Search results for: point of sales

Authors: A. Alamäki, T. Kaski

Abstract:

The value co-creation has gained much attention in sales research, but less is known about how salespeople and customers interact in the authentic business to business (B2B) sales meetings. The study presented in this paper empirically contributes to existing research by presenting authentic B2B sales meetings that were video recorded and analyzed using observation and qualitative content analysis methods. This paper aims to study key elements of successful sales interactions between salespeople and customers/ buyers. This study points out that salespeople are selling value rather than the products or services themselves, which are only enablers in realizing business benefits. Therefore, our findings suggest that promoting and easing open discourse is an essential part of a successful sales encounter. A better understanding of how salespeople and customers successfully interact would help salespeople to develop their interpersonal sales skills.

Keywords: Personal selling, Relationship, Sales Management, Value Co-Creation.

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Authors: Gen Sakoda, Hideki Takayasu, Misako Takayasu

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Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant  of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual  value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.

Keywords: Food waste reduction, particle filter, point of sales, sustainable development goals, Taylor's Law, time series analysis.

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Authors: Jasna Prester, Najla Podrug, Davor Filipović

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Manufacturing companies invest a significant amount of sales into material resources for production. In our sample, 58% of sales is used for manufacturing inputs, while only 24% of sales is used for salaries. This means that if a company is looking to reduce costs, the greater potential is in reduction of material costs than downsizing. This research shows that manufacturing companies in Croatia did realize material savings in last three years. It is also shown by which technologies they achieved materials cost savings. Through literature research, we found research gap as to which technologies reduce material consumption. As methodology of research four regression analyses are used to prove our findings.

Keywords: Croatia, materials savings strategies, technologies, return on sales.

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Authors: Masao Ohta, Yoshiyuki Higuchi

Abstract:

This study analyses store layout among the many factors that underlie supermarket store design, this; in terms of what to display in a shop and where to place the items. This report examines newly-opened stores and evaluates their interior shop floor layouts, which we then attempt to categorize by various styles. We then consider the interaction between shop floor layout and customer behavior from the perspective of the supermarket as the seller. At this point, we focus on the “store magnets"–the main sections within the shop likely to attract customers into the store.

Keywords: Supermarket Store Layout, Sales magnet, Customer Circulation Rate, Section Drop-by Rates.

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Authors: H. Izadbakhsh, M.Hour Ali, A. Amirkhani, A. Montazeri, M. Saberi

Abstract:

The after–sales activities are nowadays acknowledged as a relevant source of revenue, profit and competitive advantage in most manufacturing industries. Top and middle management, therefore, should focus on the definition of a structured business performance measurement system for the after-sales business. The paper aims at filling this gap, and presents an integrated methodology for the after-sales network performance measurement, and provides an empirical application to automotive case companies and their official service network. This is the first study that presents an integrated multivariate approach for total assessment and improvement of after-sale services.

Keywords: Data Envelopment Analysis (DEA), Principal Component Analysis (PCA), Automotive companies, After-sale services.

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Authors: Shahin Mirshekari, Mohammadreza Moradi, Hossein Jafari, Mehdi Jafari, Mohammad Ensaf

Abstract:

This research employs Gaussian Process Regression (GPR) with an ensemble kernel, integrating Exponential Squared, Revised Matérn, and Rational Quadratic kernels to analyze pharmaceutical sales data. Bayesian optimization was used to identify optimal kernel weights: 0.76 for Exponential Squared, 0.21 for Revised Matérn, and 0.13 for Rational Quadratic. The ensemble kernel demonstrated superior performance in predictive accuracy, achieving an R² score near 1.0, and significantly lower values in MSE, MAE, and RMSE. These findings highlight the efficacy of ensemble kernels in GPR for predictive analytics in complex pharmaceutical sales datasets.

Keywords: Gaussian Process Regression, Ensemble Kernels, Bayesian Optimization, Pharmaceutical Sales Analysis, Time Series Forecasting, Data Analysis.

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Authors: Madhukar Nagare, Pankaj Dutta, Amey Kambli

Abstract:

Perishable goods constitute a large portion of retailer inventory and lose value with time due to deterioration and/or obsolescence. Retailers dealing with such goods required considering the factors of short shelf life and the dependency of sales on inventory displayed in determining optimal procurement policy. Many retailers follow the practice of using two bins - primary bin sales fresh items at a list price and secondary bin sales unsold items at a discount price transferred from primary bin on attaining certain age. In this paper, mathematical models are developed for primary bin and for secondary bin that maximizes profit with decision variables of order quantities, optimal review period and optimal selling price at secondary bin. The demand rates in two bins are assumed to be deterministic and dependent on displayed inventory level, price and age but independent of each other. The validity of the model is shown by solving an example and the sensitivity analysis of the model is also reported.

Keywords: Retail Inventory, Perishable Products, Two Bin, Profitable Sales.

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Authors: Sanja Pfeifer, Nataša Šarlija, Marina Jeger, Ana Bilandžić

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The purpose of this study is to explore the different facets of growth among micro, small and medium-sized firms in Croatia and to analyze the differences between models designed for all micro, small and medium-sized firms and those in creative industries. Three growth prediction models were designed and tested using the growth of sales, employment and assets of the company as dependent variables. The key drivers of sales growth are: prudent use of cash, industry affiliation and higher share of intangible assets. Growth of assets depends on retained profits, internal and external sources of financing, as well as industry affiliation. Growth in employment is closely related to sources of financing, in particular, debt and it occurs less frequently than growth in sales and assets. The findings confirm the assumption that growth strategies of small and medium-sized enterprises (SMEs) in creative industries have specific differences in comparison to SMEs in general. Interestingly, only 2.2% of growing enterprises achieve growth in employment, assets and sales simultaneously.

Keywords: Creative industries, growth prediction model, growth determinants, growth measures.

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Authors: V. Churkin, M. Lopatin

Abstract:

The purpose of the paper is to estimate the US small wind turbines market potential and forecast the small wind turbines sales in the US. The forecasting method is based on the application of the Bass model and the generalized Bass model of innovations diffusion under replacement purchases. In the work an exponential distribution is used for modeling of replacement purchases. Only one parameter of such distribution is determined by average lifetime of small wind turbines. The identification of the model parameters is based on nonlinear regression analysis on the basis of the annual sales statistics which has been published by the American Wind Energy Association (AWEA) since 2001 up to 2012. The estimation of the US average market potential of small wind turbines (for adoption purchases) without account of price changes is 57080 (confidence interval from 49294 to 64866 at P = 0.95) under average lifetime of wind turbines 15 years, and 62402 (confidence interval from 54154 to 70648 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 90,7%, while in the second - 91,8%. The effect of the wind turbines price changes on their sales was estimated using generalized Bass model. This required a price forecast. To do this, the polynomial regression function, which is based on the Berkeley Lab statistics, was used. The estimation of the US average market potential of small wind turbines (for adoption purchases) in that case is 42542 (confidence interval from 32863 to 52221 at P = 0.95) under average lifetime of wind turbines 15 years, and 47426 (confidence interval from 36092 to 58760 at P = 0.95) under average lifetime of wind turbines 20 years. In the first case the explained variance is 95,3%, while in the second – 95,3%.

Keywords: Bass model, generalized Bass model, replacement purchases, sales forecasting of innovations, statistics of sales of small wind turbines in the United States.

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

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Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: Bootstrap, Edgeworth approximation, independent and Identical distributed, quantile.

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Authors: M. G. Mattos, J. E. Pécora Jr, T. A. Briso

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Today's challenging business environment, with unpredictable demand and volatility, requires a supply chain strategy that handles uncertainty and risks in the right way. Even though inventory models have been previously explored, this paper seeks to apply these concepts on a practical situation. This study involves the inventory replenishment problem, applying techniques that are mainly based on mathematical assumptions and modeling. The primary goal is to improve the retailer’s supply chain processes taking store differences when setting the various target stock levels. Through inventory review policy, picking piece implementation and minimum exposure definition, we were able not only to promote the inventory reduction as well as improve sales results. The inventory management theory from literature review was then tested on a single case study regarding a particular department in one of the largest Latam retail chains.

Keywords: Inventory, distribution, retail, risk, safety stock, sales, uncertainty.

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Authors: Miho Tsukamoto

Abstract:

Since “Hello Kitty” was manufactured in the market in 1974, the manufacturer, Sanrio Co., Ltd. gains high profits not only Kitty’s products but also Kitty license, which gives us a picture of Sanrio’s sales strategy in the global market. Kitty’s history, its products, and Sanrio’s sales strategy are researched in this paper. Comparing it to American Girl, and focusing on KITTYLAB, a type of attraction where you can enjoy games with Kitty, and choose its parts to build your own Kitty, the image of the cultural icon can be altered.

Keywords: American Girl, Change, Kitty, Popularity.

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Authors: Guixia Lv, Longjun Shen

Abstract:

This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.

Keywords: Finite point method, directional derivatives, diffusionequation, method for selecting neighbor point set.

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Authors: Abhijit Mitra

Abstract:

A special case of floating point data representation is block floating point format where a block of operands are forced to have a joint exponent term. This paper deals with the finite wordlength properties of this data format. The theoretical errors associated with the error model for block floating point quantization process is investigated with the help of error distribution functions. A fast and easy approximation formula for calculating signal-to-noise ratio in quantization to block floating point format is derived. This representation is found to be a useful compromise between fixed point and floating point format due to its acceptable numerical error properties over a wide dynamic range.

Keywords: Block floating point, Roundoff error, Block exponent dis-tribution fuction, Signal factor.

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Authors: K. B. Cullen, G. C. M. Silvestre, N. J. Hurley

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This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.

Keywords: DSP devices, DSP algorithm, simulation model, software

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Authors: Soon-Tai Park, Haeryong Park, Myoung-sun Noh, Yoo-Jae Won

Abstract:

There are many expand of Wi-Fi zones provided mobile careers and usage of wireless access point at home as increase of usage of wireless internet caused by the use of smart phone. This paper shows wireless local area network status, security threats of WLAN and functionality of major wireless access point in Korea. We propose security countermeasures concerned with life cycle of access point from manufacturing to installation, using and finally disposal. There needed to releasing with configured secure at access point. Because, it is most cost effective resolution than stage of installation or other life cycle of access point.

Keywords: Wireless LAN Security, Wi-Fi Security, Wireless Access Point, Product Life-Cycle

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Authors: Wenhao Lan, Ning Li, Qiang Tong

Abstract:

To improve the registration accuracy of a source point cloud and template point cloud when the initial relative deflection angle is too large, a PointNetLK algorithm combined with an oriented bounding box (PointNetLK-OBB) is proposed. In this algorithm, the OBB of a 3D point cloud is used to represent the macro feature of source and template point clouds. Under the guidance of the iterative closest point algorithm, the OBB of the source and template point clouds is aligned, and a mirror symmetry effect is produced between them. According to the fitting degree of the source and template point clouds, the mirror symmetry plane is detected, and the optimal rotation and translation of the source point cloud is obtained to complete the 3D point cloud registration task. To verify the effectiveness of the proposed algorithm, a comparative experiment was performed using the publicly available ModelNet40 dataset. The experimental results demonstrate that, compared with PointNetLK, PointNetLK-OBB improves the registration accuracy of the source and template point clouds when the initial relative deflection angle is too large, and the sensitivity of the initial relative position between the source point cloud and template point cloud is reduced. The primary contribution of this paper is the use of PointNetLK to avoid the non-convex problem of traditional point cloud registration and leveraging the regularity of the OBB to avoid the local optimization problem in the PointNetLK context.

Keywords: Mirror symmetry, oriented bounding box, point cloud registration, PointNetLK-OBB.

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Authors: Amitava Chakraborty, Sudip Kumar De, Ranjan Dasgupta

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Point quad tree is considered as one of the most common data organizations to deal with spatial data & can be used to increase the efficiency for searching the point features. As the efficiency of the searching technique depends on the height of the tree, arbitrary insertion of the point features may make the tree unbalanced and lead to higher time of searching. This paper attempts to design an algorithm to make a nearly balanced quad tree. Point pattern analysis technique has been applied for this purpose which shows a significant enhancement of the performance and the results are also included in the paper for the sake of completeness.

Keywords: Algorithm, Height balanced tree, Point patternanalysis, Point quad tree.

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Authors: Ling-fei Xu, Qi Zhao, Yan-ru Chen, Mu-chun Zhou, Meng Zhang, Shi-xue Xu

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SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we found that there exist some regular in the characteristic curve of the flame from the mouse of pudding. And we can use SVM to predict end point of the BOF, just single spectrum intensity should be required as the input parameter. Moreover, its compatibility for the input space is better than the BP network.

Keywords: SVM, predict, BOF, single spectrum intensity.

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Authors: J. Sulaiman, M. Othman, M. K. Hasan

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Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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Authors: Jianqin Qu

Abstract:

This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: Covariant point, point matching, dimension free, rigid registration.

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Authors: Revoti Prasad Bora, Nikita Katyal

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Promotion is a key element in the retail business. Thus, analysis of promotions to quantify their effectiveness in terms of Revenue and/or Margin is an essential activity in the retail industry. However, measuring the sales/revenue uplift is based on estimations, as the actual sales/revenue without the promotion is not present. Further, the presence of Halo and Cannibalization in a multiple parallel promotions’ scenario complicates the problem. Calculating Baseline by considering inter-brand/competitor items or using Halo and Cannibalization's impact on Revenue calculations by considering Baseline as an interpretation of items’ unit sales in neighboring nonpromotional weeks individually may not capture the overall Revenue uplift in the case of multiple parallel promotions. Hence, this paper proposes a Machine Learning based method for calculating the Revenue uplift by considering the Halo and Cannibalization impact on the Baseline and the Revenue. In the first section of the proposed methodology, Baseline of an item is calculated by incorporating the impact of the promotions on its related items. In the later section, the Revenue of an item is calculated by considering both Halo and Cannibalization impacts. Hence, this methodology enables correct calculation of the overall Revenue uplift due a given promotion.

Keywords: Halo, cannibalization, promotion, baseline, temporary price reduction, retail, elasticity, cross price elasticity, machine learning, random forest, linear regression.

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Authors: José M. Brotons, Manuel E. Sansalvador

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The relationship between Corporate Social Responsibility (CSR) and financial performance (FP) is a subject of great interest that has not yet been resolved. In this work, we have developed a new and original tool to measure this relation. The tool quantifies the value contributed to companies that are committed to CSR. The theoretical model used is the fuzzy discounted cash flow method. Two assumptions have been considered, the first, the company has implemented the IQNet SR10 certification, and the second, the company has not implemented that certification. For the first one, the growth rate used for the time horizon is the rate maintained by the company after obtaining the IQNet SR10 certificate. For the second one, both, the growth rates company prior to the implementation of the certification, and the evolution of the sector will be taken into account. By using triangular fuzzy numbers, it is possible to deal adequately with each company’s forecasts as well as the information corresponding to the sector. Once the annual growth rate of the sales is obtained, the profit and loss accounts are generated from the annual estimate sales. For the remaining elements of this account, their regression with the nets sales has been considered. The difference between these two valuations, made in a fuzzy environment, allows obtaining the value of the IQNet SR10 certification. Although this study presents an innovative methodology to quantify the relation between CSR and FP, the authors are aware that only one company has been analyzed. This is precisely the main limitation of this study which in turn opens up an interesting line for future research: to broaden the sample of companies.

Keywords: Corporate social responsibility, case study, financial performance, company valuation.

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Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

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Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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Authors: Hiroki Satou, Kayoko Yamamoto

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This study aims to propose three evaluation methods to evaluate the Tokyo Cap and Trade Program when emissions trading is performed virtually among enterprises, focusing on carbon dioxide (CO2), which is the only emitted greenhouse gas that tends to increase. The first method clarifies the optimum reduction rate for the highest cost benefit, the second discusses emissions trading among enterprises through market trading, and the third verifies long-term emissions trading during the term of the plan (2010-2019), checking the validity of emissions trading partly using Geographic Information Systems (GIS). The findings of this study can be summarized in the following three points. 1. Since the total cost benefit is the greatest at a 44% reduction rate, it is possible to set it more highly than that of the Tokyo Cap and Trade Program to get more total cost benefit. 2. At a 44% reduction rate, among 320 enterprises, 8 purchasing enterprises and 245 sales enterprises gain profits from emissions trading, and 67 enterprises perform voluntary reduction without conducting emissions trading. Therefore, to further promote emissions trading, it is necessary to increase the sales volumes of emissions trading in addition to sales enterprises by increasing the number of purchasing enterprises. 3. Compared to short-term emissions trading, there are few enterprises which benefit in each year through the long-term emissions trading of the Tokyo Cap and Trade Program. Only 81 enterprises at the most can gain profits from emissions trading in FY 2019. Therefore, by setting the reduction rate more highly, it is necessary to increase the number of enterprises that participate in emissions trading and benefit from the restraint of CO2 emissions.

Keywords: Emissions Trading, Tokyo Cap and Trade Program, Carbon Dioxide (CO2), Global Warming, Geographic Information Systems (GIS)

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Authors: M. Moosavi, H. Khatibzadeh

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In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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Authors: Jelena Zagorska, Inga Ciprovica

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The freezing point of milk is in important indicator of the milk quality. The freezing point of milk is determined primarily to prove milk adulteration with water and to determine the amount of water in it. Chemical composition and properties of milk, thermal treatment and presence of any substance can influence freezing point of product. There are different substances, which can be added to milk with main purpose to prolong shelf-life of raw milk. There are detergent, preservatives, formaldehyde, hydrogen peroxide, antibiotics, sodium carbonate, and hydrogen peroxide. Therefore the aim of the present study was to determine freezing point of milk, skimmed milk, pasteurized milk and milk with different substances (formaldehyde, antibiotics, sodium carbonate, hydrogen peroxide, disinfectant, and detergent) in different concentrations. The thermal treatment and different undesirable substances presence in milk have significant influence on freezing point of it.

Keywords: Antibiotics, freezing point, milk, pH, thermal treatment.

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Authors: Mojtaba Molaahmadi, Morteza Raei Dehaghi, Abdolrahim Arghavan

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The present study aims to explore the effect of computerization on marketing performance in Snowa Company. In other words, this study intends to respond to this question that whether or not, is there any relationship between utilization of computerization in marketing activities and marketing performance? The statistical population included 60 marketing managers of Snowa Company. In order to test the research hypotheses, Pearson correlation coefficient was employed. The reliability was equal to 96.8%. In this study, computerization was the independent variable and marketing performance was the dependent variable with characteristics of market share, improving the competitive position, and sales volume. The results of testing the hypotheses revealed that there is a significant relationship between utilization of computerization and market share, sales volume and improving the competitive position.

Keywords: Computerization, e-marketing information, information technology, marketing performance.

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Authors: Ali Ihtiyar, Serdar Durdyev, Syuhaida Ismail

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Marketing is an essential issue to the survival of any real estate company in Turkey. There are some factors which are constraining the achievements of the marketing and sales strategies in the Turkey real estate industry. This study aims to identify and prioritise the most significant constraints to marketing in real estate sector and new strategies based on those constraints. This study is based on survey method, where the respondents such as credit counsellors, real estate investors, consultants, academicians and marketing representatives in Turkey were asked to rank forty seven sub-factors according to their levels of impact. The results of Multiattribute analytical technique indicated that the main subcomponents having impact on marketing in real estate sector are interest rates, real estate credit availability, accessibility, company image and consumer real income, respectively. The identified constraints are expected to guide the marketing team in a sales-effective way.

Keywords: Marketing, marketing constraints, Real estate marketing, Turkey real estate sector

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Authors: Pakkinee Chitsakul

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In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: Cut locus, flat torus, geodesics.

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