A Stochastic Rolling Horizon-Based Approach for Power Generation Expansion Planning

Variable renewable energy sources introduce significant amounts of short-term uncertainty that should be considered when making investment decisions. In this work, we present a method for representing stochastic power system operation in day-ahead and real-time electricity markets within a capacity expansion model. We use Benders’ cuts and a stochastic rolling-horizon dispatch to represent operational costs in the capacity expansion problem (CEP) and investigate different formulations for the cuts. We test the model on a two-bus case study with wind power, energy storage, and a constrained transmission line. The case study shows that cuts created from the day-ahead problem gives the lowest expected total cost for the stochastic CEP. The stochastic CEP results in 3% lower expected total cost compared to the deterministic CEP capacities evaluated under uncertain operation. The number of required stochastic iterations is efficiently reduced by introducing a deterministic lower bound, while extending the horizon of the operational problem by persistence forecasting leads to reduced operational costs.

Optimization of Leased Equipment Maintenance Policy Based on History Failure Data

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

An EPQ Model of Stock Dependent Demand Subject to Epidemic with Stochastic Lockdown Time

The model created considers the effect of the epidemic on the classical Economic Production Quality (EPQ) model for a production unit exposed to stochastic lockdown time. Expected production time is evaluated utilizing continuous probability density function. The investigation is done to decide the ideal arrangement for the production system which limits the expected total cost per unit time exposed to certain conditions. Here EPQ model is created by taking lockdown time due to epidemic as stochastic. Machine breakdown affects the manufacturer but disaster like epidemic affects the manufacturer as well as the customer (or in other words, demand). During the production uptime, demand depend upon stock and decline in selling price, but in case of disaster (epidemic) selling price has no consideration and demand depends only on stock. The model is discussed by means of a numerical example and a case study.

Coordinating Supply Chain Inventory Model for Deteriorating Products

The paper manages an optimal inventory replenishment policy for a deteriorating item with two part coordination technique (coordination and non coordination). The aim of this model is to determine the optimal values for every strategy such that the expected total cost is minimized. The model is solved analytically to get the ideal solution. It is then outlined with the assistance of numerical models.

Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback–Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.

El gasto fiscal de la guerra contra los portadores de drogas ilícitas: una aproximación para Colombia

Around the world, governments spend enormous amounts of public funds in controlling possession, manufacturing and trafficking of illicit drugs. These costs are usually difficult to observe, as they correspond to the opportunity cost of many bureaucrats involved in the process. In this paper, we estimate the expected cost per arrest for possession, manufacturing or trafficking of illicit drugs for the case of Colombia. We find that the expected cost of an arrest is roughly COP$11 million, hence the expected total cost associated with the 984,106 arrests carried out between 2001 and 2015 adds up to COP$10.6 billion. Also, we analyse whether these expenditures are justified by the control of international drug trafficking, crime associated with drug dealing in local markets or drug abuse deterrence. We conclude that none of these reasons justify such fiscal expenditures; rather, these seem to be explained by an issue of incentive compatibility in Colombian authorities.

Optimum process mean, standard deviation and specification limits settings under the Burr distribution

Purpose The quality level setting problem determines the optimal process mean, standard deviation and specification limits of product/process characteristic to minimize the expected total cost associated with products. Traditionally, it is assumed that the product/process characteristic is normally distributed. However, this may not be true. This paper aims to explore the quality level setting problem when the probability distribution of the process characteristic deviates from normality. Design/methodology/approach Burr developed a density function that can represent a wide range of normal and non-normal distributions. This can be applied to investigate the effect of non-normality on the studies of statistical quality control, for example, designs of control charts and sampling plans. The quality level setting problem is examined by introducing Burr’s density function as the underlying probability distribution of product/process characteristic such that the effect of non-normality to the determination of optimal process mean, standard deviation and specification limits of product/process characteristic can be studied. The expected total cost associated with products includes the quality loss of conforming products, the rework cost of non-conforming products and the scrap cost of non-conforming products. Findings Numerical results show that the expected total cost associated with products is significantly influenced by the parameter of Burr’s density function, the target value of product/process characteristic, quality loss coefficient, unit rework cost and unit scrap cost. Research limitations/implications The major assumption of the proposed model is that the lower specification limit must be positive for practical applications, which definitely affects the space of feasible solution for the different combinations of process mean and standard deviation. Social implications The proposed model can provide industry/business application for promoting the product/service quality assurance for the customer. Originality/value The authors adopt the Burr distribution to determine the optimum process mean, standard deviation and specification limits under non-normality. To the best of their knowledge, this is a new method for determining the optimum process and product policy, and it can be widely applied.

Selective maintenance optimization under schedule and quality constraints

Purpose – The traditional practice for maintenance, quality control and production scheduling is to plan independently irrespective of an interrelationship exist between them. The purpose of this paper is to develop an approach for integrating maintenance, quality control and production scheduling. The objective is to investigate the benefits of the integrated effect in terms of the expected total cost of system operation of the three functions. Design/methodology/approach – The proposed approach is based on the conditional reliability of the components. Cost model for integrating selective maintenance, quality control using sampling-based procedure and production scheduling is developed using the conditional reliability. An integrated approach is such that, first an optimal schedule for the batches to be processed is obtained independently while the maintenance and quality control decisions are optimized considering the optimal schedule on the machine. The expected total cost of conventional approach, i.e. “No integration” is calculated to compare the effectiveness of integrated approach. Findings – The integrated approach have shown a higher cost saving as compared to the independent planning approach. The approach is practical to implement as the results are obtained in a reasonable computational time. Practical implications – The approach presented in this paper is generic and can be applied at planned as well as unplanned opportunities. The proposed integrated approach is dynamic in nature, as during maintenance opportunities, it is possible to optimize the decision on maintenance, quality control and production scheduling considering the current age of components and production requirement. Originality/value – The originality of the paper is in the approach for integration of the three elements of shop floor operations that are usually treated separately and rarely touched upon by researchers in the literature.

Mathematical analysis of single queue multi server and multi queue multi server queuing models: comparison study

<p>In the research paper entitled Mathematical Analysis of Single Queue Multi Server and Multi Queue Multi Server Queuing Model, Prasad and Badshah [7] were proved that single queue multi server model is better than multi queue multi server model, and discussed the relation between the performance measures of these two models, and derive the mathematical equations. In this paper we derive the total cost with assumption of certain Waiting cost in both cases. Also, prove that the expected total cost is less for single queue multi server model as comparing with multi queue multi server model.</p>