scholarly journals A Two-Period Newsvendor Model with Product Extension and Shortage-Making Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Kuo-Hsien Wang ◽  
Che-Tsung Tung ◽  
Yuan-Chih Huang
Keyword(s):  
Optimal Order ◽  
Ripple Effect ◽  
Newsvendor Model ◽  
Numerical Examples ◽  
Deterministic Demand ◽  
Proposed Model ◽  
Demand Rate ◽  
Order Quantities ◽  
Second Period ◽  
Product Extension

This study deals with a two-period newsvendor setting in which the item in the second period is a product extension of the item in the first period. A shortage strategy toward the first item is intentionally made so as to stimulate more sales amounts of the second item. The stochastic demand of these two items is assumed to be a linear-additive pattern comprising a deterministic demand and an error demand, where the deterministic demand consists of a primary demand and a consumer price elasticity, and the error demand is hypothesized to be exponentially distributed. The objective of this study is to optimize system's overall expected profit by jointly determining the optimal order quantities and selling prices of these two items. We first compare our proposed model with the classical newsvendor model in light of profit performances, and it reveals that a higher shifting demand rate makes our model a more profitable setting. Impact on profit performances caused by an increasing primary demand of the second item is then demonstrated by numerical examples that an unthought-of ripple effect of an increasing error demand of the second item also occurs.

scholarly journals Optimal Sales Discount Decision Model with Fixed Ordered Quantities

2014 ◽  
Vol 2 (4) ◽  
pp. 345-357
Author(s):  
Shi Zheng ◽  
Wen Zheng
Keyword(s):  
Mathematical Model ◽  
Optimal Solution ◽  
Decision System ◽  
Sales Price ◽  
Maximum Profit ◽  
Proposed Model ◽  
Demand Rate ◽  
Total Profit ◽  
Fixed Order ◽  
Order Quantities

AbstractThe purpose of this paper is to study sales pricing and discount strategy for sellers. Here, the suppliers require fixed order quantities to the sellers. Therefore, to incorporate the concept of sellers’ maximum profit and sales discount into the model, the author classifies the multi-category goods into backlog, flat and profitable one. Then the model to determine the optimal sales price strategy for a sales discount decision system with fixed order quantities is analyzed. As most of the non-linear model can be linearization, a mathematical model for sales discount decision system is developed when demand rate is a liner function of the sales price. By analyzing the total profit function, the authors developed some useful results to characterize the optimal solution and provided a method to find the sales discount for holdovers. By developing a solution algorithm, the optimal retail price and sales discount for holdovers are provided. Case scenarios are presented to validate the proposed model. Through case scenarios analyses, it is observed that optimal sales discount can help the sellers earn maximum profit with constraints of fixed order quantities. Most of the research articles available in the literature assumed that the sellers are always in optimal situation. In fact, sellers’ decisions rely on suppliers’ decisions in most cases. In this paper, determination of sales discounts can be seen as sellers compromise to suppliers by seeking the optimal strategy with downstream customers. In view of this fact, a mathematical model is developed considering sales price dependent linear demand and sellers’ profit. Very few researchers have investigated optimal sales discount decision system with fixed order quantities; although it is a real situation the sellers should be faced.

scholarly journals Opportunity Loss Minimization and Newsvendor Behavior

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Xinsheng Xu ◽  
Hong Yan ◽  
Chi Kin Chan
Keyword(s):  
Conditional Value At Risk ◽  
Optimal Order ◽  
Market Demand ◽  
Newsvendor Model ◽  
Order Quantity ◽  
Loss Minimization ◽  
Decision Bias ◽  
Optimal Order Quantity ◽  
Opportunity Loss ◽  
Order Quantities

To study the decision bias in newsvendor behavior, this paper introduces an opportunity loss minimization criterion into the newsvendor model with backordering. We apply the Conditional Value-at-Risk (CVaR) measure to hedge against the potential risks from newsvendor’s order decision. We obtain the optimal order quantities for a newsvendor to minimize the expected opportunity loss and CVaR of opportunity loss. It is proven that the newsvendor’s optimal order quantity is related to the density function of market demand when the newsvendor exhibits risk-averse preference, which is inconsistent with the results in Schweitzer and Cachon (2000). The numerical example shows that the optimal order quantity that minimizes CVaR of opportunity loss is bigger than expected profit maximization (EPM) order quantity for high-profit products and smaller than EPM order quantity for low-profit products, which is different from the experimental results in Schweitzer and Cachon (2000). A sensitivity analysis of changing the operation parameters of the two optimal order quantities is discussed. Our results confirm that high return implies high risk, while low risk comes with low return. Based on the results, some managerial insights are suggested for the risk management of the newsvendor model with backordering.

scholarly journals A Price-Dependent Demand Model in the Single Period Inventory System with Price Adjustment

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kamran Forghani ◽  
Abolfazl Mirzazadeh ◽  
Mehdi Rafiee
Keyword(s):  
Optimal Order ◽  
Selling Price ◽  
Inventory Problem ◽  
Demand Model ◽  
Inventory Costs ◽  
Single Period ◽  
Proposed Model ◽  
Demand Rate ◽  
Total Inventory ◽  
Dependent Demand

The previous efforts toward single period inventory problem with price-dependent demand only investigate the optimal order quantity to minimize the total inventory costs; however, there is no method in the literature to avoid unwanted costs due to the deviation between the actual demand and the previously estimated demand. To fill this gap, the present paper supposes that stochastic demand rate with normal distribution is sensitive to the selling price; this means that increasing the selling price would decrease the demand rate and vice versa. After monitoring the consumption trend within a section of the period, a new selling price is implemented to change the demand rate and reduce the shortage or salvage costs at the end of the period. Three functions were suggested to represent the demand rate as a function of selling price, and the numerical analysis was implemented to solve the proposed problem. Finally, an illustrative numerical example was solved for different configurations in order to show the advantages of the proposed model. The results revealed that there is a significant improvement in the system costs when price revision is considered.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

scholarly journals Coping with Loss Aversion in the Newsvendor Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwu Sun ◽  
Xinsheng Xu
Keyword(s):  
Expected Utility ◽  
Loss Aversion ◽  
Confidence Level ◽  
Profit Maximization ◽  
Optimal Order ◽  
Market Demand ◽  
Newsvendor Model ◽  
Order Quantity ◽  
Decision Bias ◽  
Optimal Order Quantity

We introduce loss aversion into the decision framework of the newsvendor model. By introducing the loss aversion coefficientλ, we propose a novel utility function for the loss-averse newsvendor. First, we obtain the optimal order quantity to maximize the expected utility for the loss-averse newsvendor who is risk-neutral. It is found that this optimal order quantity is smaller than the expected profit maximization order quantity in the classical newsvendor model, which may help to explain the decision bias in the classical newsvendor model. Then, to reduce the risk which originates from the fluctuation in the market demand, we achieve the optimal order quantity to maximize CVaR about utility for the loss-averse newsvendor who is risk-averse. We find that this optimal order quantity is smaller than the optimal order quantity to maximize the expected utility above and is decreasing in the confidence levelα. Further, it is proved that the expected utility under this optimal order quantity is decreasing in the confidence levelα, which verifies that low risk implies low return. Finally, a numerical example is given to illustrate the obtained results and some management insights are suggested for the loss-averse newsvendor model.

scholarly journals Supply Chain Coordination under Stock- and Price-Dependent Selling Rates under Declining Market

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Subrata Saha ◽  
Sambhu Das ◽  
Manjusri Basu
Keyword(s):  
Supply Chain ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Stackelberg Games ◽  
Numerical Examples ◽  
Revenue Sharing Contract ◽  
Demand Rate ◽  
Time Price

We explore coordination issues of a two-echelon supply chain, consisting of a distributor and a retailer. The effect of revenue-sharing contract mechanism is examined under stock-time-price-sensitive demand rate. First, we investigate relationships between distributor and retailer under noncooperative distributor-Stackelberg games. Then we establish analytically that revenue sharing contact is able to coordinate the system and leads to the win-win outcomes. Finally, numerical examples are presented to compare results between the different models.

scholarly journals Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2208
Author(s):  
Ekaterina Morozova ◽  
Vladimir Panov
Keyword(s):  
Stock Returns ◽  
Mixture Models ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Numerical Examples ◽  
Proposed Model ◽  
Mixing Parameter ◽  
Heavy Tailed ◽  
Regularly Varying Distribution

This paper deals with the extreme value analysis for the triangular arrays which appear when some parameters of the mixture model vary as the number of observations grows. When the mixing parameter is small, it is natural to associate one of the components with “an impurity” (in the case of regularly varying distribution, “heavy-tailed impurity”), which “pollutes” another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher–Tippett–Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

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