Search results for: Production costs

Authors: L. Krpalkova, N. O' Mahony, A. Carvalho, S. Campbell, S. Harapanahalli, J. Walsh

Abstract:

The objective of this study was to determine the effects of environmental stressors on the performance of lactating dairy cows and discuss some future trends. There exists a relationship between the meteorological data and milk yield prediction accuracy in pasture-based dairy systems. New precision technologies are available and are being developed to improve the sustainability of the dairy industry. Some of these technologies focus on welfare of individual animals on dairy farms. These technologies allow the automatic identification of animal behaviour and health events, greatly increasing overall herd health and yield while reducing animal health inspection demands and long-term animal healthcare costs. The data set consisted of records from 489 dairy cows at two dairy farms and temperature measured from the nearest meteorological weather station in 2018. The effects of temperature on milk production and behaviour of animals were analyzed. The statistical results indicate different effects of temperature on milk yield and behaviour. The “comfort zone” for animals is in the range 10 °C to 20 °C. Dairy cows out of this zone had to decrease or increase their metabolic heat production, and it affected their milk production and behaviour.

Keywords: Behaviour, milk yield, temperature, precision technologies.

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Authors: Govind Sharan Dangayach, Himanshu Bhatt

Abstract:

The paper attempts to overcome the fluctuations occurring in demand of the components in an automotive sector company. Resource and time being the strict constraints, the production is not able to match the pace of the fluctuating demand. So, we introduce some production schedules that help in meeting out the required demand. The merits and demerits of the approaches are also highlighted.

Keywords: Production scheduling, Demand rise, Capacity constrained resource (CCR), Overtime.

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Authors: G. Schuh, T. Potente, D. Kupke, S. Ivanescu

Abstract:

As German companies roll out their standardized production systems to offshore manufacturing plants, they face the challenge of implementing them in different cultural environments. Studies show that the local adaptation is one of the key factors for a successful implementation. Thus the question arises of where the line between standardization and adaptation can be drawn. To answer this question the influence of culture on production systems is analysed in this paper. The culturally contingent components of production systems are identified. Also the contingency factors are classified according to their impact on the necessary adaptation changes and implementation effort. Culturally specific decision making, coordination, communication and motivation patterns require one-time changes in organizational and process design. The attitude towards rules requires more intense coaching and controlling. Lastly a framework is developed to depict standardization and adaption needs when transplanting production systems into different cultural environments.

Keywords: Culture, influence of national culture on production systems, lean production, production systems.

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Authors: J. Ranogajec, O. Rudic, S. Pasalic, S. Vucetic, D. Cjepa

Abstract:

The paper involves a chain of activities from synthesis, establishment of the methodology for characterization and testing of novel protective materials through the pilot production and application on model supports. It summarizes the results regarding the development of the pilot production protocol for newly developed self-cleaning materials. The optimization of the production parameters was completed in order to improve the most important functional properties (mineralogy characteristics, particle size, self-cleaning properties and photocatalytic activity) of the newly designed nanocomposite material.

Keywords: Cultural heritage. Materials compatibility. Pilot production. Self-cleaning.

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Authors: Ons Sassi, Wahiba Ramdane Cherif-Khettaf, Ammar Oulamara

Abstract:

In this paper, we consider the vehicle routing problem with mixed fleet of conventional and heterogenous electric vehicles and time dependent charging costs, denoted VRP-HFCC, in which a set of geographically scattered customers have to be served by a mixed fleet of vehicles composed of a heterogenous fleet of Electric Vehicles (EVs), having different battery capacities and operating costs, and Conventional Vehicles (CVs). We include the possibility of charging EVs in the available charging stations during the routes in order to serve all customers. Each charging station offers charging service with a known technology of chargers and time dependent charging costs. Charging stations are also subject to operating time windows constraints. EVs are not necessarily compatible with all available charging technologies and a partial charging is allowed. Intermittent charging at the depot is also allowed provided that constraints related to the electricity grid are satisfied. The objective is to minimize the number of employed vehicles and then minimize the total travel and charging costs. In this study, we present a Mixed Integer Programming Model and develop a Charging Routing Heuristic and a Local Search Heuristic based on the Inject-Eject routine with different insertion methods. All heuristics are tested on real data instances.

Keywords: charging problem, electric vehicle, heuristics, local search, optimization, routing problem.

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Authors: F. Keller, G. Reinhart

Abstract:

The efficient and economic allocation of resources is one main goal in the field of production planning and control. Nowadays, a new variable gains in importance throughout the planning process: Energy. Energy-efficiency has already been widely discussed in literature, but with a strong focus on reducing the overall amount of energy used in production. This paper provides a brief systematic approach, how energy-supply-orientation can be used for an energy-cost-efficient production planning and thus combining the idea of energy-efficiency and energy-flexibility.

Keywords: Production planning and control, energy, efficiency, flexibility.

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Authors: Seung Woo Lee, So Jeong Nam, Jai-Kyung Lee

Abstract:

It can be said that the business sector is faced with a range of challenges–a rapidly changing business environment, an increase and diversification of customers- demands and the consequent need for quick response–for having in place flexible management and production info systems. As a matter of fact, many manufacturers have adopted production info management systems such as MES and ERP. Nevertheless, managers are having difficulties obtaining ever-changing production process information in real time, or responding quickly to any change in production related needs on the basis of such information. This is because they rely on poor production info systems which are not capable of providing real-time factory settings. If the manufacturer doesn-t have a capacity for collecting or digitalizing the 4 Ms (Man, Machine, Material, Method), which are resources for production, on a real time basis, it might to difficult to effectively maintain the information on production process. In this regard, this paper will introduce some new alternatives to the existing methods of collecting the 4 Ms in real time, which are currently comprise the production field.

Keywords: 4M, Acquisition of Data on shop-floor, Real-time machine interface

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Authors: Chia-Chen Wei, Pack Hsieh, Jeffrey Chen

Abstract:

Surface Mount Technology (SMT) is widely used in the area of the electronic assembly in which the electronic components are mounted to the surface of the printed circuit board (PCB). Most of the defects in the SMT process are mainly related to the quality of solder paste printing. These defects lead to considerable manufacturing costs in the electronics assembly industry. Therefore, the solder paste inspection (SPI) machine for controlling and monitoring the amount of solder paste printing has become an important part of the production process. So far, the setting of the SPI threshold is based on statistical analysis and experts’ experiences to determine the appropriate threshold settings. Because the production data are not normal distribution and there are various variations in the production processes, defects related to solder paste printing still occur. In order to solve this problem, this paper proposes an online machine learning algorithm, called the automatic threshold adjustment (ATA) algorithm, and closed-loop architecture in the SMT process to determine the best threshold settings. Simulation experiments prove that our proposed threshold settings improve the accuracy from 99.85% to 100%.

Keywords: Big data analytics, Industry 4.0, SPI threshold setting, surface mount technology.

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Authors: S. Kreitlein, N. Eder, A. Syed-Khaja, J. Franke

Abstract:

The importance of energy efficiency within the production processes increases steadily. For a comprehensive assessment of energy efficiency within the production process, unfortunately no tools exist or have been developed yet. Therefore the Institute for Factory Automation and Production Systems at the Friedrich-Alexander-University Erlangen-Nuremberg has developed two methods with the goal of achieving transparency and a quantitative assessment of energy efficiency namely EEV (Energy Efficiency Value) and EPE (Energetic Process Efficiency). This paper describes the basics and state-of-the-art as well as the developed approaches.

Keywords: Energy efficiency, energy efficiency value, energetic process efficiency, production.

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Authors: Sebastian Bertsch

Abstract:

In the past decades, the environment of production companies showed a permanent increase in dynamic and volatility in the form of demand fluctuations, new technologies or global crises. As a reaction to these new requirements, changeability of production systems came into attention. A changeable production system can adapt to these changes quickly and with little effort. Even though demand for changeable production exists for some time, the practical application is still insufficient.

To overcome this deficit, a three year research project at the Department of Production Systems and Logistics at the Leibniz University of Hanover/ Germany was initiated. As a result of this project, different concepts have been developed to design production changeable. An excerpt of the results will be presented in this paper. An eight step procedure will be presented to design the changeability of production logistics. This procedure has been applied at a German manufacturer of high demanding weighing machines. The developed procedure, their application in industry, as well as the major results of the application will be presented.

Keywords: Changeability, Change Drivers, Production Logistics.

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Authors: K. Knüppel, G. Meyer, P. Nyhuis

Abstract:

The increasing interconnectedness and complexity of  production processes raise the susceptibility of production systems to  failure. Therefore, the ability to respond quickly to failures is  increasingly becoming a competitive factor. The research project  "Sustainable failure management in manufacturing SMEs" is  developing a methodology to identify failures in the production and  select preventive and reactive measures in order to correct failures  and to establish sustainable failure management systems.

 

Keywords: Failure categorization, failure management, logistic performance, production optimization.

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Authors: Tomas Cechura, Michal Simon

Abstract:

This paper describes a proposal for cost calculation of warehouse processes and its usage for setting standards for performance evaluation. One of the most common options of monitoring process performance is benchmarking. The typical outcome is whether the monitored object is better or worse than an average or standard. Traditional approaches, however, cannot find any specific opportunities to improve performance or eliminate inefficiencies in processes. Higher process efficiency can be achieved for example by cost reduction assuming that the same output is generated. However, costs can be reduced only if we know their structure and we are able to calculate them accurately. In the warehouse process area it is rather difficult because in most cases we have available only aggregated values with low explanatory ability. The aim of this paper is to create a suitable method for calculating the storage costs. At the end is shown a practical example of process calculation.

Keywords: Calculation, Costs, Performance, Process, Warehouse.

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Authors: Michael Grigutsch, Marco Kennemann, Peter Nyhuis

Abstract:

Due to the recovering global economy, enterprises are increasingly focusing on logistics. Investing in logistic measures for a production generates a large potential for achieving a good starting point within a competitive field. Unlike during the global economic crisis, enterprises are now challenged with investing available capital to maximize profits. In order to be able to create an informed and quantifiably comprehensible basis for a decision, enterprises need an adequate model for logistically and monetarily evaluating measures in production. The Collaborate Research Centre 489 (SFB 489) at the Institute for Production Systems (IFA) developed a Logistic Information System which provides support in making decisions and is designed specifically for the forging industry. The aim of a project that has been applied for is to now transfer this process in order to develop a universal approach to logistically and monetarily evaluate measures in production.

Keywords: Measures in Production, Logistic Operating Curves, Transfer Functions, Production Logistics

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Authors: Baby Joseph, Sankarganesh Palaniyandi

Abstract:

The enzyme alkaline protease production was determined under solid state fermentation using the soil bacteria Serratia marcescens sp7. The maximum production was obtained from wheat bran medium than ground nut shell and chemically defined medium. The physiological fermentation factors such as pH of the medium (pH 8), Temperature (40oC) and incubation time (48 hrs) played a vital role in alkaline protease production in all the above. 100Mm NaCl has given better resolution during elution of the enzymes. The enzyme production was found to be associated with growth of the bacterial culture.

Keywords: Alkaline protease, Wheat bran, Ground nut shell, Serratia marcescens

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Authors: A. O. Salami

Abstract:

The transportation problems are primarily concerned with the optimal way in which products produced at different plants (supply origins) are transported to a number of warehouses or customers (demand destinations). The objective in a transportation problem is to fully satisfy the destination requirements within the operating production capacity constraints at the minimum possible cost. The objective of this study is to determine ways of minimizing transportation cost in order to maximum profit. Data were sourced from the records of the Distribution Department of 7-Up Bottling Company Plc., Ilorin, Kwara State, Nigeria. The data were computed and analyzed using the three methods of solving transportation problem. The result shows that the three methods produced the same total transportation costs amounting to N1, 358, 019, implying that any of the method can be adopted by the company in transporting its final products to the wholesale dealers in order to minimize total production cost. 

Keywords: Allocation problem, Cost Minimization, Distribution system, Resources utilization.

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Authors: Mehmet Savsar

Abstract:

This paper presents a model for an unreliable production line, which is operated according to demand with constant work-in-process (CONWIP). A simulation model is developed based on the discrete model and several case problems are analyzed using the model. The model is utilized to optimize storage space capacities at intermediate stages and the number of kanbans at the last stage, which is used to trigger the production at the first stage. Furthermore, effects of several line parameters on production rate are analyzed using design of experiments.

Keywords: Production line simulator, Push-pull system, JIT system, Constant WIP, Machine failures.

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Authors: Behrouz Afshar Nadjafi

Abstract:

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where production period length is constrained. In this paper, we address the problem of deciding the optimal production quantity and the number of minor setups within each cycle, in which, production period length is constrained but a minor setup is possible for pass the constraint. A mathematical model is developed and Iterated Local Search (ILS) is proposed to solve this problem. Finally, solution procedure illustrated with a numerical example and results are analyzed.

Keywords: EPQ, Inventory control, minor setup, ILS.

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Authors: Chan-Sik Kim, Jong-Seong Kim, Se Won Lee, Hoo-Gon Choi

Abstract:

In rapidly changing market environment, firms are investing a lot of time and resources into new product development (NPD) projects to make profit and to obtain competitive advantage. However, failure rate of NPD projects is becoming high due to various internal and external risks which hinder successful NPD projects. To reduce the failure rate, it is critical that risks have to be managed effectively and efficiently through good strategy, and treated by optimal responses to minimize risk cost. Four strategies are adopted to handle the risks in this study. The optimal responses are characterized by high reduction of risk costs with high efficiency. This study suggests a framework to decide the optimal responses considering the core risks, risk costs, response efficiency and response costs for successful NPD projects. Both binary particles warm optimization (BPSO) and multi-objective particle swarm optimization (MOPSO) methods are mainly used in the framework. Although several limitations exist in use for real industries, the frame work shows good strength for handling the risks with highly scientific ways through an example.

Keywords: NPD projects, risk cost, strategy, optimal responses, Particle Swarm Optimization.

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Authors: Amir Azizi, Amir Yazid B. Ali, Loh Wei Ping

Abstract:

Throughput is an important measure of performance of production system. Analyzing and modeling of production throughput is complex in today-s dynamic production systems due to uncertainties of production system. The main reasons are that uncertainties are materialized when the production line faces changes in setup time, machinery break down, lead time of manufacturing, and scraps. Besides, demand changes are fluctuating from time to time for each product type. These uncertainties affect the production performance. This paper proposes Bayesian inference for throughput modeling under five production uncertainties. Bayesian model utilized prior distributions related to previous information about the uncertainties where likelihood distributions are associated to the observed data. Gibbs sampling algorithm as the robust procedure of Monte Carlo Markov chain was employed for sampling unknown parameters and estimating the posterior mean of uncertainties. The Bayesian model was validated with respect to convergence and efficiency of its outputs. The results presented that the proposed Bayesian models were capable to predict the production throughput with accuracy of 98.3%.

Keywords: Bayesian inference, Uncertainty modeling, Monte Carlo Markov chain, Gibbs sampling, Production throughput

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Authors: F. Brunke, L. Waalkes, C. Siemers

Abstract:

Due to reduced stiffness, research on second generation titanium alloys for implant applications, like the metastable β-titanium alloy Ti-15Mo, become more and more important in the recent years. The machinability of these alloys is generally poor leading to problems during implant production and comparably large production costs. Therefore, in the present study, Ti-15Mo was alloyed with 0.8 wt.-% of the rare earth metals lanthanum (Ti-15Mo+0.8La) and neodymium (Ti-15Mo+0.8Nd) to improve its machinability. Their microstructure consisted of a titanium matrix and micrometer-size particles of the rare earth metals and two of their oxides. The particles stabilized the microstructure as grain growth was minimized. As especially the ductility might be affected by the precipitates, the behavior of Ti-15Mo+0.8La and Ti- 15Mo+0.8Nd was investigated during static and dynamic deformation at elevated temperature to develop a processing route. The resulting mechanical properties (static strength and ductility) were similar in all investigated alloys.

Keywords: Ti-15Mo, Titanium alloys, Rare earth metals, Free-machining alloy.

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Authors: Bashir Ahmmad, Kensaku Kanomata, Fumihiko Hirose

Abstract:

The effect of carbon materials on TiO₂ for the photocatalytic hydrogen gas production from water / alcohol mixtures was investigated. Single walled carbon nanotubes (SWNTs), multi walled carbon nanotubes (MWNTs), carbon nanofiber (CNF), fullerene (FLN), graphite (GP), and graphite silica (GS) were used as co-catalysts by directly mixing with TiO₂. Drastic synergy effects were found with increase in the amount of hydrogen gas by a factor of ca. 150 and 100 for SWNTs and GS with TiO₂, respectively. Moreover, the increment factor of hydrogen production reached to 180, when the mixture of SWNTs and TiO₂ were smashed in an agate mortar before photocatalytic reactions. The order of H₂ gas production for these carbon materials was SWNTs > GS >> MWNTs > FLN > CNF > GP. To maximize the hydrogen production from SWNTs/TiO₂, various parameters of experimental condition were changed. Also, a comparison between Pt/TiO₂, SWNTs/TiO₂ and GS/TiO₂ was made for the amount of H₂ gas production. Finally, the recyclability of SWNTs/TiO₂or GS/TiO₂ was tested.

Keywords: Photocatalysis, carbon materials, alcohol reforming, hydrogen production, titanium oxide.

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Authors: F. Ardestani, S.A. Fatemi, B. Yakhchali, M. Hosseyni, G. Najafpour

Abstract:

Mycophenolic acid “MPA" is a secondary metabolite of Penicillium bervicompactum with antibiotic and immunosuppressive properties. In this study, fermentation process was established for production of mycophenolic acid by Penicillium bervicompactum MUCL 19011 in shake flask. The maximum MPA production, product yield and productivity were 1.379 g/L, 18.6 mg/g glucose and 4.9 mg/L.h respectively. Glucose consumption, biomass and MPA production profiles were investigated during fermentation time. It was found that MPA production starts approximately after 180 hours and reaches to a maximum at 280 h. In the next step, the effects of methionine and acetate concentrations on MPA production were evaluated. Maximum MPA production, product yield and productivity (1.763 g/L, 23.8 mg/g glucose and 6.30 mg/L. h respectively) were obtained with using 2.5 g/L methionine in culture medium. Further addition of methionine had not more positive effect on MPA production. Finally, results showed that the addition of acetate to the culture medium had not any observable effect on MPA production.

Keywords: Penicillium bervicompactum, Methionine, Mycophenolic acid, Submerged culture

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Authors: Tomáš Brabenec

Abstract:

Cost contribution arrangements (CCAs) and Cost sharing agreements (CCAs) belong to the tools of modern finance management. Costs spend by associated enterprises on developing producing or obtaining assets, services or rights (in general - benefits) are used for tax optimizing too. The main purpose of joint research and development, producing or obtaining benefits is to lower these costs as much as possible or to maximize the benefits. In this article is mentioned the problematic of transfer pricing and arm's length principle with connection of CCAs, CSAs. Next, there is mentioned how to settle participation shares of the total cost and benefits contributions with respect to the OECD Transfer pricing for MNEs Guidelines and with respect to other significant regulations.

Keywords: Arm's length principle, Cost contribution arrangements, Cost sharing agreements, Reasonable anticipated benefits, Relevant costs, Transfer prices.

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Authors: Mahdieh Allahviranloo

Abstract:

This paper introduces a mixed integer programming model to find the optimum development plan for port Anzali. The model minimizes total system costs taking into account both port infrastructure costs and shipping costs. Due to the multipurpose function of the port, the model consists of 1020 decision variables and 2490 constraints. Results of the model determine the optimum number of berths that should be constructed in each period and for each type of cargo. In addition to, the results of sensitivity analysis on port operation quantity provide useful information for managers to choose the best scenario for port planning with the lowest investment risks. Despite all limitations-due to data availability-the model offers a straightforward decision tools to port planners aspiring to achieve optimum port planning steps.

Keywords: MILP, Multipurpose Terminal, Port Operation Optimization, Port Anzali.

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Authors: M. H. M. Rusli, A. Jaffar, M. T. Ali, S. Muhamud @ Kayat

Abstract:

Lean manufacturing is a production philosophy made popular by Toyota Motor Corporation (TMC). It is globally known as the Toyota Production System (TPS) and has the ultimate aim of reducing cost by thoroughly eliminating wastes or muda. TPS embraces the Just-in-time (JIT) manufacturing; achieving cost reduction through lead time reduction. JIT manufacturing can be achieved by implementing Pull system in the production. Furthermore, TPS aims to improve productivity and creating continuous flow in the production by arranging the machines and processes in cellular configurations. This is called as Cellular Manufacturing Systems (CMS). This paper studies on integrating the CMS with the Pull system to establish a Big Island-Pull system production for High Mix Low Volume (HMLV) products in an automotive component industry. The paper will use the build-in JIT system steps adapted from TMC to create the Pull system production and also create a shojinka line which, according to takt time, has the flexibility to adapt to demand changes simply by adding and taking out manpower. This will lead to optimization in production.

Keywords: Big Island layout, Lean manufacturing, Material and Information Flow Chart, Pull system production, TPS.

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Authors: S. F. Wong, W. I. Ho, B. Lin, Q. Huang

Abstract:

ERP has been used in many enterprises for management, the accuracy of the production forecasting module is vital to the decision making of the enterprise, and the profit is affected directly. Therefore, enhancing the accuracy of the production forecasting module can also increase the efficiency and profitability. To deal with a lot of data, a suitable, reliable and accurate statistics model is necessary. LSSVM and Grey System are two main models to be studied in this paper, and a case study is used to demonstrate how the combination model is effective to the result of forecasting.

Keywords: ERP, Grey System, LSSVM, production forecasting.

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Authors: Anna Dolinayova, Juraj Camaj, Martin Loch

Abstract:

Presently, it is necessary to ensure the sustainable development of passenger and freight transport. Increasing performance of road freight has had a negative impact to environment and society. It is therefore necessary to increase the competitiveness of intermodal transport, which is more environmentally friendly. The study describes the effectiveness of logistical centers realization for companies and society and research how the partial internalization of external costs reflected in the efficient use of these centers and increase the competitiveness of intermodal transport to road freight. In our research, we use the method of comparative analysis and market research to describe the advantages of logistic centers for their users as well as for society as a whole. Method normal costing is used for calculation infrastructure and total costs, method of conversion costing for determine the external costs. We modelled total society costs for road freight transport and inter modal transport chain (we assumed that most of the traffic is carried by rail) with different loading schemes for condition in the Slovak Republic. Our research has shown that higher utilization of inter modal transport chain do good not only for society, but for companies providing freight services too. Increase in use of inter modal transport chain can bring many benefits to society that do not bring direct immediate financial return. They often bring the multiplier effects, such as greater use of environmentally friendly transport mode and reduce the total society costs.

Keywords: Delivery time, economy effectiveness, logistical centers, ecological efficiency, optimization, society.

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Authors: Donglan Zha, Jiansong Si

Abstract:

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

Keywords: Bias of technical change, CES production function, elasticity of substitution, energy input.

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Authors: Fatemeh Ardestani, Seyed Safa-ali Fatemi, Bagher Yakhchali, Seyed Morteza Hosseyni, Ghasem Najafpour

Abstract:

Mycophenolic acid “MPA" is a secondary metabolite of Penicillium bervicompactum with antibiotic and immunosuppressive properties. In this study, fermentation process was established for production of mycophenolic acid by Penicillium bervicompactum MUCL 19011 in shake flask. The maximum MPA production, product yield and productivity were 1.379 g/L, 18.6 mg/g glucose and 4.9 mg/L.h respectively. Glucose consumption, biomass and MPA production profiles were investigated during fermentation time. It was found that MPA production starts approximately after 180 hours and reaches to a maximum at 280 h. In the next step, the effects of methionine and acetate concentrations on MPA production were evaluated. Maximum MPA production, product yield and productivity (1.763 g/L, 23.8 mg/g glucose and 6.30 mg/L. h respectively) were obtained with using 2.5 g/L methionine in culture medium. Further addition of methionine had not more positive effect on MPA production. Finally, results showed that the addition of acetate to the culture medium had not any observable effect on MPA production

Keywords: Penicillium bervicompactum, Methionine, Mycophenolic acid, Submerged culture.

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Authors: S. Hamid Mirmohammadi, Shahrazad Tamjidzad

Abstract:

This paper is concerned with the single-item continuous review inventory system in which demand is stochastic and discrete. The budget consumed for purchasing the ordered items is not restricted but it incurs extra cost when exceeding specific value. The unit purchasing price depends on the quantity ordered under the all-units discounts cost structure. In many actual systems, the budget as a resource which is occupied by the purchased items is limited and the system is able to confront the resource shortage by charging more costs. Thus, considering the resource shortage costs as a part of system costs, especially when the amount of resource occupied by the purchased item is influenced by quantity discounts, is well motivated by practical concerns. In this paper, an optimization problem is formulated for finding the optimal (r, Q) policy, when the system is influenced by the budget limitation and a discount pricing simultaneously. Properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs.

Keywords: (r, Q) policy, Stochastic demand, backorders, limited resource, quantity discounts.

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