变质性产品库存模型研究:延期支付策略或延期交货策略
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摘要
对于变质性产品的销售,批发商为了减少变质带来的损失以及缩短流通时间,通常会在两种不同营销策略(给予顾客延期支付策略增加市场订购积极性或者采取延期交货策略减少变质损失)中做选择或者采取集成策略.但在实际操作中,如何在这两种营销策略中作出最佳选择是批发商需要考虑的问题.本文分别构建基于延期支付和延期交货的变质性产品库存决策模型,通过对两个库存模型进行分析,给出了最优策略.两个决策模型的最优策略对比结果发现:在其他参数给定的前提下,当产品的售价与进价比偏低时,批发商适合采取延期支付策略;反之,采取延期交货策略.最后利用数值算例分析了相关参数扰动对最优策略的影响,并提出了针对批发商合理制定运营策略的建议.
To sell the deteriorating products timely, distributors want to use different marketing strategies to maximize their profits, i.e. providing the credit period to increase the enthusiasm of buying or taking the delayed delivery strategy to reduce the deteriorating cost. However, for distributors, how to select the optimal strategy is a genuine problem. This paper constructs an inventory model based on a delay-in-payment strategy for deteriorating products and an inventory model based on the delayed delivery strategy, respectively. For such two models, optimal strategies are proposed, respectively. Furthermore, by comparing the two optimal strategies, we find that when the ratio of the sale price and the wholesale price is relatively low while other parameters are given, distributors can take delay-in-payment strategy, otherwise, retailers can take delayed delivery strategy. Finally, by utilizing the numerical examples, we discuss the disturbance of related parameters for the optimal strategy, and also put forward several reasonable suggestions for the distributors.
To sell the deteriorating products timely, distributors want to use different marketing strategies to maximize their profits, i.e. providing the credit period to increase the enthusiasm of buying or taking the delayed delivery strategy to reduce the deteriorating cost. However, for distributors, how to select the optimal strategy is a genuine problem. This paper constructs an inventory model based on a delay-in-payment strategy for deteriorating products and an inventory model based on the delayed delivery strategy, respectively. For such two models, optimal strategies are proposed, respectively. Furthermore, by comparing the two optimal strategies, we find that when the ratio of the sale price and the wholesale price is relatively low while other parameters are given, distributors can take delay-in-payment strategy, otherwise, retailers can take delayed delivery strategy. Finally, by utilizing the numerical examples, we discuss the disturbance of related parameters for the optimal strategy, and also put forward several reasonable suggestions for the distributors.
引文
[1] Goyal S K. Economic order quantity under conditions of permissible delay in payments[J]. Journal of the Operational Research Society, 1985, 36(4):335-338.
[2]周永务.购买费用的滞后支付对库存系统最优订货策略的影响[J].系统工程理论与实践,1997, 17(4):116-120.Zhou Y W. The effect of the delayed payment for purchasing cost on the optimal order policy of inventory system[J]. Systems Engineering-Theory&Practice, 1997, 17(4):116-120.
[3]夏海洋,黄培清.允许延期支付条件下考虑营销投入水平的退化性商品库存模型[J].中国管理科学,2008, 16(4):55-61.Xia H Y, Huang P Q. Determine optimal marketing investment level and lot sizing policy for deteriorating products under the condition of permissible delay in payments[J]. Chinese Journal of Management Science, 2008,16(4):55-61.
[4] Chang C T, Wu S J, Chen L C. Optimal payment time with deteriorating items under inflation and permissible delay in payments[J]. International Journal of Systems Science, 2009, 40(10):985-993.
[5] 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.
[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] Soni H N. Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity[J]. Applied Mathematical Modelling, 2013, 37(8):5887-5895.
[8] Lou K R, Wang W C. Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk[J]. Journal of the Operational Research Society, 2013, 64:1551—1556.
[9] 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):315-321.
[10] Sarkar B, Mandal B, Sarkar S. Quality improvement and backorder price discount under controllable lead time in an inventory model[J]. Journal of Manufacturing Systems, 2015, 35:26-36.
[11] Wu J, Ouyang L Y, Eduardo C B, et al. Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing[J]. European Journal of Operational Research, 2014, 237(3):898-908.
[12] Bhunia A K, Shaikh A A, Gupta R K. A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimization[J]. International Journal of Systems Science, 2015, 46(6):1036-1050.
[13] Zia N P, Taleizadeh A A. A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment[J]. Transportation Research Part E, 2015, 82:19-37.
[14] Chang H J, Dye C Y. An inventory model for deteriorating items with partial backlogging and permissible delay in payments[J]. International Journal of Systems Science, 2001, 32(3):345—352.
[15] Cheng M B, Zhang B X, Wang G Q. Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging[J]. Applied Mathematical Modelling, 2011, 35:3552-3560.
[16]刘斌,崔文田.缺货损失高于补货成本的易逝品供应链协调[J].管理工程学报,2009,23(3):150-153.Liu B, Cui W T. Supply coordination for perishable commodities with goodwill cost more than replenishing cost[J]. Journal of Industrial Engineering and Engineering Management, 2009, 23(3):150—153.
[17]曹裕,易超群,万光羽.易逝品随机生产库存动态模型动态定价、服务水平和生产控制策略[J].系统工程理论与实践,2018, 38(7):1717-1731.Cao Y, Yi C Q, Wan G Y. Dynamic pricing, service and production control strategy of stochastic productioninventory models with perishable products[J]. Systems Engineering—Theory&Practice, 2018, 38(7):1717-1731.
[18] Min J, Zhou Y W. A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint[J]. International Journal of Systems Science, 2009, 40(1):33-44.
[19] Sarkar B, Sarkar S. An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand[J]. Economic Modelling, 2013, 30:924-932.
[20]徐春明,赵道致,闵杰.减排规制下基于存货影响销售模式的易变质产品库存优化模型[J].系统工程理论与实践,2018,38(6):1512-1524.Xu C M, Zhao D Z, Min J. Optimal inventory models for deteriorating items with stock dependent demand under carbon emissions reduction[J]. Systems Engineering—Theory&Practice, 2018, 38(6):1512—1524.
[21]罗兵,冯晖,李淑梅.需求相关下顾客等待意愿不相同的特价商品的EOQ模型[J].系统工程理论与实践,2016, 36(4):884-896.Luo B, Feng H, Li S M. EOQ model for off-price merchandize with related demand under different waiting will of customers[J]. Systems Engineering—Theory&Practice, 2016, 36(4):884-896.
[22]周永务,郭金森,钟远光.基于提前订货折扣和延期支付策略下两零售商竞争问题研究[J].控制与决策,2012, 27(3):468-472.Zhou Y W, Guo J S, Zhong Y G. Research on the two retailers'competition with the advanced booking discount and delay in payment[J]. Control and Decision, 2012, 27(3):468-472.
[23] Jaggi C K, Khanna A, Verma P. Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions[J]. International Journal of Systems Science, 2011, 42(7):1185-1196.
[24] Hsieh T P, Dye C Y, Ouyang L Y. Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level[J]. Mathematical and Computer Modelling, 2010, 51(1):13-32.
[25] Zhao L. An inventory model under trapezoidal type demand, Weibull-distributed deterioration, and partial backlogging[J]. Journal of Applied Mathematics, 2014, Article ID 747419:1-10.
[26] Zhao L. Optimal replenishment policy for Weibull-distributed deteriorating items with trapezoidal demand rate and partial backlogging[J]. Mathematical Problems in Engineering, 2016, Article ID 1490712:1-10.
[27]李贵萍,段永瑞,霍佳震.非立即变质品的订购、定价与保鲜投资决策[J].系统工程理论与实践,2016, 36(6):1422-1434.Li G P, Duan Y R, Huo J Z. Ordering, pricing and preservation investment decision for non-instantaneously deteriorating items[J]. Systems Engineering—Theory&Practice, 2016, 36(6):1422-1434.
[2]周永务.购买费用的滞后支付对库存系统最优订货策略的影响[J].系统工程理论与实践,1997, 17(4):116-120.Zhou Y W. The effect of the delayed payment for purchasing cost on the optimal order policy of inventory system[J]. Systems Engineering-Theory&Practice, 1997, 17(4):116-120.
[3]夏海洋,黄培清.允许延期支付条件下考虑营销投入水平的退化性商品库存模型[J].中国管理科学,2008, 16(4):55-61.Xia H Y, Huang P Q. Determine optimal marketing investment level and lot sizing policy for deteriorating products under the condition of permissible delay in payments[J]. Chinese Journal of Management Science, 2008,16(4):55-61.
[4] Chang C T, Wu S J, Chen L C. Optimal payment time with deteriorating items under inflation and permissible delay in payments[J]. International Journal of Systems Science, 2009, 40(10):985-993.
[5] 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.
[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] Soni H N. Optimal replenishment policies for deteriorating items with stock sensitive demand under two-level trade credit and limited capacity[J]. Applied Mathematical Modelling, 2013, 37(8):5887-5895.
[8] Lou K R, Wang W C. Optimal trade credit and order quantity when trade credit impacts on both demand rate and default risk[J]. Journal of the Operational Research Society, 2013, 64:1551—1556.
[9] 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):315-321.
[10] Sarkar B, Mandal B, Sarkar S. Quality improvement and backorder price discount under controllable lead time in an inventory model[J]. Journal of Manufacturing Systems, 2015, 35:26-36.
[11] Wu J, Ouyang L Y, Eduardo C B, et al. Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing[J]. European Journal of Operational Research, 2014, 237(3):898-908.
[12] Bhunia A K, Shaikh A A, Gupta R K. A study on two-warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimization[J]. International Journal of Systems Science, 2015, 46(6):1036-1050.
[13] Zia N P, Taleizadeh A A. A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment[J]. Transportation Research Part E, 2015, 82:19-37.
[14] Chang H J, Dye C Y. An inventory model for deteriorating items with partial backlogging and permissible delay in payments[J]. International Journal of Systems Science, 2001, 32(3):345—352.
[15] Cheng M B, Zhang B X, Wang G Q. Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging[J]. Applied Mathematical Modelling, 2011, 35:3552-3560.
[16]刘斌,崔文田.缺货损失高于补货成本的易逝品供应链协调[J].管理工程学报,2009,23(3):150-153.Liu B, Cui W T. Supply coordination for perishable commodities with goodwill cost more than replenishing cost[J]. Journal of Industrial Engineering and Engineering Management, 2009, 23(3):150—153.
[17]曹裕,易超群,万光羽.易逝品随机生产库存动态模型动态定价、服务水平和生产控制策略[J].系统工程理论与实践,2018, 38(7):1717-1731.Cao Y, Yi C Q, Wan G Y. Dynamic pricing, service and production control strategy of stochastic productioninventory models with perishable products[J]. Systems Engineering—Theory&Practice, 2018, 38(7):1717-1731.
[18] Min J, Zhou Y W. A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint[J]. International Journal of Systems Science, 2009, 40(1):33-44.
[19] Sarkar B, Sarkar S. An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand[J]. Economic Modelling, 2013, 30:924-932.
[20]徐春明,赵道致,闵杰.减排规制下基于存货影响销售模式的易变质产品库存优化模型[J].系统工程理论与实践,2018,38(6):1512-1524.Xu C M, Zhao D Z, Min J. Optimal inventory models for deteriorating items with stock dependent demand under carbon emissions reduction[J]. Systems Engineering—Theory&Practice, 2018, 38(6):1512—1524.
[21]罗兵,冯晖,李淑梅.需求相关下顾客等待意愿不相同的特价商品的EOQ模型[J].系统工程理论与实践,2016, 36(4):884-896.Luo B, Feng H, Li S M. EOQ model for off-price merchandize with related demand under different waiting will of customers[J]. Systems Engineering—Theory&Practice, 2016, 36(4):884-896.
[22]周永务,郭金森,钟远光.基于提前订货折扣和延期支付策略下两零售商竞争问题研究[J].控制与决策,2012, 27(3):468-472.Zhou Y W, Guo J S, Zhong Y G. Research on the two retailers'competition with the advanced booking discount and delay in payment[J]. Control and Decision, 2012, 27(3):468-472.
[23] Jaggi C K, Khanna A, Verma P. Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions[J]. International Journal of Systems Science, 2011, 42(7):1185-1196.
[24] Hsieh T P, Dye C Y, Ouyang L Y. Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level[J]. Mathematical and Computer Modelling, 2010, 51(1):13-32.
[25] Zhao L. An inventory model under trapezoidal type demand, Weibull-distributed deterioration, and partial backlogging[J]. Journal of Applied Mathematics, 2014, Article ID 747419:1-10.
[26] Zhao L. Optimal replenishment policy for Weibull-distributed deteriorating items with trapezoidal demand rate and partial backlogging[J]. Mathematical Problems in Engineering, 2016, Article ID 1490712:1-10.
[27]李贵萍,段永瑞,霍佳震.非立即变质品的订购、定价与保鲜投资决策[J].系统工程理论与实践,2016, 36(6):1422-1434.Li G P, Duan Y R, Huo J Z. Ordering, pricing and preservation investment decision for non-instantaneously deteriorating items[J]. Systems Engineering—Theory&Practice, 2016, 36(6):1422-1434.