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Results in Journal American Journal of Operations Research: 400

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Anayo Charles Iwuji, Emeka Uchendu Agwu
American Journal of Operations Research, Volume 07, pp 307-322; https://doi.org/10.4236/ajor.2017.75023

Abstract:
A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.
Hongyun Wang, George Labaria, Cardy Moten, Hong Zhou
American Journal of Operations Research, Volume 07, pp 289-306; https://doi.org/10.4236/ajor.2017.75022

Abstract:
This paper investigates the effect of launching multiple weapons against an area target of normally distributed elements. We provide an analytical form of the average damage fraction and then apply it to obtain optimal aimpoints. To facilitate the computational efforts in practice, we also consider optimizations over given constrained patterns of aimpoints. Finally, we derive scaling laws for optimal aimpoints and optimal damage fraction with respect to the radius of the area target.
R. R. K. Sharma, Syed Moize Ali
American Journal of Operations Research, Volume 07, pp 282-284; https://doi.org/10.4236/ajor.2017.75020

Abstract:
We reduce lot sizing problem with (a) Set Up, Production, Shortage and Inventory Costs to lot sizing problem with (b) Set Up, Production, and Inventory Costs. For lot sizing problem (as in (b)), Pochet and Wolsey [1] have given already integral polyhedral with polynomial separation where a linear program yield “integer” solutions. Thus problem (b) which we have created can be more easily solved by methods available in literature. Also with the removal of shortage variables is an additional computational advantage.
R. R. K. Sharma
American Journal of Operations Research, Volume 07, pp 285-288; https://doi.org/10.4236/ajor.2017.75021

Abstract:
For the transportation problem, Sharma and Sharma [1] have given a very computationally efficient heuristic (runs in O(c*n2) time) to give very good dual solution to transportation problem. Sharma and Prasad [2] have given an efficient heuristic (complexity O(n3) procedure to give a very good primal solution (that is generally non-basic feasible solution) to transportation problem by using the very good dual solution given by Sharma and Sharma [2]. In this paper we use the solution given by Sharma and Prasad [2] to get a very good Basic Feasible Solution to transportation problem, so that network simplex (worst case complexity (O(n3*(log(n))) can be used to reach the optimal solution to transportation problem. In the second part of this paper, we give a simple heuristic procedure to get a very good BFS to linear programming problem from the solution given by Karmarkar [3] (that generally produces a very good non-basic feasible solution in polynomial time (O(n5.5)). We give a procedure to obtain a good BFS for LP by starting from the solution given by Karmarkar [3]. We note that this procedure (given here) is significantly different from the procedure given in [4].
R. R. K. Sharma, Vimal Kumar, Nilanjan Das Khan
American Journal of Operations Research, Volume 07, pp 272-281; https://doi.org/10.4236/ajor.2017.75019

Abstract:
Formulation of SLCLSP given by Pochet and Wolsey [1] had set up, variables, inventory and shortage cost. We give a new reformulation where SLCLSP is reduced to set up and inventory variables. We find that this reformulation has less number of real variables than the reformulation of Pochet and Wolsey [1]. It is argued that this leads to computations advantages, and this is supported by the empirical investigation that we carried out.
Idorenyin Etukudo
American Journal of Operations Research, Volume 07, pp 263-271; https://doi.org/10.4236/ajor.2017.75018

Abstract:
A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.
Mohamad Sayed Al-Ashhab, Taiser Attia, Shadi Mohammad Munshi
American Journal of Operations Research, Volume 07, pp 174-186; https://doi.org/10.4236/ajor.2017.73012

Abstract:
This paper presents a multi-objective production planning model for a factory operating under a multi-product, and multi-period environment using the lexicographic (pre-emptive) procedure. The model objectives are to maximize the profit, minimize the total cost, and maximize the Overall Service Level (OSL) of the customers. The system consists of three potential suppliers that serve the factory to serve three customers/distributors. The performance of the developed model is illustrated using a verification example. Discussion of the results proved the efficacy of the model. Also, the effect of the deviation percentages on the different objectives is discussed.
Mauricio Benegas
American Journal of Operations Research, Volume 07, pp 187-200; https://doi.org/10.4236/ajor.2017.73013

Abstract:
This paper proposes a new method to reduce the dimensionality of input and output spaces in DEA models. The method is based on Yanai’s Generalized Coefficient of Determination and on the concept of pseudo-rank of a matrix. In addition, the paper suggests a rule to determine the cardinality of the subset of selected variables in a way to gain the maximal discretionary power and to suffer a minimal informational loss.
Rashmi Birla, Vijay K. Agarwal, Idrees A. Khan, Vishnu Narayan Mishra
American Journal of Operations Research, Volume 07, pp 239-247; https://doi.org/10.4236/ajor.2017.73016

Thomas Ugbe, Polycarp Chigbu
American Journal of Operations Research, Volume 07, pp 225-238; https://doi.org/10.4236/ajor.2017.73015

Abstract:
The solutions of Linear Programming Problems by the segmentation of the cuboidal response surface through the Super Convergent Line Series methodologies were obtained. The cuboidal response surface was segmented up to four segments, and explored. It was verified that the number of segments, S, for which optimal solutions are obtained is two (S = 2). Illustrative examples and a real-life problem were also given and solved.
Mohamed-Larbi Rebaiaia,
American Journal of Operations Research, Volume 07, pp 201-224; https://doi.org/10.4236/ajor.2017.73014

Abstract:
The purpose of this paper is to propose a computational technique for evaluating the reliability of networks subject to stochastic failures. In this computation, a mathematical model is provided using a technique which incorporates the effect of the factoring decomposition theorem using polygon-to-chain and series-parallel reductions. The algorithm proceeds by identifying iteratively one of seven polygons and when it is discovered, the polygon is immediately removed and replaced by a simple chain after having changed the individual values of the reliability of each edge and each node of the polygon. Theoretically, the mathematical development follows the results presented by Satyanarayana & Wood and Theologou & Carlier. The computation process is recursively performed and less constrained in term of execution time and memory space, and generates an exact value of the reliability.
Luca Iseppi, Franco Rosa, Mario Taverna
American Journal of Operations Research, Volume 07, pp 153-173; https://doi.org/10.4236/ajor.2017.73011

Abstract:
The scope of this research is to elaborate a strategy to minimize the logistic cost of the whey collection. The problem consists of the description of the whey collection basin and transport from CP (Cheese plant) to WPP (Whey processing plant). We started with an initial basic solution and proceeded with successive iterations to find the final optimal solution. Two numeric methods are proposed to solve iteratively the problem: the first one emulates the simplex method, the second one is an empirical solution to find the optimal route. Both are solved with an Excel and Google map software and do not require a dedicated LP program for calculus. The results demonstrate that both methods contribute to solve the transport problem and generate valuable information for the achievement of economic and environmental targets.
Dahande Balme, Laure Pauline Fotso
American Journal of Operations Research, Volume 07, pp 121-132; https://doi.org/10.4236/ajor.2017.72009

Abstract:
In this paper, we find the solution of a quasiconcave bilevel programming problem (QCBPP). After formulating a Bilevel Multiobjective Programming Problem (BMPP), we characterize its leader objective function and its feasible set. We show some necessary and sufficient conditions to establish a convex union of set of efficient point, an efficient set at the QCBPP. Based on this result, we formulate and solve a new QCBPP. Finally, we illustrate our approach with a numerical example.
Patrick R. McMullen
American Journal of Operations Research, Volume 07, pp 99-112; https://doi.org/10.4236/ajor.2017.72007

Abstract:
This research presents an approach based upon ant-colony optimization to address the system reliability problem. For each component of a system, the number of units in parallel needs to be chosen to maximize the reliability for the entire system. As more parallel units are selected, costs increase in a proportional fashion. For this effort, quantity discounts for additional parallel units are considered, and the budget for purchase of parallel units is limited. Ant colony optimization methodology is employed to find an optimal system reliability that satisfies the budget constraint. The methodology is employed for several test problems, and near-optimal solutions are found.
Hajime Yokoyama,
American Journal of Operations Research, Volume 07, pp 113-120; https://doi.org/10.4236/ajor.2017.72008

Abstract:
This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling; for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.
American Journal of Operations Research, Volume 07, pp 83-98; https://doi.org/10.4236/ajor.2017.72006

Abstract:
Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. This problem is NP-hard in the strong sense. Moreover, it is very difficult to solve with an exact method; it is for that reason we have made use of the approximate methods. We improved the variable neighborhood search (VNS) algorithm, which is efficient for solving hard combinatorial optimization problems. This problem can be viewed as an optimization problem with mixed variables (binary variables and real variables). The new VNS algorithm was tested against 540 benchmark problems. The performance of most of our approaches was satisfactory and performed better than the algorithms already proposed in the literature.
Prem Prakash Mishra, S. S. Mishra, S. K. Yadav, R. S. Singh, Ravendra Kumar
American Journal of Operations Research, Volume 07, pp 64-82; https://doi.org/10.4236/ajor.2017.71005

Abstract:
In this paper, we focus on the intermediate nodes of network and quantification of level of commodity and its cost on each node because intermediate nodes have stocking capacities which we generally see in the supply chain network. The commodity is supplied from a node to node in response to the power form of demand at a particular time. Since the traffic intensity of the demand of commodity also affects the flow of the commodity in the network, hence study of flow of commodity in the network is believed to be a significant contribution in this area. Several cases of quantifying the level of commodity in different situations as well as the cost analysis of incoming and outgoing commodity at a particular node have been thoroughly discussed in the paper. The present problem, presumably seeks to contribute to managerial decision making in supply chain network.
Ruiping Yuan, Tingting Dong, Juntao Li
American Journal of Operations Research, Volume 06, pp 442-449; https://doi.org/10.4236/ajor.2016.66041

Abstract:
Path planning problem is the core and hot research topic of multiple Automatic Guided Vehicles (multi-AGVs) system. Although there are many research results, they do not solve the path planning problem from the perspective of reducing traffic congestion. A collision-free path planning method based on improved A* Algorithm for multi-AGVs logistics sorting system is proposed in this paper. In the method, the environment of warehouse operation for AGVs is described by using grid method. The estimated cost of A* algorithm is improved by adding the penalty value of the paths that AGVs share with each other to alleviate traffic congestion and collision resolution rules are made according to different types of collisions. Then the collision-free path planning is done by combing the improved A* algorithm and collision resolution rules. The sorting efficiency of the method is compared with that of original A* algorithm. Simulation results show that the new collision-free path planning method can improve the sorting efficiency of multi-AGVs system and relieve traffic congestion.
Hongyun Wang, Cardy Moten, Morris Driels, Don Grundel, Hong Zhou
American Journal of Operations Research, Volume 06, pp 450-467; https://doi.org/10.4236/ajor.2016.66042

Abstract:
We study the damage probability when M weapons are used against a unitary target. We use the Carleton damage function to model the distribution of damage probability caused by each weapon. The deviation of the impact point from the aimpoint is attributed to both the dependent error and independent errors. The dependent error is one random variable affecting M weapons the same way while independent errors are associated with individual weapons and are independent of each other. We consider the case where the dependent error is significant, non-negligible relative to independent errors. We first derive an explicit exact solution for the damage probability caused by M weapons for any M. Based on the exact solution, we find the optimal aimpoint distribution of M weapons to maximize the damage probability in several cases where the aimpoint distribution is constrained geometrically with a few free parameters, including uniform distributions around a circle or around an ellipse. Then, we perform unconstrained optimization to obtain the overall optimal aimpoint distribution and the overall maximum damage probability, which is carried out for different values of M, up to 20 weapons. Finally, we derive a phenomenological approximate expression for the damage probability vs. M, the number of weapons, for the parameters studied here.
Brou Aguié Pacôme Bertrand, Diaby Moustapha, Soro Etienne, Oumtanaga Souleymane, Aka Boko
American Journal of Operations Research, Volume 06, pp 355-370; https://doi.org/10.4236/ajor.2016.64033

Rais Ahmad, Mohammad Dilshad
American Journal of Operations Research, Volume 01, pp 305-311; https://doi.org/10.4236/ajor.2011.14035

Abstract:
In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of H(.,.)- φ - η - accretive operator
Qiang Song
American Journal of Operations Research, Volume 01, pp 293-304; https://doi.org/10.4236/ajor.2011.14034

Abstract:
This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented
Jinnian Wang, Yongjun Li
American Journal of Operations Research, Volume 01, pp 284-292; https://doi.org/10.4236/ajor.2011.14033

Abstract:
The perspective of internal structure of the decision making units (DMUs) was considered as the “black box” when employing data envelopment analysis (DEA) models. However, in the actual world there are always some DMUs that are composed of several sub-units or subsystems, each utilizes the same inputs to generate same outputs. Numerous instances can be listed, such as a firm with a few of plants. In this paper we present models that evaluated the efficiency of DMU which is comprised of same several parallel subsystems, the foremost contribution of our work is that we take the different importance of the subsystems into account in the model, which can be obviously distinguished to the existing DEA model. Secondly, since the alternative optimal multipliers may emerge in the model, the efficiency of each subsystem may be non-unique and we simultaneously develop models of efficiency decomposition for each subsystem. At last a case of technological innovation activities of each province in China is used as an example to state the models
, Huayong Xiao, Yuxi Quan
American Journal of Operations Research, Volume 01, pp 277-283; https://doi.org/10.4236/ajor.2011.14032

Abstract:
We view a facility system as a kind of supply chain and model it as a connected graph in which the nodes represent suppliers, distribution centers or customers and the edges represent the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. In this paper, we consider facility systems' reliability analysis based on the classical p-median problem when subject to edge failures. We formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example
Shengyuan Chen,
American Journal of Operations Research, Volume 01, pp 268-276; https://doi.org/10.4236/ajor.2011.14031

Abstract:
The global liberalization of energy market and the evolving carbon policy have profound implication on a producer’s optimal generator portfolio problem. On one hand, the daily operational flexibility from a well- composed generator portfolio enables the producer to implement a more aggressive bidding strategy in the liberalized day-ahead market on a daily basis; on the other hand, the evolving carbon policy demands the long term robustness of a generator portfolio: it should be able to generate stable cash flow under different stages of the evolving carbon tax policy. It is computationally very challenging to incorporate the daily bidding strategy into such a long term generator portfolio study. We overcome the difficulty by a powerful vertical decomposition. The long term uncertainty of carbon tax policy is simulated by scenarios; while the daily electricity price fluctuation with jumps is modeled by a more complicated Markov Regime Switching model. The proposed model provides the senior executives an efficient quantitative tool to select an optimal generator portfolio in the deregulated market under evolving carbon tax policy.
Monga K. Luhandjula
American Journal of Operations Research, Volume 01, pp 259-267; https://doi.org/10.4236/ajor.2011.14030

Abstract:
In this paper, we propose a novel approach for Fuzzy random-valued Optimization. The main idea behind our approach consists of taking advantage of interplays between fuzzy random variables and random sets in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. We consider a numerical example that shows the efficiency of the proposed method
P. C. Jha, Ritu Arora, U. Dinesh Kumar
American Journal of Operations Research, Volume 01, pp 249-258; https://doi.org/10.4236/ajor.2011.14029

Abstract:
Software projects generally have to deal with producing and managing large and complex software products. As the functionality of computer operations become more essential and yet more critical, there is a great need for the development of modular software system. Component-Based Software Engineering concerned with composing, selecting and designing components to satisfy a set of requirements while minimizing cost and maximizing reliability of the software system. This paper discusses the fuzzy approach for component selection using “Build-or-Buy” strategy in designing a software structure. We introduce a framework that helps developers to decide whether to buy or build components. In case a commercial off-the-shelf (COTS) component is selected then different versions are available for each alternative of a module and only one version will be selected. If a component is an in-house built component, then the alternative of a module is selected. Numerical illustrations are provided to demonstrate the model developed
Guolin Yu, Min Wang
American Journal of Operations Research, Volume 01, pp 243-248; https://doi.org/10.4236/ajor.2011.14028

Abstract:
This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality results are proposed for non-differentiable multi-objective programming problem
Jelena Vidović
American Journal of Operations Research, Volume 01, pp 236-242; https://doi.org/10.4236/ajor.2011.14027

Abstract:
Aim of this paper is to characterize different risk measures in portfolio construction on seven Central and South-East European stock markets; Slovenia, Croatia, Hungary, Poland, Chez Republic, Bulgaria and Romania. Selected countries are members of EU, except Croatia and Turkey which have candidate status. Empirical part of this paper consists of three stages; at first descriptive statistic on stock returns was performed, afterwards different risk measures were employed in portfolio construction and in the last part, portfolios were tested in the out-of-sample period. Results indicate presence of extreme kurtosis and skewness in stock return series. Resulting portfolios incorporate stocks with extremely high kurtosis and stocks with negative skewness. Portfolio construction based only on risk and return results in major exposure to extreme returns and unsatisfactory portfolio out of sample results
, , Min Jiang
American Journal of Operations Research, Volume 01, pp 229-235; https://doi.org/10.4236/ajor.2011.14026

Abstract:
By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains; and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an interactive algorithm of MP is designed accordingly. Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker
Patrick R. McMullen
American Journal of Operations Research, Volume 01, pp 220-228; https://doi.org/10.4236/ajor.2011.14025

Abstract:
This research presents a problem relevant to production scheduling for mixed models – production schedules that contain several unique items, but each unique item may have multiple units that require processing. The presented research details a variant of this problem where, over multiple processes, resequencing is permitted to a small degree so as to exploit efficiencies with the intent of optimizing the objectives of required set-ups and parts usage rate via an efficient frontier. The problem is combinatorial in nature. Enumeration is used on a variety of test problems from the literature, and a search heuristic is used to compare optimal solutions with heuristic based solutions. Experimentation shows that the heuristic solutions approach optimality, but with opportunities for improvement
American Journal of Operations Research, Volume 01, pp 214-219; https://doi.org/10.4236/ajor.2011.14024

Abstract:
This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented
A. Segun Adeyefa, Monga K. Luhandjula
American Journal of Operations Research, Volume 01, pp 203-213; https://doi.org/10.4236/ajor.2011.14023

Abstract:
Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones
American Journal of Operations Research, Volume 01, pp 191-202; https://doi.org/10.4236/ajor.2011.14022

Abstract:
Optimal adjustment algorithm for p coordinates is a generalization of the optimal pair adjustment algorithm for linear programming, which in turn is based on von Neumann’s algorithm. Its main advantages are simplicity and quick progress in the early iterations. In this work, to accelerate the convergence of the interior point method, few iterations of this generalized algorithm are applied to the Mehrotra’s heuristic, which determines the starting point for the interior point method in the PCx software. Computational experiments in a set of linear programming problems have shown that this approach reduces the total number of iterations and the running time for many of them, including large-scale ones
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