Nicole Megow

Optimizing the landside operation of a container terminal

This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three-stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short-term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most 8% above a lower bound on optimal RMG utilization.

On-line scheduling to minimize average completion time revisited

We consider the scheduling problem of minimizing the average-weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smiths ratio rule yield smaller competitive ratios than the previously best-known deterministic on-line algorithms.

Dual techniques for scheduling on a machine with varying speed

We study scheduling problems on a machine of varying speed. Assuming a known speed function (given through an oracle) we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time on a machine of varying speed. This implies also a PTAS for the closely related problem of scheduling to minimize generalized global cost functions. The key to our results is a re-interpretation of the problem within the well-known two-dimensional Gantt chart: instead of the standard approach of scheduling in the time-dimension, we construct scheduling solutions in the weight-dimension. We also consider a dynamic problem variant in which deciding upon the speed is part of the scheduling problem and we are interested in the tradeoff between scheduling cost and speed-scaling cost, which is typically the energy consumption. We obtain two insightful results: (1) the optimal scheduling order is independent of the energy consumption and (2) the problem can be reduced to the setting where the speed of the machine is fixed, and thus admits a PTAS.

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 )f or 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 .W e 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.

Decision Support and Optimization in Shutdown and Turnaround Scheduling

Large-scale maintenance in industrial plants requires the entire shutdown of production units for disassembly, comprehensive inspection, and renewal. We derive models and algorithms for this so-called turnaround scheduling that include different features such as time-cost trade-off, precedence constraints, external resource units, resource leveling, different working shifts, and risk analysis. We propose a framework for decision support that consists of two phases. The first phase supports the manager in finding a good makespan for the turnaround. It computes an approximate project time-cost trade-off curve together with a stochastic evaluation. Our risk measures are the expected tardiness at time t and the probability of completing the turnaround within time t. In the second phase, we solve the actual scheduling optimization problem for the makespan chosen in the first phase heuristically and compute a detailed schedule that respects all side constraints. Again, we complement this by computing upper bounds for the same two risk measures. Our experimental results show that our methods solve large real-world instances from chemical manufacturing plants quickly and yield an excellent resource utilization. A comparison with solutions of a mixed-integer program on smaller instances proves the high quality of the schedules that our algorithms produce within a few minutes.

A New Approach to Online Scheduling: Approximating the Optimal Competitive Ratio

We propose a new approach to competitive analysis in online scheduling by introducing the novel concept of competitive-ratio approximation schemes. Such a scheme algorithmically constructs an online algorithm with a competitive ratio arbitrarily close to the best possible competitive ratio for any online algorithm. We study the problem of scheduling jobs online to minimize the weighted sum of completion times on parallel, related, and unrelated machines, and we derive both deterministic and randomized algorithms that are almost best possible among all online algorithms of the respective settings. We also generalize our techniques to arbitrary monomial cost functions and apply them to the makespan objective. Our method relies on an abstract characterization of online algorithms combined with various simplifications and transformations. We also contribute algorithmic means to compute the actual value of the best possible competitive ratio up to an arbitrary accuracy. This strongly contrasts with nearly all previous manually obtained competitiveness results, and, most importantly, it reduces the search for the optimal competitive ratio to a question that a computer can answer. We believe that our concept can also be applied to many other problems and yields a new perspective on online algorithms in general.

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(logn/ loglogn) 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.

Approximation in preemptive stochastic online scheduling

We present a first constant performance guarantee for preemptive stochastic scheduling to minimize the sum of weighted completion times. For scheduling jobs with release dates on identical parallel machines we derive a policy with a guaranteed performance ratio of 2 which matches the currently best known result for the corresponding deterministic online problem. Our policy applies to the recently introduced stochastic online scheduling model in which jobs arrive online over time. In contrast to the previously considered nonpreemptive setting, our preemptive policy extensively utilizes information on processing time distributions other than the first (and second) moments. In order to derive our result we introduce a new nontrivial lower bound on the expected value of an unknown optimal policy that we derive from an optimal policy for the basic problem on a single machine without release dates. This problem is known to be solved optimally by a Gittins index priority rule. This priority index also inspires the design of our policy.

Polynomial-Time Exact Schedulability Tests for Harmonic Real-Time Tasks

We study the preemptive scheduling of real-time sporadic tasks on a uniprocessor. We consider both fixed priority (FP) scheduling as well as dynamic priority scheduling by the Earliest Deadline First (EDF) algorithm. We investigate the problems of testing schedulability and computing the response time of tasks. Generally these problems are known to be computationally intractable for task systems with constrained deadlines. In this paper, we focus on the particular case of task systems with harmonic period lengths, meaning that the periods of the tasks pair wise divide each other. This is a special case of practical relevance. We present provably efficient exact algorithms for constrained-deadline task systems with harmonic periods. In particular, we provide an exact polynomial-time algorithm for computing the response time of a task in a system with an arbitrary fixed priority order. This also implies an exact FP-schedulability test. For dynamic priority scheduling, we show how to test EDF-schedulability in polynomial time. Additionally, we give a very simple EDF-schedulability test for the simpler case where relative deadlines and periods are jointly harmonic.

Meeting deadlines: how much speed suffices?

We consider the online problem of scheduling real-time jobs with hard deadlines on m parallel machines. Each job has a processing time and a deadline, and the objective is to schedule jobs so that they complete before their deadline. It is known that even when the instance is feasible it may not be possible to meet all deadlines when jobs arrive online over time. We therefore consider the setting when the algorithm has available machines with speed s > 1. We present a new online algorithm that finds a feasible schedule on machines of speed e/(e-1) ≈ 1.58 for any instance that is feasible on unit speed machines. This improves on the previously best known result which requires a speed of 2 - 2/(m + 1). Our algorithm only uses the relative order of job deadlines and is oblivious of the actual deadline values. It was shown earlier that the minimum speed required for such algorithms is e/(e-1), and thus, our analysis is tight. We also show that our new algorithm outperforms two other well-known algorithms by giving the first lower bounds on their minimum speed requirement.