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 Yuan-Shyi Peter Chiu Mathematical Problems in Engineering , 2006, DOI: 10.1155/mpe/2006/98502 Abstract: We study the effect of service level constraint on the economic production quantity (EPQ) model with random defective rate. We first prove that the expected overall cost for imperfect quality EPQ model with backlogging permitted is less than or equal to that of the same model without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation is proposed for calculating the intangible backorder cost for the situation when the required service level is not attainable. By including this intangible backorder cost in the mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the service level constraint. Numerical example is provided to demonstrate its practical usage.
 Yuan-Shyi Peter Chiu Mathematical Problems in Engineering , 2006, Abstract: We study the effect of service level constraint on the economic production quantity (EPQ) model with random defective rate. We first prove that the expected overall cost for imperfect quality EPQ model with backlogging permitted is less than or equal to that of the same model without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation is proposed for calculating the intangible backorder cost for the situation when the required service level is not attainable. By including this intangible backorder cost in the mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the service level constraint. Numerical example is provided to demonstrate its practical usage.
 ISRN Operations Research , 2013, DOI: 10.1155/2013/485172 Abstract: Economic production quantity (EPQ) inventory model for trended demand has been analyzed with rework facility and stochastic preventive machine time. Due to the complexity of the model, search method is proposed to determine the best optimal solution. A numerical example and sensitivity analysis are carried out to validate the proposed model. From the sensitivity analysis, it is observed that the rate of change of demand has significant impact on the optimal inventory cost. The model is very sensitive to the production and demand rate. 1. Introduction An item that does not satisfy quality standards but can be attained after reprocess is termed as a recoverable item and the process is known as rework. It is observed that in an industrial sector, the rework reduced production cost and maintained quality standard of the item. Schrady [1] debated rework process. Khouja [2] formulated an economic lot-size and shipment policy by incorporating a fraction of defective items and direct rework. Koh et al. [3] and Dobos and Richter [4] discussed two production policies with options to order new products externally or recover old products. Chiu et al. [5] analyzed an imperfect rework process for EPQ model with repairable and scrapped items. Jamal et al. [6] advocated the policy for rework of defective items in the same cycle which was extended by Cárdenas-Barrón [7]. Widyadana and Wee [8] gave an analysis of these problems using an algebraic approach. Chiu [9] and Chiu et al. [10] discussed EPQ model by allowing shortages and considering service level constraint. Yoo et al. [11] discussed an EPQ model with imperfect production quality, imperfect inspection, and rework. Meller and Kim [12], Sheu and Chen [13] and Tsou and Chen [14] studied Variants of EPQ model with preventive maintenance. Abboud et al. [15] analyzed an economic order quantity model by considering machine unavailability owing to preventive maintenance and shortage. Chung et al. [16] extended the previous model to compute an economic production quantity for deteriorating inventory model with stochastic machine unavailable time and shortage. Wee and Widyadana [17] revisited the previous model incorporating rework. In this paper, we analyze an economic production quantity (EPQ) model with rework and random preventive maintenance time together when demand is increasing function of time. The consideration of random preventive maintenance time, rework, and trended demand in the model increases its applicability in the electronic and automobile industries. In this production system, produced items are
 Yung-Fu Huang Journal of Applied Sciences , 2006, Abstract: The present note studied the effect of random defective rate and imperfect rework process on the Economic Production Quantity (EPQ) model. They demonstrate that the optimal lot size can be solved algebraically and the expected inventory cost can be derived immediately as well. In this note, we will offer a simple algebraic approach to replace their algebraic skill to find the optimal solution under the expected annual cost minimized.
 Hsien-Jen Lin Mathematical Problems in Engineering , 2012, DOI: 10.1155/2012/689061 Abstract: This paper investigates the impact of setup cost reduction on an inventory policy for a continuous review mixture inventory model involving controllable backorder rate and variable lead time with a service level constraint, in which the order quantity, setup cost, and lead time are decision variables. Our objective is to develop an algorithm to determine the optimal order quantity, setup cost, and lead time simultaneously, so that the total expected annual cost incurred has a minimum value. Furthermore, four numerical examples are provided to illustrate the results, and the effects of system parameters are also included for decision making.
 Behrouz Afshar-Nadjafi Modelling and Simulation in Engineering , 2013, DOI: 10.1155/2013/727685 Abstract: Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where unit production and set-up costs must be considered as functions of production rate. In this paper, we address the problem of determining the optimal production quantity and rate of production in which unit production and set-up costs are assumed to be continuous functions of production rate. Based on the traditional economic production quantity (EPQ) formula, the cost function associated with this model is proved to be nonconvex and a procedure is proposed to solve this problem. Finally, utility of the model is presented using some numerical examples and the results are analyzed. 1. Introduction The economic production quantity (EPQ) model has been widely used in practice because of its simplicity. However, there are some drawbacks in the assumption of the original EPQ model and many researchers have tried to improve it with different viewpoints. Recently, the classical EPQ model has been generalized in many directions. Some authors extended the EPQ model by incorporating the effect of learning in setups and process quality. Also, set-up time reduction on production run length and varying parameters have received significant attention. The relationship between set-up cost and production run length is also influenced by the learning and forgetting effects. The effect of learning and forgetting in setups and in product quality is investigated by Jaber and Bonney [1]. Porteus studied the effect of process deterioration on the optimal production cycle time [2]. Darwish generalized the EPQ model by considering a relationship between the set-up cost and the production run length [3]. Jaber investigated the lot sizing problem for reduction in setups with reworks and interruptions to restore the process to an “in-control’’ state [4]. Unlike the model presented by Khouja [5], he considered that the set-up cost and defect rate decrease as the number of restoration activities increases. Afshar-Nadjafi and Abbasi considered an EPQ model with depreciation cost and process quality cost as continuous functions of time [6]. Freimer et al. studied the effect of imperfect yield on EPQ decisions. They considered set-up cost reductions and process quality improvements as types of investments in the production processes [7]. Furthermore, the classical EPQ model has been investigated in many other ways; for example, the effect of varying production rate on the EPQ model was investigated by Khouja [8]. Huang introduced the EPQ model under
 Information Technology Journal , 2011, Abstract: The Web service composition system with static configuration can not adapt to the failure-prone environment and the variable Quality-of-Service (QoS) of component services. Therefore, a dynamic configuration method of Web service composition, Service Selection Constraint Model, is presented in this study. The candidate component services with same functionality are organized as a service class. The functional dependency relationships between component services are reflected as the service selection constraints. The optimal configurations conforming to multi-objective QoS constraints, known as the Pareto optimal solutions, are searched by a special ant colony optimization algorithm for Web service (ACO4WS). The feasibility and soundness of the method are proved by simulation experiments and corresponding analysis. By using the presented method, not only the QoS of service composition system is greatly improved, but also the multiple functional and non-functional constraints are satisfied.
 Discrete Dynamics in Nature and Society , 2012, DOI: 10.1155/2012/313518 Abstract: This paper presents an improved model for improving headway-based bus route service reliability at bus stops using real-time preventive operation control, taking into account dynamic interaction among random passenger demand, stochastic driving conditions of route segments, and vehicle load capacity constraint. In this model, the real-time information of passenger demand and vehicle operation is involved to predict the imminent unacceptable headway deviation, in the case of which some in-time preventive control strategies are deployed according to the given control rules. As a case study, a single fixed bus route with high-frequency services was simulated and different scenarios of real-time preventive operation control were performed. Headway adherence and average passenger wait time were used to measure bus service reliability. The results show that the improved model is closer to the real bus route service, and using real-time information to predict potential service unreliability and trigger in-time preventive control can reduce bus bunching and avoid big gap. 1. Introduction Giving priority to the development of urban public transit is becoming the common view on reducing urban traffic jam and improving urban travel efficiency [1]. But it is not just a policy issue to attract more and more people to choose transit for travelling. A challenging problem faced by the government, researchers, and transit agencies is how to provide better transit service by using up-to-date technologies. Reliability is one of the most important attributes of quality of transit service and always the top concerned issue for both passengers and transit agencies [2, 3]. From the perception of the passengers, service unreliability means more average wait time, which is identified by Welding’s assertion that the more regular service means the lower average wait time for potential passengers, especially on high-frequency bus routes with random passenger demand [4]. For transit agencies, service delays and disruptions have a real monetary cost in terms of lower utilization of vehicles and operators, which account for 3–5% of operating and vehicle costs by conservative estimate [5, 6]. In terms of the causes of unreliability, running time variability and passenger demand fluctuation are generally noted to be significant factors for service unreliability [7, 8]. Moreover, the initial headway irregularity, either at the beginning or the mid-route, will propagate downstream and this kind of propagation tends to worsen passenger load fluctuation and contributes to worse
 Journal of Chongqing Normal University , 2011, Abstract: Quality of service (QoS)is a key issue in web service discovery. This paper proposes a QoS-supported model for web service discovery, the model adds a mechanism called agent center of QoS and introduces monitoring and feedback mechanism.It satisfies users' functional requirements of web service and estimates web service's non-functional criteria dynamically based on the criteria registered by web service, information fed back by users and service's realtime data which using monitor, quantizer, selector and manager of agent center of QoS,in order to evaluate quality of service dynamically and real-time updates, ensures that QoS information is impartiality, trustworthiness, and real-time. It realizes the dynamic sorting of web services and improves the precision of selection, which not only meets the popular requirements but also meets the personal requirements of consumers by introducing the concept weight and weight of service request in finding services, and using the five-stage selection algorithm which includes keyword maching ,functional constraints matching, quantification of the demand for non-functional, requirements normalization of non-functional and comprehensive assessment and global optimization.
 Mathematics , 2015, Abstract: To transmit a mixture of real-time and non-real-time traffic in a broadcast system, we impose a basic service rate \$r_0\$ for real-time traffic and use the excess rate beyond \$r_0\$ to transmit non-real-time traffic. Considering the time-varying nature of wireless channels, the basic service rate is guaranteed with a service outage constraint, where service outage occurs when the channel capacity is below the basic service rate. This approach is well suited for providing growing services like video, real-time TV, etc., in group transportation systems such as coach, high-speed train, and airplane. We show that the optimal power allocation policy depends only on the statistics of the minimum gain of all user channels, and it is a combination of water-filling and channel inversion. We provide the optimal power allocation policy, which guarantees that real-time traffic be delivered with quality of service (QoS) for every user. Moreover, we show that the required minimum average power to satisfy the service outage constraint increases linearly with the number of users.
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