考虑保质期的非即时易腐品最优订购与定价决策
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摘要
针对有保质期约束的非即时易腐品,零售商可以在产品非腐败阶段和腐败阶段进行差异化定价来调整市场需求。即零售商可以调整产品非腐败阶段的定价策略,使得非即时易腐品在进入腐败阶段之前全部售出;或者在产品腐败阶段降低零售价格以刺激市场需求。因此,在需求依赖价格的假设下,本文研究了零售商关于有保质期约束的非即时易腐品的最优订购与定价决策。通过分析零售商单位时间利润函数的理论性质,得到了零售商的最优订购与定价策略。基于线性和指数型两种需求函数形式进行数值算例,可以发现针对保质期较长或者非腐败阶段较长的易腐品,零售商会延长订货周期来增加销售收入。特别是在指数型需求函数情境下,当市场需求与零售价格高度相关时,零售商更有意愿降价来刺激销量,从而使得易腐品在非腐败阶段内销售完毕。
Practically, the retailer could adopt differential pricing policy for the non-instantaneous deteriorating items with maximum lifetime, i.e., different selling prices would be assigned to the items with different quality. Specifically, the retailer could adjust the pricing policy for selling out the items before they start to deteriorate, or lower the selling price for the deteriorated items to stimulate the market demand. Thus, in this paper, we study the retailer's optimal ordering and pricing policies for the non-instantaneous deteriorating items with maximum lifetime, when the market demand depends on the selling price. By analyzing theoretical results of the retailer's profit functions per unit time, the retailer's optimal solution would be derived. Based on the linear and exponential demand functions, it is apparent that for the deteriorating items with longer maximum lifetime or non-deterioration stage, the retailer would adopt a longer order cycle to accumulate sales revenue. Additionally, in the context of exponential demand function, when the market demand is relatively sensitive to the selling price, the retailer is more willing to sell out the deteriorating items within the non-deterioration stage by price promotion.
Practically, the retailer could adopt differential pricing policy for the non-instantaneous deteriorating items with maximum lifetime, i.e., different selling prices would be assigned to the items with different quality. Specifically, the retailer could adjust the pricing policy for selling out the items before they start to deteriorate, or lower the selling price for the deteriorated items to stimulate the market demand. Thus, in this paper, we study the retailer's optimal ordering and pricing policies for the non-instantaneous deteriorating items with maximum lifetime, when the market demand depends on the selling price. By analyzing theoretical results of the retailer's profit functions per unit time, the retailer's optimal solution would be derived. Based on the linear and exponential demand functions, it is apparent that for the deteriorating items with longer maximum lifetime or non-deterioration stage, the retailer would adopt a longer order cycle to accumulate sales revenue. Additionally, in the context of exponential demand function, when the market demand is relatively sensitive to the selling price, the retailer is more willing to sell out the deteriorating items within the non-deterioration stage by price promotion.
引文
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[15] Wu J,Chan Y L.Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers[J].International Journal of Production Economics,2014,155:292-301.
[16] Wu J,Al-Khateeb F B,Teng J T,Cardenas-Barron L E.Inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit-risk customers by discounted cash-flow analysis[J].International Journal of Production Economics,2016,171:105-115.
[17] Teng J T,Chang C T.Economic production quantity models for deteriorating items with price-and stock-dependent demand[J].Computers & Operations Research,2005,32(2):297-308.
[18] Avinadav T,Herbon A,Spiegel U.Optimal inventory policy for a perishable item with demand function sensitive to price and time[J].International Journal of Production Economics,2013,144(2):497-506.
[19] Soni H N.Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment[J].International Journal of Production Economics,2013,146(1):259-268.
[20] Maihami R,Karimi B.Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts[J].Computers & Operations Research,2014,51:302-312.
[21] Xu M,Lu Y.The effect of supply uncertainty in price-setting newsvendor models[J].European Journal of Operational Research,2013,227(3):423- 433.
[22] Besbes O,Zeevi A.Dynamic Pricing Without Knowing the Demand Function:Risk Bounds and Near-Optimal Algorithms[J].Operations Research,2009,57(6):1407-1420.
[23] Sarkar B.An EOQ model with delay in payments and time varying deterioration rate[J].Mathematical and Computer Modelling,2012,55(3- 4):367-377.
[24] Jia T,Liu Y,Wang N,Lin F.Optimal production-delivery policy for a vendor-buyers integrated system considering postponed simultaneous delivery[J].Computers & Industrial Engineering,2016,99:1-15.
[2] Hou K L.An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting[J].European Journal of Operational Research,2006,168(2):463- 474.
[3] Chan T Y,Narasimhan C,Yoon Y.Advertising and price competition in a manufacturer-retailer channel[J].International Journal of Research in Marketing,2017,34(3):694-716.
[4] Manna S K,Chaudhuri K S.An EOQ model with ramp type demand rate,time dependent deterioration rate,unit production cost and shortages[J].European Journal of Operational Research,2006,171(2):557-566.
[5] 苏菊宁,刘晨光,殷勇,张娜.基于时间可控和随机损失的生鲜农产品供应链协调[J].运筹与管理,2015,24(5):34- 43.
[6] Liang Y,Zhou F.A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment[J].Applied Mathematical Modelling,2011,35(5):2221-2231.
[7] 贾涛,郑毅,常建龙.两级商业信用下存在顾客预付的易腐品库存模型[J].中国管理科学,2013,21(006):80- 87.
[8] Ghiami Y,Williams T,Wu Y.A two-echelon inventory model for a deteriorating item with stock-dependent demand,partial backlogging and capacity constraints[J].European Journal of Operational Research,2013,231(3):587-597.
[9] Wu K S,Ouyang L Y,Yang C T.An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging[J].International Journal of Production Economics,2006,101(2):369-384.
[10] Ouyang L Y,Wu K S,Yang C T.A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments[J].Computers & Industrial Engineering,2006,51(4):637- 651.
[11] Yang H L,Chang C T.A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation[J].Applied Mathematical Modelling,2013,37(5):2717-2726.
[12] Tat R,Taleizadeh A A,Esmaeili M.Developing economic order quantity model for non-instantaneous deteriorating items in vendor-managed inventory(VMI)system[J].International Journal of Systems Science,2015,46(7):1257-1268.
[13] Chen S C,Teng J T.Retailer’s optimal ordering policy for deteriorating items with maximum lifetime under supplier’s trade credit financing[J].Applied Mathematical Modelling,2014,38(15-16):4049- 4061.
[14] Wang W C,Teng J T,Lou K R.Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime[J].European Journal of Operational Research,2014,232(2):315-321.
[15] Wu J,Chan Y L.Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers[J].International Journal of Production Economics,2014,155:292-301.
[16] Wu J,Al-Khateeb F B,Teng J T,Cardenas-Barron L E.Inventory models for deteriorating items with maximum lifetime under downstream partial trade credits to credit-risk customers by discounted cash-flow analysis[J].International Journal of Production Economics,2016,171:105-115.
[17] Teng J T,Chang C T.Economic production quantity models for deteriorating items with price-and stock-dependent demand[J].Computers & Operations Research,2005,32(2):297-308.
[18] Avinadav T,Herbon A,Spiegel U.Optimal inventory policy for a perishable item with demand function sensitive to price and time[J].International Journal of Production Economics,2013,144(2):497-506.
[19] Soni H N.Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment[J].International Journal of Production Economics,2013,146(1):259-268.
[20] Maihami R,Karimi B.Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts[J].Computers & Operations Research,2014,51:302-312.
[21] Xu M,Lu Y.The effect of supply uncertainty in price-setting newsvendor models[J].European Journal of Operational Research,2013,227(3):423- 433.
[22] Besbes O,Zeevi A.Dynamic Pricing Without Knowing the Demand Function:Risk Bounds and Near-Optimal Algorithms[J].Operations Research,2009,57(6):1407-1420.
[23] Sarkar B.An EOQ model with delay in payments and time varying deterioration rate[J].Mathematical and Computer Modelling,2012,55(3- 4):367-377.
[24] Jia T,Liu Y,Wang N,Lin F.Optimal production-delivery policy for a vendor-buyers integrated system considering postponed simultaneous delivery[J].Computers & Industrial Engineering,2016,99:1-15.