We extend the classical newsvendor problem by introducing a downside risk constraint from the perspective of inventory control. At the beginning of a replenishment period the newsvendor will place an order, then he wi...We extend the classical newsvendor problem by introducing a downside risk constraint from the perspective of inventory control. At the beginning of a replenishment period the newsvendor will place an order, then he will review the inventory level at the end of the period. If the inventory level is positive then he will bear the holding cost and if the inventory level is negative then he will bear the backorder cost. The optimal order quantity has a simple form. We analyze the form of the optimal order quantity when we restrict that the probability that the cost level is larger than or equal to a fixed cost constant is less than a fixed value of probability. At last, we analyze the case that the fixed cost constant is equal to the expected cost.展开更多
We consider an extension of the standard newsvendor problem by allowing for multiple classes of customers. The product is first sold to customers with the highest priority, and the remaining units (if any) are sold at...We consider an extension of the standard newsvendor problem by allowing for multiple classes of customers. The product is first sold to customers with the highest priority, and the remaining units (if any) are sold at a discounted price to customers in decreasing order of priority until all classes of customers have been served, limited only by the available stock. Unsold items, if any, have a salvage value. The demands of different priority customers are independent random variables with known probability distributions. The problem is to find the purchase quantity that maximizes the expected profit. We show that this problem actually reduces to the standard newsvendor problem with the demand distribution being a mixture of the input demand distributions. Since this mixture of distributions is typically hard to handle analytically, we propose a simple general heuristic which can be implemented using different types of distributions. Some of these implementations produce near optimal solutions. We tested these implementations for the case of two demand classes of customers and found that they outperform previously published heuristics in almost all instances. We suggest applications for this model in the Chinese pharmaceutical industry, apparel industry, and perishable goods among others. We also propose an extension involving shortage cost.展开更多
In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the ...In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting Conditional value-at-risk （CVaR） as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perforl~, comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include： （i） For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. （it） In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk- neutral counterpart. （iii） For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.展开更多
This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk （CVaR） in a newsvendor model setting. We find out that： i） The optimal order quantity is increas...This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk （CVaR） in a newsvendor model setting. We find out that： i） The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective, ii） For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution, iii） Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.展开更多
For seasonal products, the retailers usually launch various marketing ettorts, llKe aaverusmg tmu promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capac...For seasonal products, the retailers usually launch various marketing ettorts, llKe aaverusmg tmu promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capacity constraint and outsotlrcing into consideration. Considering the shorten life cycles of most products, in this paper we adopt the traditional newsvendor model to investigate the optimal marketing effort along with optimal order quantity. We address the risk aversion issue and characterize the influence of the sellers＇ risk propensity with CVaR criterion, and we develop an effective algorithm to obtain the optimal strategy. The impact of sellers＇ risk propensity on the performance of the system is illustrated via numerical examples, The innovation of this paper is threefold. First, the optimal joint strategy of the marketing effort and order quantity is investigated and an efficient algorithm to find the optimal strategy is developed. Second, the capacity constraint option and an outsourcing strategy are studied jointly for excess products. Finally, the risk propensity of the seller and its influence are investigated by using the CVaR criterion, through which we obtain some new managerial insights.展开更多
This paper investigates the ordering policy for the newsvendor problem with customer balking and penalties for balking and stockout. Our analysis is based on the assumption that only the mean and the variance of the d...This paper investigates the ordering policy for the newsvendor problem with customer balking and penalties for balking and stockout. Our analysis is based on the assumption that only the mean and the variance of the demand distribution are known. In contrast to the existing research, we provide a new tradeoff tool as a replacement of the traditional one to weigh the holding cost and the goodwill cost segment： the balking penalty cost and the stockout penalty cost. Specifically, in addition to the stockout penalty, we also introduce the balking penalty, provide a new proof of the optimality of robust ordering policy to guarantee that the lower bound of expected profit obtained by us is tight, and get an robust optimal order quantity which is an exact solution but not an approximate one as before. Numerical experiments are conducted to illustrate the effect of penalties for balking and stockout.展开更多
基金Supported by the National Natural Science Foundation of China (70471034, A0324666)
文摘We extend the classical newsvendor problem by introducing a downside risk constraint from the perspective of inventory control. At the beginning of a replenishment period the newsvendor will place an order, then he will review the inventory level at the end of the period. If the inventory level is positive then he will bear the holding cost and if the inventory level is negative then he will bear the backorder cost. The optimal order quantity has a simple form. We analyze the form of the optimal order quantity when we restrict that the probability that the cost level is larger than or equal to a fixed cost constant is less than a fixed value of probability. At last, we analyze the case that the fixed cost constant is equal to the expected cost.
文摘We consider an extension of the standard newsvendor problem by allowing for multiple classes of customers. The product is first sold to customers with the highest priority, and the remaining units (if any) are sold at a discounted price to customers in decreasing order of priority until all classes of customers have been served, limited only by the available stock. Unsold items, if any, have a salvage value. The demands of different priority customers are independent random variables with known probability distributions. The problem is to find the purchase quantity that maximizes the expected profit. We show that this problem actually reduces to the standard newsvendor problem with the demand distribution being a mixture of the input demand distributions. Since this mixture of distributions is typically hard to handle analytically, we propose a simple general heuristic which can be implemented using different types of distributions. Some of these implementations produce near optimal solutions. We tested these implementations for the case of two demand classes of customers and found that they outperform previously published heuristics in almost all instances. We suggest applications for this model in the Chinese pharmaceutical industry, apparel industry, and perishable goods among others. We also propose an extension involving shortage cost.
基金supported by the Social Science Foundation of the Ministry of Education of China(Grant No.07JA630015)the Natural Science Foundation of China(Grant No.70901059)Wuhan University Science Foundation for Youths Scholars(Grant No.105-275171)
文摘In this paper, we consider a newsvendor model in which a risk-averse manager faces a stochastic price-dependent demand in either an additive or a multiplicative form. An emergency purchase option is allowed after the realization of demand to satisfy the units that are short. By adopting Conditional value-at-risk （CVaR） as the decision criterion, we aim to investigate the optimal pricing and ordering decisions, and the effects of parameter changes in such a setting. We provide sufficient conditions for the uniqueness of the optimal policy for both demand models. We perforl~, comparative statics analysis to show how the optimal pricing and ordering decision behaves when changing parameters. We also compare our results with those of the newsvendor with a general utility function and with CVaR criterion under lost sales assumption. Our key results include： （i） For both demand models, the optimal selling price is decreasing in risk aversion. Hence, the optimal price of a risk-averse newsvendor is not greater than the optimal price of a risk-neutral newsvendor. （it） In contrary to the lost sales case, for the multiplicative demand model, the optimal order quantity may not be monotonic in risk aversion. Consequently, the optimal risk-averse order quantity may be lower or higher than the optimal risk- neutral counterpart. （iii） For the additive model, the optimal order quantity is strictly increasing in the emergency purchase price, while for the multiplicative model the optimal order quantity has no such a monotonic property. Some numerical examples are conducted to verify our claims and gain more insights about the risk-averse decision-making behaviors.
基金This research was supported by the Social Science Foundation of the Ministry of Education of China under Grant No. 07JA630015, the National Natural Science Foundation of China under Grant Nos. 70901059 and 70901029, and the Fundamental Research Funds for the Central Universities under Grant No. 105-275171.
文摘This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk （CVaR） in a newsvendor model setting. We find out that： i） The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective, ii） For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution, iii） Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.
基金partially supported by the National Science Foundation of China(Nos. 11171019 and 71390334)the Program for New Century Excellent Talents in University (No.NCET-11-0568)
文摘For seasonal products, the retailers usually launch various marketing ettorts, llKe aaverusmg tmu promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capacity constraint and outsotlrcing into consideration. Considering the shorten life cycles of most products, in this paper we adopt the traditional newsvendor model to investigate the optimal marketing effort along with optimal order quantity. We address the risk aversion issue and characterize the influence of the sellers＇ risk propensity with CVaR criterion, and we develop an effective algorithm to obtain the optimal strategy. The impact of sellers＇ risk propensity on the performance of the system is illustrated via numerical examples, The innovation of this paper is threefold. First, the optimal joint strategy of the marketing effort and order quantity is investigated and an efficient algorithm to find the optimal strategy is developed. Second, the capacity constraint option and an outsourcing strategy are studied jointly for excess products. Finally, the risk propensity of the seller and its influence are investigated by using the CVaR criterion, through which we obtain some new managerial insights.
文摘This paper investigates the ordering policy for the newsvendor problem with customer balking and penalties for balking and stockout. Our analysis is based on the assumption that only the mean and the variance of the demand distribution are known. In contrast to the existing research, we provide a new tradeoff tool as a replacement of the traditional one to weigh the holding cost and the goodwill cost segment： the balking penalty cost and the stockout penalty cost. Specifically, in addition to the stockout penalty, we also introduce the balking penalty, provide a new proof of the optimality of robust ordering policy to guarantee that the lower bound of expected profit obtained by us is tight, and get an robust optimal order quantity which is an exact solution but not an approximate one as before. Numerical experiments are conducted to illustrate the effect of penalties for balking and stockout.
