scholarly journals Dynamic Programming as a Scheduling Tool in Multiprogrammed Computing Systems

2021 ◽  
Author(s):  
◽  
Raymond Douglas Brownrigg
Keyword(s):  
Dynamic Programming ◽  
Solution Method ◽  
Test Problems ◽  
Dynamic Feedback ◽  
Scheduling Problems ◽  
Variable Metric ◽  
University Environment ◽  
Scheduling Tool ◽  
Parallel Iterative ◽  
Programming Solution

<p>A potentially parallel iterative algorithm for the solution of the unconstrained N-stage decision problem of Dynamic Programming is developed. This new solution method, known as Variable Metric Dynamic Programming, is based on the use of variable metric minimisation techniques to develop quadratic approximations to the optimal cost function for each stage. The algorithm is applied to various test problems, and a comparison with an existing similar algorithm proves favourable. The Variable Metric Dynamic Programming solution method is used in the implementation of an adaptive highlevel scheduling mechanism on a multiprogrammed computer in a university environment. This demonstrates a practical application of the new algorithm. More importantly, the application of Variable Metric Dynamic Programming to a scheduling problem illustrates how Mathematical Programming may be used in complex computer scheduling problems to provide in a natural way the required dynamic feedback mechanisms.</p>

scholarly journals Dynamic Programming as a Scheduling Tool in Multiprogrammed Computing Systems

2021 ◽  
Author(s):  
◽  
Raymond Douglas Brownrigg
Keyword(s):  
Dynamic Programming ◽  
Solution Method ◽  
Test Problems ◽  
Dynamic Feedback ◽  
Scheduling Problems ◽  
Variable Metric ◽  
University Environment ◽  
Scheduling Tool ◽  
Parallel Iterative ◽  
Programming Solution

<p>A potentially parallel iterative algorithm for the solution of the unconstrained N-stage decision problem of Dynamic Programming is developed. This new solution method, known as Variable Metric Dynamic Programming, is based on the use of variable metric minimisation techniques to develop quadratic approximations to the optimal cost function for each stage. The algorithm is applied to various test problems, and a comparison with an existing similar algorithm proves favourable. The Variable Metric Dynamic Programming solution method is used in the implementation of an adaptive highlevel scheduling mechanism on a multiprogrammed computer in a university environment. This demonstrates a practical application of the new algorithm. More importantly, the application of Variable Metric Dynamic Programming to a scheduling problem illustrates how Mathematical Programming may be used in complex computer scheduling problems to provide in a natural way the required dynamic feedback mechanisms.</p>

Designing an uncertain bi-objective green leagile capacitated lot sizing problem considering FM/M/C queue system

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Masoud Rabbani ◽  
Soroush Aghamohamadi Bosjin ◽  
Neda Manavizadeh ◽  
Hamed Farrokhi-Asl
Keyword(s):  
Mathematical Model ◽  
Solution Method ◽  
Lot Sizing ◽  
Test Problems ◽  
Content Type ◽  
Queue System ◽  
Proposed Model ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing ◽  
To Receive

Purpose This paper aims to present a novel bi-objective mathematical model for a production-inventory system under uncertainty. Design/methodology/approach This paper addresses agile and lean manufacturing concepts alongside with green production methods to design an integrated capacitated lot sizing problem (CLSP). From a methodological perspective, the problem is solved in three phases. In the first step, an FM/M/C queuing system is used to minimize the number of customers waited to receive their orders. In the second step, an effective approach is applied to deal with the fuzzy bi-objective model and finally, a hybrid metaheuristic algorithm is used to solve the problem. Findings Some numerical test problems and sensitivity analyzes are conducted to measure the efficiency of the proposed model and the solution method. The results validate the model and the performance of the solution method compared to Gams results in small size test problems and prove the superiority of the hybrid algorithm in comparison with the other well-known metaheuristic algorithms in large size test problems. Originality/value This paper presents a novel bi-objective mathematical model for a CLSP under uncertainty. The proposed model is conducted on a practical case and several sensitivity analysis are conducted to assess the behavior of the model. Using a queue system, this problem aims to reduce the items waited in the queue to receive service. Two objective functions are considered to maximize the profit and minimize the negative environmental effects. In this regard, the second objective function aims to reduce the amount of emitted carbon.

A column generation-based exact solution method for seru scheduling problems

Omega ◽  
2021 ◽  
pp. 102581
Author(s):  
Zhe Zhang ◽  
Xue Gong ◽  
Xiaoling Song ◽  
Yong Yin ◽  
Benjamin Lev ◽  
...  
Keyword(s):  
Exact Solution ◽  
Column Generation ◽  
Solution Method ◽  
Scheduling Problems

Using Cluster Analysis and Dynamic Programming for Demand Response Applied to Electricity Load in Residential Homes

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Pattanun Chanpiwat ◽  
Steven A. Gabriel ◽  
Rachel L. Moglen ◽  
Michael J. Siemann
Keyword(s):  
Dynamic Programming ◽  
Demand Response ◽  
Power Market ◽  
Practical Method ◽  
Important Application ◽  
Homogeneous Groups ◽  
Market Participants ◽  
Electricity Load ◽  
Scheduling Tool ◽  
Business As Usual

Abstract This paper develops means to analyze and cluster residential households into homogeneous groups based on the electricity load. Classifying customers by electricity load profiles is a top priority for retail electric providers (REPs), so they can plan and conduct demand response (DR) effectively. We present a practical method to identify the most DR-profitable customer groups as opposed to tailoring DR programs for each separate household, which may be computationally prohibitive. Electricity load data of 10,000 residential households from 2017 located in Texas was used. The study proposed the clustered load-profile method (CLPM) to classify residential customers based on their electricity load profiles in combination with a dynamic program for DR scheduling to optimize DR profits. The main conclusions are that the proposed approach has an average 2.3% profitability improvement over a business-as-usual heuristic. In addition, the proposed method on average is approximately 70 times faster than running the DR dynamic programming separately for each household. Thus, our method not only is an important application to provide computational business insights for REPs and other power market participants but also enhances resilience for power grid with an advanced DR scheduling tool.

On the optimality of LEPT and μc rules for parallel processors and dependent arrival processes

1993 ◽  
Vol 25 (04) ◽  
pp. 979-996
Author(s):  
Arie Hordijk ◽  
Ger Koole
Keyword(s):  
Dynamic Programming ◽  
Parallel Processors ◽  
Arrival Process ◽  
Scheduling Problems ◽  
Cost Structures ◽  
Markov Decision ◽  
New Type ◽  
Arrival Processes ◽  
Special Case

In this paper we study scheduling problems of multiclass customers on identical parallel processors. A new type of arrival process, called a Markov decision arrival process, is introduced. This arrival process can be controlled and allows for an indirect dependence on the numbers of customers in the queues. As a special case we show the optimality of LEPT and the µc-rule in the last node of a controlled tandem network for various cost structures. A unifying proof using dynamic programming is given.

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