Advances in Operations Research The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Scheduling Jobs Families with Learning Effect on the Setup Thu, 19 Feb 2015 07:10:47 +0000 The present paper aims to address the flow-shop sequence-dependent group scheduling problem with learning effect (FSDGSLE). The objective function to be minimized is the total completion time, that is, the makespan. The workers are required to carry out manually the set-up operations on each group to be loaded on the generic machine. The operators skills improve over time due to the learning effects; therefore the set-up time of a group under learning effect decreases depending on the order the group is worked in. In order to effectively cope with the issue at hand, a mathematical model and a hybrid metaheuristic procedure integrating features from genetic algorithms (GA) have been developed. A well-known problem benchmark risen from literature, made by two-, three- and six-machine instances, has been taken as reference for assessing performances of such approach against the two most recent algorithms presented by literature on the FSDGS issue. The obtained results, also supported by a properly developed ANOVA analysis, demonstrate the superiority of the proposed hybrid metaheuristic in tackling the FSDGSLE problem under investigation. Sergio Fichera, Antonio Costa, and Fulvio Cappadonna Copyright © 2015 Sergio Fichera et al. All rights reserved. Preventive Maintenance Scheduling for Multicogeneration Plants with Production Constraints Using Genetic Algorithms Tue, 10 Feb 2015 09:09:27 +0000 This paper describes a method developed to schedule the preventive maintenance tasks of the generation and desalination units in separate and linked cogeneration plants provided that all the necessary maintenance and production constraints are satisfied. The proposed methodology is used to generate two preventing maintenance schedules, one for electricity and the other for distiller. Two types of crossover operators were adopted, 2-point and 4-point. The objective function of the model is to maximize the available number of operational units in each plant. The results obtained were satisfying the problem parameters. However, 4-point slightly produce better solution than 2-point ones for both electricity and water distiller. The performance as well as the effectiveness of the genetic algorithm in solving preventive maintenance scheduling is applied and tested on a real system of 21 units for electricity and 21 units for water. The results presented here show a great potential for utility applications for effective energy management over a time horizon of 52 weeks. The model presented is an effective decision tool that optimizes the solution of the maintenance scheduling problem for cogeneration plants under maintenance and production constraints. Khaled Alhamad, Mohsen Alardhi, and Abdulla Almazrouee Copyright © 2015 Khaled Alhamad et al. All rights reserved. Passenger Traffic Evaluation and Price Formation on the Transportation Services Market Tue, 03 Feb 2015 06:47:25 +0000 This paper investigates equilibrium formation in the passenger traffic model. First, we propose an estimation technique for the distribution of incoming passengers at each stop with respect to subsequent stops of a route based on available information on incoming and outgoing passengers. Second, we employ the obtained information on passenger traffic to introduce a game-theoretic model of passenger traffic distribution with respect to transport facilities. V. M. Bure, V. V. Mazalov, A. V. Melnik, and N. V. Plaksina Copyright © 2015 V. M. Bure et al. All rights reserved. Analysis of a Multiserver Queueing-Inventory System Tue, 20 Jan 2015 08:21:37 +0000 We attempt to derive the steady-state distribution of the queueing-inventory system with positive service time. First we analyze the case of servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair and the corresponding expected minimum cost are computed. As in the case of retrial queue with , we conjecture that for , queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutive to transitions of the inventory level (i.e., the first return time to ) is computed. We also obtain several system performance measures. A. Krishnamoorthy, R. Manikandan, and Dhanya Shajin Copyright © 2015 A. Krishnamoorthy et al. All rights reserved. A Hybrid Grey Relational Analysis and Nondominated Sorting Genetic Algorithm-II for Project Portfolio Selection Wed, 24 Dec 2014 09:07:29 +0000 Project selection and formation of an optimal portfolio of selected projects are among the main challenges of project management. For this purpose, several factors and indicators are simultaneously examined considering the terms and conditions of the decision problem. Obviously, both qualitative and quantitative factors may influence the formation of a portfolio of projects. In this study, the projects were first ranked using grey relational analysis to form an optimal portfolio of projects and to create an expert system for the final project selection. Because of the fuzzy nature of the environmental risk of each project, the environmental risk was predicted and analyzed using the fuzzy inference system and failure mode and effect analysis based on fuzzy rules. Then, the rank and risk of each project were optimized using a two-objective zero-one mathematical programming model considering the practical constraints of the decision problem through the nondominated sorting genetic algorithm-II (NSGA-II). A case study was used to discuss the practical methodology for selecting a portfolio of projects. Farshad Faezy Razi Copyright © 2014 Farshad Faezy Razi. All rights reserved. Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process Wed, 10 Dec 2014 07:29:42 +0000 Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST), which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom called nonmembership function into the set description. In this paper, we proposed a triangular intuitionistic fuzzy number based approach for the vendor selection problem using analytical hierarchy process. The crisp data of the vendors is represented in the form of triangular intuitionistic fuzzy numbers. By applying AHP which involves decomposition, pairwise comparison, and deriving priorities for the various levels of the hierarchy, an overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our method. Lastly a sensitivity analysis is performed to find the most critical criterion on the basis of which vendor is selected. Prabjot Kaur Copyright © 2014 Prabjot Kaur. All rights reserved. Mathematical Analysis of Queue with Phase Service: An Overview Wed, 10 Dec 2014 00:10:08 +0000 We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent. Richa Sharma Copyright © 2014 Richa Sharma. All rights reserved. Production Scheduling of Open Pit Mines Using Particle Swarm Optimization Algorithm Tue, 25 Nov 2014 11:45:44 +0000 Determining an optimum long term production schedule is an important part of the planning process of any open pit mine; however, the associated optimization problem is demanding and hard to deal with, as it involves large datasets and multiple hard and soft constraints which makes it a large combinatorial optimization problem. In this paper a procedure has been proposed to apply a relatively new and computationally less expensive metaheuristic technique known as particle swarm optimization (PSO) algorithm to this computationally challenging problem of the open pit mines. The performance of different variants of the PSO algorithm has been studied and the results are presented. Asif Khan and Christian Niemann-Delius Copyright © 2014 Asif Khan and Christian Niemann-Delius. All rights reserved. An Optimization Model for Product Placement on Product Listing Pages Tue, 11 Nov 2014 11:43:20 +0000 The design of product listing pages is a key component of Website design because it has significant influence on the sales volume on a Website. This study focuses on product placement in designing product listing pages. Product placement concerns how venders of online stores place their products over the product listing pages for maximization of profit. This problem is very similar to the offline shelf management problem. Since product information sources on a Web page are typically communicated through the text and image, visual stimuli such as color, shape, size, and spatial arrangement often have an effect on the visual attention of online shoppers and, in turn, influence their eventual purchase decisions. In view of the above, this study synthesizes the visual attention literature and theory of shelf-space allocation to develop a mathematical programming model with genetic algorithms for finding optimal solutions to the focused issue. The validity of the model is illustrated with example problems. Yan-Kwang Chen, Fei-Rung Chiu, and Ciao-Jyun Yang Copyright © 2014 Yan-Kwang Chen et al. All rights reserved. Lot Size Decisions for Vendor-Buyer System with Quantity Discount, Partial Backorder, and Stochastic Demand Tue, 11 Nov 2014 00:00:00 +0000 This paper presents production-inventory model for two-echelon system consisting of single vendor and single buyer. The proposed model contributes to the current inventory literature by incorporating quantity discount scheme into stochastic vendor-buyer model. Almost all vendor-buyer inventory models have discussed this scheme in single-echelon system and deterministic demand situation. Here, we assume that the demand of the buyer is normally distributed and the unmet demand is considered to be partially backordered. In addition, the lead time is variable and consists of production time and nonproductive time. The quantity discount is developed by using all-units quantity discounts. Finally, an iterative procedure is proposed to obtain all decision variables and numerical examples are provided to show the application of the proposed procedure. Wakhid Ahmad Jauhari Copyright © 2014 Wakhid Ahmad Jauhari. All rights reserved. Heuristic-Based Firefly Algorithm for Bound Constrained Nonlinear Binary Optimization Wed, 08 Oct 2014 09:48:25 +0000 Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid “erf” function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid “erf” function with “movements in continuous space” is the best, in terms of both computational requirements and accuracy. M. Fernanda P. Costa, Ana Maria A. C. Rocha, Rogério B. Francisco, and Edite M. G. P. Fernandes Copyright © 2014 M. Fernanda P. Costa et al. All rights reserved. Multimode Preemptive Resource Investment Problem Subject to Due Dates for Activities: Formulation and Solution Procedure Mon, 29 Sep 2014 11:48:00 +0000 The preemptive Multimode resource investment problem is investigated. The Objective is to minimize the total renewable/nonrenewable resource costs and earliness-tardiness costs by a given project deadline and due dates for activities. In this problem setting preemption is allowed with no setup cost or time. The project contains activities interrelated by finish-start type precedence relations with a time lag of zero, which require a set of renewable and nonrenewable resources. The problem formed in this way is an NP-hard. A mixed integer programming formulation is proposed for the problem and parameters tuned genetic algorithm (GA) is proposed to solve it. To evaluate the performance of the proposed algorithm, 120 test problems are used. Comparative statistical results reveal that the proposed GA is efficient and effective in terms of the objective function and computational times. Behrouz Afshar-Nadjafi and Mohammad Arani Copyright © 2014 Behrouz Afshar-Nadjafi and Mohammad Arani. All rights reserved. Algorithms for Location Problems Based on Angular Distances Thu, 25 Sep 2014 11:19:55 +0000 This paper describes four mathematical models for the single-facility location problems based on four special distance metrics and algorithms for solving such problems. In this study, algorithms of solving Weber problems using four distance predicting functions (DPFs) are proposed in accordance with four strategies for manipulator control. A numerical example is presented in this proposal as an analytical proof of the optimality of their results. Lev A. Kazakovtsev, Predrag S. Stanimirović, Idowu A. Osinuga, Mikhail N. Gudyma, and Alexander N. Antamoshkin Copyright © 2014 Lev A. Kazakovtsev et al. All rights reserved. The Supplying Chain Scheduling with the Cost Constraint and Subcontracting Tue, 02 Sep 2014 12:26:58 +0000 We propose an analytical scheduling model with subcontracting. Each job can be processed either on a single machine at a manufacturer or outsourced to a subcontractor, possibly at a higher cost. For a given set of jobs, the decisions the manufacturer needs to make include the selection of a subset of jobs to be outsourced and the schedule of all the jobs. The objective functions are to minimize the commonly used scheduling measures, subject to a constraint on the total production and subcontracting cost. We show the NP-hardiness for the problems with different objective functions and develop dynamic programming algorithms for solving them. Guo Sun and Liying Yu Copyright © 2014 Guo Sun and Liying Yu. All rights reserved. On One Approach to TSP Structural Stability Thu, 26 Jun 2014 08:12:01 +0000 In this paper we study an inverse approach to the traveling salesman reoptimization problem. Namely, we consider the case of the addition of a new vertex to the initial TSP data and fix the simple “adaptation” algorithm: the new vertex is inserted into an edge of the optimal tour. In the paper we consider the conditions describing the vertexes that can be inserted by this algorithm without loss of optimality, study the properties of stability areas, and address several model applications. Evgeny Ivanko Copyright © 2014 Evgeny Ivanko. All rights reserved. Combining Diffusion Models and Macroeconomic Indicators with a Modified Genetic Programming Method: Implementation in Forecasting the Number of Mobile Telecommunications Subscribers in OECD Countries Mon, 16 Jun 2014 13:12:48 +0000 This paper proposes a modified Genetic Programming method for forecasting the mobile telecommunications subscribers’ population. The method constitutes an expansion of the hybrid Genetic Programming (hGP) method improved by the introduction of diffusion models for technological forecasting purposes in the initial population, such as the Logistic, Gompertz, and Bass, as well as the Bi-Logistic and LogInLog. In addition, the aforementioned functions and models expand the function set of hGP. The application of the method in combination with macroeconomic indicators such as Gross Domestic Product per Capita (GDPpC) and Consumer Prices Index (CPI) leads to the creation of forecasting models and scenarios for medium- and long-term level of predictability. The forecasting module of the program has also been improved with the multi-levelled use of the statistical indices as fitness functions and model selection indices. The implementation of the modified-hGP in the datasets of mobile subscribers in the Organisation for Economic Cooperation and Development (OECD) countries shows very satisfactory forecasting performance. Konstantinos Salpasaranis, Vasilios Stylianakis, and Stavros Kotsopoulos Copyright © 2014 Konstantinos Salpasaranis et al. All rights reserved. Disaggregation of Statistical Livestock Data Using the Entropy Approach Tue, 03 Jun 2014 08:08:03 +0000 A process of agricultural data disaggregation is developed to address the lack of updated disaggregated data concerning main livestock categories at subregional and county level in the Alentejo Region, southern Portugal. The model developed considers that the number of livestock units is a function of the agricultural and forest occupation, and data concerning the existing agricultural and forest occupation, as well as the conversion of livestock numbers into normal heads, are needed in order to find this relation. The weight of each livestock class is estimated using a dynamic process based on a generalized maximum entropy model and on a crossentropy minimization model, which comprises two stages. The model was applied to the county of Castelo de Vide and their results were validated in cross reference to real data from different sources. António Xavier, Maria de Belém Costa Freitas, and Rui Fragoso Copyright © 2014 António Xavier et al. All rights reserved. A Mathematical Model for Optimizing Organizational Learning Capability Mon, 05 May 2014 12:34:01 +0000 Learning capability is the basis of evolution in every organization. Since the simplification and development of learning level in any organization seems to be necessary, in this paper we represent a mathematical model to maximize organizational learning capability. The proposed mathematical model focuses on required cost, labor, and capital, for implementation of ten effective factors on learning capability in different parts of an organization so that they are effective in learning capability with least cost for organization. To measure the factors in different parts of an organization some metrics are introduced. Computational tests confirm the effectiveness of the model. The model is optimized by epsilon constraint while it is multiobjective one. The validation of the model is also reported to emphasize the validity and applicability of the proposed methodology. Masoomeh Alikhani and Hamed Fazlollahtabar Copyright © 2014 Masoomeh Alikhani and Hamed Fazlollahtabar. All rights reserved. Resource Constrained Project Scheduling Subject to Due Dates: Preemption Permitted with Penalty Wed, 16 Apr 2014 14:08:13 +0000 Extensive research works have been carried out in resource constrained project scheduling problem. However, scarce researches have studied the problems in which a setup cost must be incurred if activities are preempted. In this research, we investigate the resource constrained project scheduling problem to minimize the total project cost, considering earliness-tardiness and preemption penalties. A mixed integer programming formulation is proposed for the problem. The resulting problem is NP-hard. So, we try to obtain a satisfying solution using simulated annealing (SA) algorithm. The efficiency of the proposed algorithm is tested based on 150 randomly produced examples. Statistical comparison in terms of the computational times and objective function indicates that the proposed algorithm is efficient and effective. Behrouz Afshar-Nadjafi Copyright © 2014 Behrouz Afshar-Nadjafi. All rights reserved. Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns Mon, 24 Mar 2014 07:29:23 +0000 The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results. Mohamed Boualem Copyright © 2014 Mohamed Boualem. All rights reserved. Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming Thu, 13 Feb 2014 12:42:30 +0000 Data Envelopment Analysis (DEA) is a nonparametric technique to estimate the current level of efficiency of a set of entities. DEA also provides information on how to remove inefficiency through the determination of benchmarking information. This paper is devoted to study DEA models based on closest efficient targets, which are related to the shortest projection to the production frontier and allow inefficient firms to find the easiest way to improve their performance. Usually, these models have been solved by means of unsatisfactory methods since all of them are related in some sense to a combinatorial NP-hard problem. In this paper, the problem is approached by genetic algorithms and parallel programming. In addition, to produce reasonable solutions, a particular metaheuristic is proposed and checked through some numerical instances. Juan Aparicio, Jose J. Lopez-Espin, Raul Martinez-Moreno, and Jesus T. Pastor Copyright © 2014 Juan Aparicio et al. All rights reserved. Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems Wed, 27 Nov 2013 15:16:28 +0000 Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on the -convex, -convex, and -convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving -convex, -convex, and generalized -convex functions. Xiaomin Zhang and Zezhong Wu Copyright © 2013 Xiaomin Zhang and Zezhong Wu. All rights reserved. An Optimal Number-Dependent Preventive Maintenance Strategy for Offshore Wind Turbine Blades Considering Logistics Wed, 31 Jul 2013 13:35:15 +0000 In offshore wind turbines, the blades are among the most critical and expensive components that suffer from different types of damage due to the harsh maritime environment and high load. The blade damages can be categorized into two types: the minor damage, which only causes a loss in wind capture without resulting in any turbine stoppage, and the major (catastrophic) damage, which stops the wind turbine and can only be corrected by replacement. In this paper, we propose an optimal number-dependent preventive maintenance (NDPM) strategy, in which a maintenance team is transported with an ordinary or expedited lead time to the offshore platform at the occurrence of the th minor damage or the first major damage, whichever comes first. The long-run expected cost of the maintenance strategy is derived, and the necessary conditions for an optimal solution are obtained. Finally, the proposed model is tested on real data collected from an offshore wind farm database. Also, a sensitivity analysis is conducted in order to evaluate the effect of changes in the model parameters on the optimal solution. Mahmood Shafiee, Michael Patriksson, and Ann-Brith Strömberg Copyright © 2013 Mahmood Shafiee et al. All rights reserved. A Partial Backlogging Inventory Model for Deteriorating Item under Fuzzy Inflation and Discounting over Random Planning Horizon: A Fuzzy Genetic Algorithm Approach Thu, 25 Jul 2013 12:02:26 +0000 An inventory model for deteriorating item is considered in a random planning horizon under inflation and time value money. The model is described in two different environments: random and fuzzy random. The proposed model allows stock-dependent consumption rate and shortages with partial backlogging. In the fuzzy stochastic model, possibility chance constraints are used for defuzzification of imprecise expected total profit. Finally, genetic algorithm (GA) and fuzzy simulation-based genetic algorithm (FSGA) are used to make decisions for the above inventory models. The models are illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Scope and Purpose. The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, to keep sales higher, the inventory level would need to remain high. Of course, this would also result in higher holding or procurement cost. Also, in many real situations, during a longer-shortage period some of the customers may refuse the management. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging is diminishing with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large-scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any more. The purpose of this paper is to maximize the expected profit in the random planning horizon. Dipak Kumar Jana, Barun Das, and Tapan Kumar Roy Copyright © 2013 Dipak Kumar Jana et al. All rights reserved. Partnership Selection Involving Mixed Types of Uncertain Preferences Thu, 27 Jun 2013 09:25:02 +0000 Partnership selection is an important issue in management science. This study proposes a general model based on mixed integer programming and goal-programming analytic hierarchy process (GP-AHP) to solve partnership selection problems involving mixed types of uncertain or inconsistent preferences. The proposed approach is designed to deal with crisp, interval, step, fuzzy, or mixed comparison preferences, derive crisp priorities, and improve multiple solution problems. The degree of fulfillment of a decision maker’s preferences is also taken into account. The results show that the proposed approach keeps more solution ratios within the given preferred intervals and yields less deviation. In addition, the proposed approach can treat incomplete preference matrices with flexibility in reducing the number of pairwise comparisons required and can also be conveniently developed into a decision support system. Li-Ching Ma Copyright © 2013 Li-Ching Ma. All rights reserved. Mathematical Programming Approach to the Optimality of the Solution for Deterministic Inventory Models with Partial Backordering Thu, 20 Jun 2013 16:41:09 +0000 We give an alternative proof of the optimality of the solution for the deterministic EPQ with partial backordering (EPQ-PBO) [Omega, vol. 37, no. 3, pp. 624–636, 2009]. Our proof is based on the mathematical programming theory. We also demonstrate the determination of the optimal decision policy through solving the corresponding mathematical programming problem. We indicate that the same approach can be used within other inventory models with partial backordering, and we consider additional models. Irena Stojkovska Copyright © 2013 Irena Stojkovska. All rights reserved. An Inventory Model with Price and Quality Dependent Demand Where Some Items Produced Are Defective Thu, 13 Jun 2013 15:24:40 +0000 This paper analyzes an inventory system for joint determination of product quality and selling price where a fraction of items produced are defective. It is assumed that only a fraction of defective items can be repaired/reworked. The demand rate depends upon both the quality and the selling price of the product. The production rate, unit price, and carrying cost depend upon the quality of the items produced. Quality index is used to determine the quality of the product. An algorithm is provided to solve the model with given values of model parameters. Sensitivity analysis has also been performed. Tapan Kumar Datta Copyright © 2013 Tapan Kumar Datta. All rights reserved. On the Nonsymmetric Longer Queue Model: Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits Mon, 13 May 2013 15:51:17 +0000 We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server. The exponential server devotes all of its capacity to the longer of the queues. If both queues are of equal length, the server devotes of its capacity to the first queue and the remaining to the second. We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network. Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable. Charles Knessl and Haishen Yao Copyright © 2013 Charles Knessl and Haishen Yao. All rights reserved. Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems Mon, 15 Apr 2013 13:49:54 +0000 We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems. The concepts of well-posedness of optimization problems in the sense of Tychonov, Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed. It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke. The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the “classical” Lagrangian. However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the “classical” Lagrangians. Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented. Stefan M. Stefanov Copyright © 2013 Stefan M. Stefanov. All rights reserved. A Generalized Learning Curve Adapted for Purchasing and Cost Reduction Negotiations Wed, 13 Feb 2013 09:54:56 +0000 This paper presents the use and validation of a generalized learning curve in the economies of scale purchasing experience. The model, based on Wright’s curve, incorporates two extra degrees of freedom to accommodate initial purchases of multiple (instead of single) units and a finite asymptotic price at high volumes. The study shows that each time the part purchase quantity is doubled, the price is reduced either by a constant percentage (a learning rate) or by an approach to an asymptotic plateau rate indicating a point of diminishing returns. Supplier price quotations at multiple purchase quantities were obtained for a pool of 17 critical parts. The data were fitted with the generalized learning curve by the method of least squares regression. The regressed learning rate, first unit price, and the asymptotic price can be used to infer supplier pricing strategies. Coupled with a “should-cost” analysis based on estimates of standard time and material, a system cost reduction task was carried out by the supply chain organization. Lam F. Wong Copyright © 2013 Lam F. Wong. All rights reserved.