Systems With Limited Capacity

2018 ◽  
pp. 172-211
Keyword(s):  
Performance Measures ◽  
Optimization Problems ◽  
Limited Capacity ◽  
Limited Space ◽  
Multi Stage

In factories it is common that there are a limited number of spaces for the pieces; similarly, waiting rooms in a hospital can accommodate a limited number of people. Chapter 6 is dedicated to multi-stage systems where the stations have limited space for the queue; the chapter begins with the M/M/1/K systems and the calculation of its performance measures; the following is the bowl phenomenon and its implications in the efficiency of a system; then the M/G/1/K systems and the approaches developed to estimate the performance of this class of systems are presented. The chapter ends with the presentation of some optimization problems related to the M/M/c/K and M/G/c/K systems. Several codes are proposed in Scilab Language to perform calculations automatically.

scholarly journals Integrated Offline and Online Decision Making under Uncertainty

2021 ◽  
Vol 70 ◽  
pp. 77-117
Author(s):  
Allegra De Filippo ◽  
Michele Lombardi ◽  
Michela Milano
Keyword(s):  
Optimization Problems ◽  
Greedy Heuristic ◽  
Management Problem ◽  
Quality Improvements ◽  
Solution Quality ◽  
Convex Optimization Problem ◽  
Routing Problem ◽  
Multi Stage ◽  
The Cost ◽  
Parametric Convex Optimization

This paper considers multi-stage optimization problems under uncertainty that involve distinct offline and online phases. In particular it addresses the issue of integrating these phases to show how the two are often interrelated in real-world applications. Our methods are applicable under two (fairly general) conditions: 1) the uncertainty is exogenous; 2) it is possible to define a greedy heuristic for the online phase that can be modeled as a parametric convex optimization problem. We start with a baseline composed by a two-stage offline approach paired with the online greedy heuristic. We then propose multiple methods to tighten the offline/online integration, leading to significant quality improvements, at the cost of an increased computation effort either in the offline or the online phase. Overall, our methods provide multiple options to balance the solution quality/time trade-off, suiting a variety of practical application scenarios. To test our methods, we ground our approaches on two real cases studies with both offline and online decisions: an energy management problem with uncertain renewable generation and demand, and a vehicle routing problem with uncertain travel times. The application domains feature respectively continuous and discrete decisions. An extensive analysis of the experimental results shows that indeed offline/online integration may lead to substantial benefits.

Vehicular Optimal Control

2018 ◽  
pp. 391-426
Author(s):  
David J. N. Limebeer ◽  
Matteo Massaro
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Optimization Problems ◽  
Structural Features ◽  
Minimum Time ◽  
Time Of Arrival ◽  
Hybrid Powertrain ◽  
Multi Stage ◽  
Time Minimization ◽  
Minimum Time Problems

Chapter 9 deals with the solution of minimum-time and minimum-fuel vehicular optimal control problems. These problems are posed as fuel usage optimization problems under a time-of-arrival constraint, or minimum-time problems under a fuel usage constraint. The first example considers three variants of a simple fuel usage minimization problem under a time-of-arrival constraint. The first variant is worked out theoretically, and serves to highlight several of the structural features of these problems; the other two more complicated variants are solved numerically.The second example is also a multi-stage fuel usage minimization problem under a timeof- arrival constraint.More complicated track and vehicle models are then employed; the problem is solved numerically. The third problem is a lap time minimization problem taken from Formula One and features a thermoelectric hybrid powertrain. The fourth and final problem is a minimum-time closed-circuit racing problem featuring a racing motorcycle and rider.

scholarly journals Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 211
Author(s):  
Lijun Xu ◽  
Yijia Zhou ◽  
Bo Yu
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Model ◽  
Multi Stage ◽  
Proposed Model ◽  
Dual Forms

In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.

Study on Modeling and Improving on the Production and Service Operations Management of Enterprise

2014 ◽  
Vol 644-650 ◽  
pp. 5832-5835
Author(s):  
Ji Rong Wang ◽  
Li Ping Cai ◽  
Yue Jiang ◽  
Guo Zhong Cheng
Keyword(s):  
Dynamic Programming ◽  
Operations Management ◽  
Optimization Problems ◽  
Service Operations ◽  
Model Solution ◽  
Service Operations Management ◽  
Multi Stage

The optimization problems about production and service operations management was proposed in the paper. Dynamic programming was introduced to optimize production and service operations. Meanwhile, the concept and principle of dynamic programming was introduced and the multi-stage decision was analyzed. Then, the model was established and the model solution is given. In the end, the example provided demonstrates the application in the service operations management and it was proved that the methods proposed efficiency to solve the optimization problems about production and service operations management.

scholarly journals Multi-Stage Dynamic Transmission Network Expansion Planning Using LSHADE-SPACMA

2021 ◽  
Vol 11 (5) ◽  
pp. 2155
Author(s):  
Mohamed M. Refaat ◽  
Shady H. E. Abdel Aleem ◽  
Yousry Atia ◽  
Ziad M. Ali ◽  
Mahmoud M. Sayed
Keyword(s):  
Fuzzy Inference ◽  
Optimization Problems ◽  
Planning Problem ◽  
Transmission Network ◽  
Inference System ◽  
Network Expansion ◽  
Expansion Planning ◽  
Covariance Matrix Adaptation ◽  
Transmission Expansion ◽  
Multi Stage

This paper introduces a multi-stage dynamic transmission network expansion planning (MSDTNEP) model considering the N-1 reliability constraint. The integrated planning problem of N-1 security and transmission expansion planning is essential because a single line outage could be a triggering event to rolling blackouts. Two suggested scenarios were developed to obtain the optimal configuration of the Egyptian West Delta Network’s realistic transmission (WDN) to meet the demand of the potential load growth and ensure the system reliability up to the year 2040. The size of a blackout, based on the amount of expected energy not supplied, was calculated to evaluate both scenarios. The load forecasting (up to 2040) was obtained based on an adaptive neuro-fuzzy inference system because it gives excellent results compared to conventional methods. The linear population size reduction—Success-History-based Differential Evolution with semi-parameter adaptation (LSHADE-SPA) hybrid—covariance matrix adaptation evolution strategy (CMA-ES) algorithm (LSHADE-SPACMA)—is proposed to solve the problem. The semi-adaptive nature of LSHADE-SPACMA and the hybridization between LSHADE and CMA-ES are able to solve complex optimization problems. The performance of LSHADE-SPACMA in solving the problem is compared to other well-established methods using three testing systems to validate its superiority. Then, the MSDTNEP of the Egyptian West Delta Network is presented, and the numerical results of the two scenarios are compared to obtain an economic plan and avoid a partial or total blackout.

scholarly journals The Power-Series Algorithm for Polling Systems with Time Limits

1998 ◽  
Vol 12 (2) ◽  
pp. 221-237 ◽  
Author(s):  
J. P. C. Blanc
Keyword(s):  
Power Series ◽  
Performance Measures ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Optimal Time ◽  
Polling Systems ◽  
Mean Values ◽  
Time Limits ◽  
Computing Performance ◽  
Derivatives Of

This paper deals with evaluation and optimization of polling systems with time limits. Performance measures are evaluated with the power-series algorithm, a flexible technique for computing performance measures for multiqueue systems. The constant time limits are approximated by Erlang distributed variables. The algorithm is extended to compute derivatives of performance measures. This allows for optimization of cost functions with respect to the mean values of the time limits by gradient methods. Several properties of the optimal time limits are revealed by the numerical solution of various optimization problems.

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