The S-shaped and Concave Shaped Advertising Effects in a Distribution Free Newsboy Problem

• Main Authors: HUNG-HSIU LIAO, 廖宏修
• Other Authors: none
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/92101095158663360236

碩士 === 東吳大學 === 企業管理學系 === 97 === Single-period problem always have features such as perishable or having a discount while overdue. The research combines the advertising effects and distribution free newsboy problem .Under the object of profit maximum, calculate the optimal order quantity and optimal advertising cost to provide a managerial insights for inventory controller and marketing persons. There are three advertising effects in this research. First, in the CVC, advertising increases only the mean demand. Second, in the CCVC, advertising increases both the mean and the variance of demand in a proportional fashion .Third, in the ICVC, advertising increases the variance of demand at a faster rate than it increases the mean demand. We consider two advertising effect functions. First, S shaped advertising effect function. And concave shaped advertising effect function. The research finds the effects of model parameters on advertising cost, order quantity and total profit through sensitivity. The result of this research are : (1) when the unit cost increases ,the optimal advertising cost, optimal order quantity and the lower bound of total profits increase. (2)when the discount rate increases, except the advertising cost in CVC case is a horizontal line, but decreases in CCVC and ICVC. The optimal order quantity and the lower bound of total profits in three case decrease. (3)when mark price increase, the advertising cost, the optimal order and the lower bound of total profits increase in three cases. In the S shaped function, the advertising cost in three case decreases concave downwards, and in concave shaped function, the advertising cost increases concave upwards. (4)when original demand average increase, in three case , the advertising cost effect in the S shaped and in concave shaped are the same . The optimal order quantity in the S shaped decreases but in concave shaped increases. The lower bound of total profits in two functions increases. (5)when original demand standard deviation increase, the advertising cost in the S shaped and in concave shaped are the same, in CVC it is a horizontal line ,and in CCVC and ICVC it decreases. The lower bound of total profits decreases in all case. There are three situations to discuss the optimal order quantity. First, when m>d the optimal order quantity increases. Second, when m=d the optimal order quantity is a horizontal line. Third, when m<d the optimal order quantity decreases. (6)when the maximum market potential increases, in three case, the advertising cost, the optimal order quantity and the lower bound of total profits increase (7)when the advertising coefficient increase, the advertising cost in S shaped decreases concave downwards, the optimal order quantity and the lower bound of total profits in S shaped are increase concave downwards . The advertising cost in concave shaped are increase concave upwards, the optimal order quantity and the profit in ICVC case increases concave downwards, and in CVC and CCVC increase concave upwards. (8)when the decay constant increases, the advertising cost increases in S shaped , but it decreases concave upward in concave shaped function.