A Note on Stochastic Scheduling on a Single Machine Subject to Breakdown and Repair

1988 ◽  
Vol 2 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Michael Pinedo ◽  
Elias Rammouz
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Stochastic Scheduling ◽  
Weighted Sum ◽  
Due Dates ◽  
Objective Functions ◽  
Weighted Number ◽  
Number Of Late Jobs ◽  
Late Jobs ◽  
Completion Times

This paper considers a single machine and n jobs. The machine is subject to breakdown and repair. Job j has a weight wj, a random processing time Xj, and is available for processing from a random time Rj on. The jobs may be subject to precedence constraints. We are interested in optimal policies that minimize the following objective functions: (i) the weighted sum of the completion times; (ii) the weighted sum of an exponential function of the completion times; and (iii) the weighted number of late jobs having due dates.

On the optimality of LEPT and cµ rules for machines in parallel

1992 ◽  
Vol 29 (3) ◽  
pp. 667-681 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Xiuli Chao ◽  
Michael Pinedo ◽  
Richard Weber
Keyword(s):  
Distributed Processing ◽  
Sufficient Conditions ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Priority Assignment ◽  
Processing Times ◽  
Weighted Number ◽  
Necessary And Sufficient ◽  
Late Jobs ◽  
Completion Times

We consider scheduling problems with m machines in parallel and n jobs. The machines are subject to breakdown and repair. Jobs have exponentially distributed processing times and possibly random release dates. For cost functions that only depend on the set of uncompleted jobs at time t we provide necessary and sufficient conditions for the LEPT rule to minimize the expected cost at all t within the class of preemptive policies. This encompasses results that are known for makespan, and provides new results for the work remaining at time t. An application is that if the cµ rule has the same priority assignment as the LEPT rule then it minimizes the expected weighted number of jobs in the system for all t. Given appropriate conditions, we also show that the cµ rule minimizes the expected value of other objective functions, such as weighted sum of job completion times, weighted number of late jobs, or weighted sum of job tardinesses, when jobs have a common random due date.

On the optimality of LEPT and cµ rules for machines in parallel

1992 ◽  
Vol 29 (03) ◽  
pp. 667-681
Author(s):  
Cheng-Shang Chang ◽  
Xiuli Chao ◽  
Michael Pinedo ◽  
Richard Weber
Keyword(s):  
Distributed Processing ◽  
Sufficient Conditions ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Priority Assignment ◽  
Processing Times ◽  
Weighted Number ◽  
Necessary And Sufficient ◽  
Late Jobs ◽  
Completion Times

We consider scheduling problems with m machines in parallel and n jobs. The machines are subject to breakdown and repair. Jobs have exponentially distributed processing times and possibly random release dates. For cost functions that only depend on the set of uncompleted jobs at time t we provide necessary and sufficient conditions for the LEPT rule to minimize the expected cost at all t within the class of preemptive policies. This encompasses results that are known for makespan, and provides new results for the work remaining at time t. An application is that if the cµ rule has the same priority assignment as the LEPT rule then it minimizes the expected weighted number of jobs in the system for all t. Given appropriate conditions, we also show that the cµ rule minimizes the expected value of other objective functions, such as weighted sum of job completion times, weighted number of late jobs, or weighted sum of job tardinesses, when jobs have a common random due date.

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