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25
A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks
 ANNALS OF OPERATIONS RESEARCH
, 1998
"... Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 20 ..."
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Cited by 16 (1 self)
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Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 2000 instances with up to 1200 activities of different testbeds. We propose a suitable numerical representation of the given distributions which is the basis for excellent computational results.
Proactive algorithms for job shop scheduling with probabilistic durations
 Journal of Artificial Intelligence Research
"... Most classical scheduling formulations assume a fixed and known duration for each activity. In this paper, we weaken this assumption, requiring instead that each duration can be represented by an independent random variable with a known mean and variance. The best solutions are ones which have a hig ..."
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Cited by 13 (2 self)
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Most classical scheduling formulations assume a fixed and known duration for each activity. In this paper, we weaken this assumption, requiring instead that each duration can be represented by an independent random variable with a known mean and variance. The best solutions are ones which have a high probability of achieving a good makespan. We first create a theoretical framework, formally showing how Monte Carlo simulation can be combined with deterministic scheduling algorithms to solve this problem. We propose an associated deterministic scheduling problem whose solution is proved, under certain conditions, to be a lower bound for the probabilistic problem. We then propose and investigate a number of techniques for solving such problems based on combinations of Monte Carlo simulation, solutions to the associated deterministic problem, and either constraint programming or tabu search. Our empirical results demonstrate that a combination of the use of the associated deterministic problem and Monte Carlo simulation results in algorithms that scale best both in terms of problem size and uncertainty. Further experiments point to the correlation between the quality of the deterministic solution and the quality of the probabilistic solution as a major factor responsible for this success. 1.
A Novel Branch and Bound Algorithm for Scheduling Flowshop Plants with Uncertain Processing Times
 Computers and Chemical Engineering
, 2001
"... We address the problem of scheduling a flowshop plant with uncertain process ing times described by discrete probability distributions. The objective is to find a sequence of batches that minimizes the expected makespan. To circumvent the prob lem of combinatorially explosive state spaces, we p ..."
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Cited by 12 (2 self)
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We address the problem of scheduling a flowshop plant with uncertain process ing times described by discrete probability distributions. The objective is to find a sequence of batches that minimizes the expected makespan. To circumvent the prob lem of combinatorially explosive state spaces, we propose a novel and rigorous branch and bound algorithm that provides the optimal solution and is based on the result that a lower bound to the expected makespan can be obtained by evaluating over an aggregated probability model. Numerical results for a number of example problems show that the solution times for the proposed method are several orders of magnitude smaller than those for a multiperiod model. In addition, an important extension of this method is proposed for the case of continuous probability distributions of certain forms, using discretization schemes that give excellent approximations.
Job Shop Scheduling with Probabilistic Durations
"... Proactive approaches to scheduling take into account information about the execution time uncertainty in forming a schedule. In this paper, we investigate proactive approaches for the job shop scheduling problem where activity durations are random variables. The main contributions are (i) the introd ..."
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Cited by 10 (2 self)
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Proactive approaches to scheduling take into account information about the execution time uncertainty in forming a schedule. In this paper, we investigate proactive approaches for the job shop scheduling problem where activity durations are random variables. The main contributions are (i) the introduction of the problem of finding probabilistic execution guarantees for difficult scheduling problems; (ii) a method for generating a lower bound on the minimal makespan; (iii) the development of the Monte Carlo approach for evaluating solutions; and (iv) the design and empirical analysis of three solution techniques: an approximately complete technique, found to be computationally feasible only for very small problems, and two techniques based on finding good solutions to a deterministic scheduling problem, which scale to much larger problems.
Scheduling optimization under uncertainty: An alternative approach
 Computers and Chemical Engineering
, 2003
"... The prevalent approach to the treatment of processing time uncertainties in production scheduling problems is through the use of probabilistic models. Apart from requiring detailed information about probability distribution functions, this approach also has the drawback that the computational expens ..."
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Cited by 8 (0 self)
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The prevalent approach to the treatment of processing time uncertainties in production scheduling problems is through the use of probabilistic models. Apart from requiring detailed information about probability distribution functions, this approach also has the drawback that the computational expense of solving these models is very high. In this work, we present a nonprobabilistic treatment of scheduling optimization under uncertainty, based on concepts from fuzzy set theory and interval arithmetic, to describe the imprecision and uncertainty in the task durations. We first provide a brief review on the fuzzy set approach, comparing it with the probabilistic approach. We then present MILP models derived from applying this approach to two different problems flowshop scheduling and new product development process scheduling. Results indicate that these MILP models are computationally tractable for reasonably sized problems. We also describe tabu search implementations in order to handle larger problems. 1
Linear Preselective Policies for Stochastic Project Scheduling
, 1998
"... We introduce a new class of policies for stochastic project scheduling with resource constraints, the linear preselective policies. They combine the benefits of two known classes of scheduling policies for stochastic and deterministic scheduling, viz. priority policies and preselective policies. Pri ..."
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Cited by 8 (1 self)
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We introduce a new class of policies for stochastic project scheduling with resource constraints, the linear preselective policies. They combine the benefits of two known classes of scheduling policies for stochastic and deterministic scheduling, viz. priority policies and preselective policies. Priority policies solve resource conflicts by means of a priority list (list scheduling). They have several computational benefits but suffer from the wellknown Graham anomalies. On the other hand, preselective policies possess favorable properties such as continuity and monotonicity and thus avoid these anomalies, but computing optimal such policies requires excessive computation time. The new class of linear preselective policies is a subclass of the class of preselective policies. Like priority policies, linear preselective policies use priority lists for their definition. They thus inherit all favorable properties of preselective policies but are far better computationally tractable. We st...
Probabilistic combinatorial optimization: Moments, semidefinite programming and asymptotic bounds
 SIAM Journal on Optimization
, 2003
"... Abstract. We address the problem of evaluating the expected optimal objective value of a 01 optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distribution information for the objective coefficients in the form of mo ..."
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Cited by 7 (3 self)
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Abstract. We address the problem of evaluating the expected optimal objective value of a 01 optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distribution information for the objective coefficients in the form of moments. We show that for a fairly general class of marginal information, a tight upper (lower) bound on the expected optimal objective value of a 01 maximization (minimization) problem can be computed in polynomial time if the corresponding deterministic problem is solvable in polynomial time. We provide an efficiently solvable semidefinite programming formulation to compute this tight bound. We also analyze the asymptotic behavior of a general class of combinatorial problems that includes the linear assignment, spanning tree, and traveling salesman problems, under knowledge of complete marginal distributions, with and without independence. We calculate the limiting constants exactly.
Evaluation and Optimization of the Robustness of DAG Schedules in Heterogeneous Environments
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A Comparison of Robustness Metrics for Scheduling DAGs on Heterogeneous Systems
 In HeteroPar’07
, 2007
"... Abstract — A schedule is said robust if it is able to absorb some degree of uncertainty in tasks duration while maintaining a stable solution. This intuitive notion of robustness has led to a lot of different interpretations and metrics. However, no comparison of these different metrics have ever be ..."
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Cited by 5 (3 self)
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Abstract — A schedule is said robust if it is able to absorb some degree of uncertainty in tasks duration while maintaining a stable solution. This intuitive notion of robustness has led to a lot of different interpretations and metrics. However, no comparison of these different metrics have ever been preformed. In this paper, we perform an experimental study of these different metrics and show how they are correlated to each other in the case of task scheduling, with dependencies between tasks. I.