Deterministic Estimation of the Expected Makespan of a POS Under Duration Uncertainty

2015 ◽  
pp. 279-294
Author(s):  
Michele Lombardi ◽  
Alessio Bonfietti ◽  
Michela Milano
Keyword(s):  
Duration Uncertainty ◽  
Expected Makespan

Scheduling jobs with exponential processing times on parallel machines

1988 ◽  
Vol 25 (04) ◽  
pp. 752-762 ◽  
Author(s):  
Tapani Lehtonen
Keyword(s):  
Binomial Distribution ◽  
Parallel Machines ◽  
Essential Feature ◽  
Stochastic Order ◽  
Partial Solution ◽  
Flow Time ◽  
Optimal Assignment ◽  
Processing Times ◽  
Expected Makespan

We consider a system where jobs are processed by parallel machines. The processing times are exponentially distributed. An essential feature is that the assignment of the jobs to the machines is decided before the system starts to work. We consider both the flow time and the makespan. In the case of the flow time we allow both the machines and the jobs to be non-homogeneous. The optimization is by minimizing the flow time in the sense of stochastic order and the optimal assignment is obtained for this case. The case of the makespan is harder. We consider the expected makespan and as a partial solution we prove an optimality result for the case where there are two non-homogeneous machines and the jobs are homogeneous. It turns out that the optimal assignment can be expressed by using a quantile of a binomial distribution.

Train Scheduling Networks under Time Duration Uncertainty

2014 ◽  
Vol 47 (3) ◽  
pp. 8762-8767 ◽  
Author(s):  
Adnen El Amraoui ◽  
Khaled Mesghouni
Keyword(s):  
Time Duration ◽  
Train Scheduling ◽  
Duration Uncertainty

scholarly journals Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohammad Bayat ◽  
Mehdi Heydari ◽  
Mohammad Mahdavi Mazdeh
Keyword(s):  
Standard Deviation ◽  
Processing Time ◽  
Heuristic Method ◽  
Heuristic Procedure ◽  
Release Date ◽  
Numerical Examples ◽  
Processing Times ◽  
Flowshop Problem ◽  
Expected Makespan ◽  
Actual Processing Time

The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

Shortening Project Makespan in the Case of Resource Constraints and Activity Durations Uncertainty

2017 ◽  
Vol 6 (3) ◽  
pp. 26-36
Author(s):  
Игорь Царьков ◽  
Igor Tsarkov
Keyword(s):  
Project Scheduling ◽  
High Efficiency ◽  
Resource Constraints ◽  
Computational Results ◽  
Decision Points ◽  
Practice Activity ◽  
Expected Makespan

Shortening project expected makespan in the case of resource constraints is the most popular problem in project scheduling. But in practice activity durations is not determined. So the problem is to find a policy which could define which activity should be started at decision points to minimize expected project makespan. This problem usually called SRCPSP. In this paper we define key research tasks of such a problem and propose extended activity-based policy XABP. Computational results show us the high efficiency of this policy.

Minimizing expected makespan in stochastic open shops

1982 ◽  
Vol 14 (4) ◽  
pp. 898-911 ◽  
Author(s):  
Michael L. Pinedo ◽  
Sheldon M. Ross
Keyword(s):  
Exponential Distribution ◽  
Decision Maker ◽  
Optimal Policy ◽  
Processing Time ◽  
Open Shop ◽  
Random Time ◽  
Two Machines ◽  
New Better Than Used ◽  
Expected Makespan ◽  
Better Than

Suppose that two machines are available to process n tasks. Each task has to be processed on both machines; the order in which this happens is immaterial. Task j has to be processed on machine 1 (2) for random time Xj (Yj) with distribution Fj (Gj). This kind of model is usually called an open shop. The time that it takes to process all tasks is normally called the makespan. Every time a machine finishes processing a task the decision-maker has to decide which task to process next. Assuming that Xj and Yj have the same exponential distribution we show that the optimal policy instructs the decision-maker, whenever a machine is freed, to start processing the task with longest expected processing time among the tasks still to be processed on both machines. If all tasks have been processed at least once, it does not matter what the decision-maker does, as long as he keeps the machines busy. We then consider the case of n identical tasks and two machines with different speeds. The time it takes machine 1 (2) to process a task has distribution F (G). Both distributions F and G are assumed to be new better than used (NBU) and we show that the decision-maker stochastically minimizes the makespan when he always gives priority to those tasks which have not yet received processing on either machine.

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