scholarly journals Fairness through Linearly Increasing Holding Costs in Systems of Parallel Servers with Setup Delays

2015 ◽  
Author(s):  
Esa Hyytia ◽  
Rhonda Righter
Keyword(s):  
Holding Costs ◽  
Parallel Servers

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (04) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (4) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

OPTIMAL CONTROL OF A TWO-STAGE TANDEM QUEUING SYSTEM WITH FLEXIBLE SERVERS

2002 ◽  
Vol 16 (4) ◽  
pp. 453-469 ◽  
Author(s):  
Hyun-soo Ahn ◽  
Izak Duenyas ◽  
Mark E. Lewis
Keyword(s):  
Optimal Control ◽  
Numerical Study ◽  
Queuing System ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Flexible Servers ◽  
Carry Over ◽  
Tandem Queuing ◽  
New Jobs

We consider the optimal control of two parallel servers in a two-stage tandem queuing system with two flexible servers. New jobs arrive at station 1, after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job at station 1 and at rate h2 per unit time for each job at station 2.The system is considered under two scenarios; the collaborative case and the noncollaborative case. In the prior, the servers can collaborate to work on the same job, whereas in the latter, each server can work on a unique job although they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the noncollaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service at station 2 to be optimal does not carry over. This case is examined via a numerical study.

scholarly journals A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers

2005 ◽  
Vol 42 (03) ◽  
pp. 778-796 ◽  
Author(s):  
Klaus Schiefermayr ◽  
Josef Weichbold
Keyword(s):  
Optimal Control ◽  
Optimal Strategy ◽  
Complete Solution ◽  
Stochastic Scheduling ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Processing Times ◽  
Flexible Servers

We consider a two-stage tandem queue with two parallel servers and two queues. We assume that initially all jobs are present and that no further arrivals take place at any time. The two servers are identical and can serve both types of job. The processing times are exponentially distributed. After being served, a job of queue 1 joins queue 2, whereas a job of queue 2 leaves the system. Holding costs per job and per unit time are incurred if there are jobs holding in the system. Our goal is to find the optimal strategy that minimizes the expected total holding costs until the system is cleared. We give a complete solution for the optimal control of all possible parameters (costs and service times), especially for those parameter regions in which the optimal control depends on how many jobs are present in the two queues.

scholarly journals A complete solution for the optimal stochastic scheduling of a two-stage tandem queue with two flexible servers

2005 ◽  
Vol 42 (3) ◽  
pp. 778-796 ◽  
Author(s):  
Klaus Schiefermayr ◽  
Josef Weichbold
Keyword(s):  
Optimal Control ◽  
Optimal Strategy ◽  
Complete Solution ◽  
Stochastic Scheduling ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Processing Times ◽  
Flexible Servers

We consider a two-stage tandem queue with two parallel servers and two queues. We assume that initially all jobs are present and that no further arrivals take place at any time. The two servers are identical and can serve both types of job. The processing times are exponentially distributed. After being served, a job of queue 1 joins queue 2, whereas a job of queue 2 leaves the system. Holding costs per job and per unit time are incurred if there are jobs holding in the system. Our goal is to find the optimal strategy that minimizes the expected total holding costs until the system is cleared. We give a complete solution for the optimal control of all possible parameters (costs and service times), especially for those parameter regions in which the optimal control depends on how many jobs are present in the two queues.

scholarly journals Improving effectiveness of spare parts supply by additive manufacturing as dual sourcing option

OR Spectrum ◽  
2020 ◽  
Author(s):  
N. Knofius ◽  
M. C. van der Heijden ◽  
A. Sleptchenko ◽  
W. H. M. Zijm
Keyword(s):  
Additive Manufacturing ◽  
Spare Parts ◽  
Aviation Industry ◽  
Failure Behavior ◽  
Dual Sourcing ◽  
Production Methods ◽  
Holding Costs ◽  
Unit Costs ◽  
Single Sourcing ◽  
Low Volume

Abstract The low-volume spare parts business is often identified as a potential beneficiary of additive manufacturing (AM) technologies. Currently, high AM unit costs or low AM part reliabilities deem the application of AM economical inferior to conventional manufacturing (CM) methods in most cases. In this paper, we investigate the potential to overcome these deficiencies by combining AM and CM methods. For that purpose, we develop an approach that is tailored toward the unique characteristics of dual sourcing with two production methods. Opposed to the traditional dual sourcing literature, we consider the different failure behavior of parts produced by AM and CM methods. Using numerical experiments and a case study in the aviation industry, we explore under which conditions dual sourcing with AM performs best. Single sourcing with AM methods typically leads to higher purchasing and maintenance costs while single sourcing with CM methods increases backorder and holding costs. Savings of more than 30% compared to the best single sourcing option are possible even if the reliability or unit costs of a part sourced with AM are three times worse than for a CM part. In conclusion, dual sourcing methods may play an important role to exploit the benefits of AM methods while avoiding its drawbacks in the low-volume spare parts business.

OPTIMAL CONTROL OF FLEXIBLE SERVERS IN TWO TANDEM QUEUES WITH OPERATING COSTS

2007 ◽  
Vol 22 (1) ◽  
pp. 107-131 ◽  
Author(s):  
Dimitrios G. Pandelis
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Optimal Allocation ◽  
Operating Costs ◽  
Queuing Systems ◽  
Tandem Queues ◽  
Holding Costs ◽  
Flexible Servers ◽  
Tandem Queuing ◽  
Dedicated Servers

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

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