal solutions in terms of solution quality, schedule stability and computational time

Predictive/reactive scheduling with controllable processing times and earliness-tardiness penalties

In this study, a machine scheduling problem with controllable processing times in a parallel-machine environment is considered. The objectives are the minimization of manufacturing cost, which is a convex function of processing time, and total weighted earliness and tardiness. It is assumed that parts have job-dependent earliness and tardiness penalties and distinct due dates, and idle time is allowed. The problem is formulated as a time-indexed integer programming model with discrete processing time alternatives for each part. A linear-relaxation-based algorithm is used to assign the parts to the machines and to find a sequence on each machine. A non-linear programming model is proposed to find the optimal starting and processing times of the parts for a given sequence. The proposed non-linear programming model is converted to a minimum-cost network flow model by piecewise linearization of the convex manufacturing cost in the objective function. The proposed method is used to find initial schedules in predictive scheduling. The proposed models are revised to incorporate a stability measure for reacting to unexpected disruptions such as machine breakdown, arrival of a new job, delay in the arrival or the shortage of materials in reactive scheduling

Platooning-based control techniques in transportation and logistic

This thesis explores the integration of autonomous vehicle technology with smart manufacturing systems. At first, essential control methods for autonomous vehicles, including Linear Matrix Inequalities (LMIs), Linear Quadratic Regulation (LQR)/Linear Quadratic Tracking (LQT), PID controllers, and dynamic control logic via flowcharts, are examined. These techniques are adapted for platooning to enhance coordination, safety, and efficiency within vehicle fleets, and various scenarios are analyzed to confirm their effectiveness in achieving predetermined performance goals such as inter-vehicle distance and fuel consumption. A first approach on simplified hardware, yet realistic to model the vehicle's behavior, is treated to further prove the theoretical results. Subsequently, performance improvement in smart manufacturing systems (SMS) is treated. The focus is placed on offline and online scheduling techniques exploiting Mixed Integer Linear Programming (MILP) to model the shop floor and Model Predictive Control (MPC) to adapt scheduling to unforeseen events, in order to understand how optimization algorithms and decision-making frameworks can transform resource allocation and production processes, ultimately improving manufacturing efficiency. In the final part of the work, platooning techniques are employed within SMS. Autonomous Guided Vehicles (AGVs) are reimagined as autonomous vehicles, grouping them within platoon formations according to different criteria, and controlled to avoid collisions while carrying out production orders. This strategic integration applies platooning principles to transform AGV logistics within the SMS. The impact of AGV platooning on key performance metrics, such as makespan, is devised, providing insights into optimizing manufacturing processes. Throughout this work, various research fields are examined, with intersecting future technologies from precise control in autonomous vehicles to the coordination of manufacturing resources. This thesis provides a comprehensive view of how optimization and automation can reshape efficiency and productivity not only in the domain of autonomous vehicles but also in manufacturing