臺灣博碩士論文加值系統

許多零售商發現提升的存貨量不只是改善服務水準而且還會刺激需求。市場學家也認定很多產品的需求會和零售商所陳列的產品數量成比例。
針對需求率會隨存貨量增加的產品，在有限規劃週期內，分別考慮在不允許缺貨、完全缺貨待補、部分缺貨待補且待補率與等待補貨時間相關的三種情況，提出需求與存貨相依下損耗性產品之存貨系統；且過去文獻較常忽略的購買成本會隨時間和數量變化的影響，本研究將此影響納入考慮，建構出零售商的成本函數。
藉由數學軟體Mathematica 5.2的幫助，找出零售商最佳的補貨次數、最佳短缺的時間點以及每週期的訂購數量，達到零售商成本極小化的目標。

In some retail contexts, stocking large quantities of inventory may not only improve service levels, but can also stimulate demand. Marketing researchers also recognize the demand of many retail items is proportional to the amount of inventory displayed.
For products having demand rates that increase with inventory levels, we present an inventory model for deteriorating items with stock-dependent demand over a finite planning horizon. In addition, we also incorporate the effect of quantity discount and time factor of purchase cost while inventory decision making. No backorders, complete backlogged and partial backlogging are considered in the model; and further, the backlogging rate is variable and dependent on the waiting time for the next replenishment.
We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs. Numerical examples are displayed to illustrate the proposed models and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

論文提要 I
ABSTRACT II
目錄 III
表目錄 V
圖目錄 VI
第一章 緒論 1
1.1 研究動機 1
1.2 研究背景 2
1.3 研究目的 5
1.4 研究架構 6
第二章 文獻回顧 8
2.1 損耗性存貨模式之相關文獻 8
2.2 數量折扣之相關文獻 9
2.3 需求模式之相關文獻 11
2.4 完全缺貨待補與部分缺貨待補之相關文獻 13
2.5 相關文獻與本研究的比較 14
第三章 模型建構 16
3.1 模式Ⅰ：不允許缺貨情況之模式建立 16
3.1.1基本假設與符號說明 16
3.1.2模型建構 17
3.2 模式Ⅱ：允許缺貨情況下完全缺貨待補之模式建立 20
3.2.1 基本假設與符號說明 20
3.2.2 模型建構 21
3.2.3求解最小值的必要與充分條件 24
3.3 模式Ⅲ：允許缺貨情況下部分 25
3.3.1 基本假設與符號說明 26
3.3.2 模型建構 26
3.3.3求解最小值的必要與充分條件 30
第四章 數值模擬分析與討論 31
4.1 模式驗證與比較 31
4.1.1 模式Ⅰ：不允許缺貨情況 31
4.1.2 模式Ⅱ：允許缺貨情況下完全缺貨待補 34
4.1.3 模式Ⅲ：允許缺貨情況下與時間相關之部分缺貨待補 38
4.1.4 三種存貨模式的比較 44
4.2 考慮品項損耗率特性的應用性 45
4.3 購買成本與時間和數量相依機制對成本的影響 47
第五章 結論與未來研究方向究方向 49
參考文獻 51
附錄 60

Abad, P. L., (1988). Determining optimal selling price and lot size when the supplier offers all-unit quantity discounts. Decision Sciences, Vol. 19, No. 3, pp. 622-634.
Abad, P. L., (1988). Joint price and lot size determination when supplier offers incremental quantity discount. Journal of the Operational Research Society, Vol. 39, No. 3, pp. 603-607.
Abad, P. L., (1996). Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Management Science, Vol. 42, No. 8, pp. 1093-1104.
Abad, P. L., (2000). Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale. Computers & Industrial Engineering, Vol. 38, No. 4, pp. 457-465.
Baker, R. C. and Urban, T. L., (1988a). A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate. The Journal of the Operational Research Society, Vol. 39, No. 9, pp. 823-831.
Baker, R. C. and Urban, T. L., (1988b). Single-period inventory dependent demand models. Omega, Vol. 16, No. 6, pp. 605–607.
Baker, R. C. and Urban, T. L., (1991). Deterministic fixed order-level inventory models: An application for replenishment of radioactive source material for irradiation sterilization. European Journal of Operational Research, Vol. 50, No. 3, pp. 249-256.
Balakrishnan, A., Pangburn, M. S. and Stavrulaki, E., (2004) Stack Them High, Let ‘em Fly”: Lot-Sizing Policies When Inventories Stimulate Demand. Management Science, Vol. 50, No. 5, pp. 630-644.
Bar-Lev, S. K., Parlar, M. and Perry, D., (1994). On the EOQ model with inventory-level-dependent demand rate and random yield. Operations Research Letters, Vol. 16, No. 3, pp. 167–176.
Benkherouf, L., Boumenir, A. and Aggoun, L., (2001). A stochastic inventory model with stock dependent demand items. Journal of Applied Mathematics and Stochastic Analysis, Vol. 14, No. 4, pp. 317-328.
Benton, W. C. and Park, S., (1996). A classification of literature on determining the lot size under quantity discounts. European Journal of Operational Research, Vol. 92, No. 2, pp. 219-238.
Bernstein, F. and Federgruen, A., (2005). Decentralized supply chains with competing retailers under demand uncertainty. Management Science, Vol. 51, No. 1, pp. 18-29.
Bhunia, A. K. and Maiti, M., (1995). A deterministic two storage inventory model for variable production and inventory-level-dependent demand rate. Cahiers du Centre d’Etudes de Recherche Operationnelle, Vol. 37, pp. 17-24.
Bhunia, A. K. and Maiti, M., (1997). A deterministic inventory model with inventory level-dependent consumption rate for two warehouses. Bulletin of the Calcutta Mathematical Society, Vol. 89, No. 2, pp. 105–114.
Bhunia, A. K. and Maiti, M., (1999). An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand. Applied Mathematical Modelling, Vol. 23, No. 4, pp. 301-308.
Chang, C. T., Goyal S. K. and Teng, J. T., (2006). On “An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging” by Dye and Ouyang. European Journal of Operational Research, 174, No. 2, pp. 923-929.
Chang, H. J. and Dye, C. Y., (1999). An EOQ model for deterioration items with time varying demand and partial backlogging. Journal of the Operational Research Society, Vol.50, No. 11, pp. 1176-1182.
Chang, H. J. and Dye, C. Y., (2001). An inventory model for deteriorating items with partial backlogging and permissible delay in payments. International Journal of Systems Science, Vol. 32, No. 3, pp. 345-352.
Chen, F., Federgruen, A. and Zheng, Y. S., (2001). Coordination mechanisms for a distribution system with one supplier and multiple retailers. Management Science, Vol. 47, No. 5, pp. 693-708.
Chung, K. J., (2003). An algorithm for an inventory model with inventory-level-dependent demand rate. Computers and Operations Research, Vol. 30, No. 9, pp. 1311–1317.
Chung, K. J., Chu, P. and Lan, S. P., (2000). A note on EOQ models for deteriorating items under stock dependent selling rate. European Journal of Operational Research, Vol. 124, No. 3, pp. 550-559.
Crowther, J. F., (1964), Rationale for Quantity Discounts. Harvard Business Review, Vol. 42, No. 2, pp.121-127.
Dana, J. D. and Petruzzi, N. C., (2001). Note: The newsvendor model with endogenous demand. Management Science, Vol. 47, No. 11, pp. 1488-1497.
Das, K. and Maiti, M., (2003). Inventory of a differential item sold from two shops under single management with shortages and variable demand. Applied Mathematical Modelling, Vol. 27, No. 7, pp. 535-549
Datta T. K., Paul, K. and Pal, A. K., (1998). Demand promotion by upgradation under stock-dependent demand situation—a model. International Journal of Production Economics, Vol. 55, No. 1, pp. 31-38.
Datta, T. K. and Pal, A. K., (1990a). A note on an inventory model with inventory-level-dependent demand rate. Journal of the Operational Research Society, Vol. 41, No. 10, pp. 971-975.
Datta, T. K. and Pal, A. K., (1990b). Deterministic inventory systems for deteriorating items with inventory-level-dependent demand rate and shortages. Opsearch, Vol. 27, pp. 213-224.
Datta, T. K. and Paul, K., (2001). An inventory system with stock-dependent, price-sensitive demand. Production Planning and Control, Vol. 12, No. 1, pp. 13-20.
Dye, C. Y. and Ouyang L. Y., (2005). An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging. European Journal of Operational Research, Vol. 163, No. 3, pp. 776-783.
Dye, C. Y., (2007). Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega, Vol. 35, No. 2, pp. 184-189.
Fabrycky, W. J., and Banks, J., (1967). Procurement and Inventory Systems. Reinhold Publishing Corporation, New York.
Fariborz, J., Tavakkoli-Moghaddam, R., Rabbani, M. and Sadoughian, M. R., (2006). An economic production lot size model with deteriorating items, stock-dependent demand, inflation, and partial backlogging. Applied Mathematics and Computation, Vol. 181, No. 1, pp. 380-398.
Gerchak, Y. and Wang, Y., (1994). Periodic-review inventory models with inventory-level-dependent demand. Naval Research Logistics, Vol. 41, No. 1, pp. 99-116.
Ghare, P. M. and Schrader, G. F., (1963). A model for an exponentially decaying inventory. Journal of Industrial Engineering, Vol. 14, No. 5, pp. 238-243.
Giri B. C., Pal, S., Goswami, A. and Chaudhuri, K. S., (1996). An inventory model for deteriorating items with stock-dependent demand rate. European Journal of Operational Research, Vol. 95, No. 3, pp. 604–610.
Giri, B. C. and Chaudhuri, K. S., (1998). Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. European Journal of Operational Research, Vol. 105, No. 3, pp. 467–474.
Goh, M., (1992). Some results for inventory models having inventory level dependent demand rate. International Journal of Production Economics, Vol. 27, No. 2, pp. 155-160.
Goh, M., (1994). EOQ models with general demand and holding cost functions. European Journal of Operational Research, Vol. 73, No. 1, pp. 50-54.
Gupta, R. and Vrat, P., (1986). Inventory model for stock-dependent consumption rate. Opsearch, Vol. 23, No. 1, pp. 19-24.
Gupta, R. and Vrat, P., (1986). Inventory model with multi-items under constraint systems for stock dependent consumption rate. Operations Research, Vol.24, pp. 41-42.
Hollier, R. H. and Mak, K. L., (1983). Inventory replenishment policies for deteriorating items in a declining market. International Journal of Production Research, Vol. 21, No. 6, pp.813-826.
Hou, K. L, (2006). An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting.. European Journal of Operational Research, Vol. 168, No. 2, pp. 463-474.
Hwang, H. and Hahn, K. H., (2000). An optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime. European Journal of Operational Research, Vol. 127, No. 3, pp. 537-545.
Jelen, F. C., (1970). Cost and Optimization Engineering. McGraw-Hill, New York.
Jørgensen, S. and Kort, P. M., (2002). Optimal pricing and inventory policies: Centralized and decentralized decision making. European Journal of Operational Research, Vol. 138, No. 3, pp. 578-600.
Kar, S., Bhunia, A. K. and Maiti, M., (2001). Inventory of multi-deteriorating items sold from two shops under single management with constraints on space and investment. Computers and Operations Research, Vol. 28, No. 12, pp. 1203-1221.
Khmelnitsky, E. and Gerchak, Y., (2002). Optimal control approach to production systems with inventory-level-dependent demand. IEEE Transactions on Automatic Control, Vol. 47, No. 2, pp. 289-292.
Larson, P.D. and DeMarais, R. A., (1990). Psychic stock: An independent variable category of inventory. International Journal of Physical Distribution and Logistics Management, Vol. 20, No. 7, pp. 28-34. (This article was again published in 1999, Vol. 29, No. 7/8, pp. 495-507).
Levin, R. I., McLaughlin, C. P., Lamone R. P. and Kottas J. F., (1972). Production/Operations Management：Contemporary Policy for Managing Operating Systems. McGraw-Hill, New York. pp. 373.
Liao, H. C., Tsai, C. H. and Su, C. T., (2000). An inventory model with deteriorating items under inflation when a delay in payment is permissible. International Journal of Production Economics, Vol. 63, No. 2, pp. 207–214.
Liu, H. A., (1999). A production lot size model for deteriorating items with inventory-level dependent production and demand rate. Journal of Interdisciplinary Mathematics, Vol. 2, No. 2-3, pp.173-183.
Mandal, B. N. and Phaujdar, S., (1989a). A note on an inventory model with stock-dependent consumption rate. Opsearch, Vol. 26, pp. 43-46.
Mandal, B. N. and Phaujdar, S., (1989b). An inventory model for deteriorating items and stock-dependent consumption rate. Journal of the Operational Research Society, Vol. 40, No. 5, pp. 483-488.
Mandal, M. and Maiti, M., (1997). Inventory model for damageable items with stock-dependent demand and shortages. Opsearch, Vol. 34, No. 3, pp. 155–166.
Mandal, M. and Maiti, M., (1999). Inventory of damagable items with variable replenishment rate, stock-dependent demand and some units in hand. Applied Mathematical Modelling, Vol. 23, No. 10, pp. 799-807.
Mandal, M. and Maiti, M., (2000). Inventory of damagable items with variable replenishment and stock-dependent demand. Asia-Pacific Journal of Operational Research, Vol. 17, No. 1, pp. 41-54.
Mandal, M., Roy, T. K. and Maiti, M., (1998). A fuzzy inventory model of deteriorating items with stock-dependent demand under limited storage space. Opsearch, Vol. 35, No. 4, pp. 323-337.
Monahan, J. P., (1984). A quantity discount pricing model to increase vendor profits. Management Science, Vol. 30, No. 6, pp. 720-726.
Montgomery, D. C., Bazaraa, M. S., and Keswani, A. K., (1973). Inventory models with a mixture of backorders and lost sales. Naval Research Logistics, Vol. 20, No. 2, pp. 255-263.
Moorthy, K. S., (1987). Managing channel profits: comment. Marketing Science, Vol. 6, No. 4, pp. 375-379.
Munson, C. L. and Rosenblatt, M. J., (2001). Coordinating a three-level supply chain with quantity discounts. IIE Transactions, Vol. 33, No. 5, pp. 371-384.
Nahmias, S., (1978). Perishable inventory theory: A review. Operations Research, Vol. 30, No. 4, pp. 680-708.
Ouyang, L. Y., Hsieh, T. P., Dye, C. Y. and Chang, H. C., (2003). An inventory model for deteriorating items with stock-dependent demand under the conditions of inflation and time-value of money. Engineering Economist, Vol. 48, No. 1, pp. 52-68.
Padmanabhan, G. and Vrat, P., (1988). Inventory models for perishable items under stock dependent consumption rate. XXIst Annual ORSI Convention, Trivandrum, India.
Padmanabhan, G. and Vrat, P., (1990a). An EOQ model for items with stock dependent consumption rate and exponential decay. Engineering Costs and Production Economics, Vol.18, No. 3, pp. 241-246.
Padmanabhan, G. and Vrat, P., (1990b). Analysis of multi-item inventory systems under resource constraints: A non-linear goal programming approach. Engineering Costs and Production Economics, Vol. 20, No. 2, pp. 121-127.
Padmanabhan, G. and Vrat, P., (1994). Inventory models for items under stock-dependent consumption rate. IAPQR Transactions, Vol. 19, No. 1, pp. 15-23.
Padmanabhan, G. and Vrat, P., (1995). EOQ models for perishable items under stock dependent selling rate. European Journal of Operational Research, Vol. 86, No. 2, pp. 281-292.
Pal, S., Goswami, A. and Chaudhuri, K. S., (1993). A deterministic inventory model for deteriorating items with stock-dependent demand rate. International Journal of Production Economics, Vol. 32, No. 3, pp. 291–299.
Papachristos, S. and Skouri, K., (2000). An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type-backlogging. Operation Research Letters, Vol. 27, No. 4, pp.175-184.
Papachristos, S. and Skouri, K., (2002). A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging. Applied Mathematical Modelling, Vol. 26, No. 5, pp.603-617.
Papachristos, S. and Skouri, K., (2003). An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, Vol. 83, No. 3, pp. 247-256.
Park, K. S., (1982). Inventory models with partial backorders. International Journal of Systems Science, Vol. 13, pp. 1313-1317.
Paul, K., Datta, T. K., Chaudhuri, K. S. and Pal, A. K., (1996). An inventory model with two-component demand rate and shortages. Journal of the Operational Research Society, Vol. 47, No. 8, pp. 1029-1036.
Raafat, F., (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research Society, Vol.42, No.1, pp. 27-37.
Ray, J. and Chaudhuri, K. S., (1997). An EOQ model with stock-dependent demand, shortage, inflation and time discounting. International Journal of Production Economics, Vol. 53, No. 2, pp. 171-180.
Ray, J., Goswami, A. and Chaudhuri, K. S., (1998). On an inventory model with two levels of storage and stock-dependent demand rate. International Journal of Systems Science, Vol. 29, pp. 249-254.
Reddy, G. S. N. and Sarma, K. V. S., (2001). A periodic review inventory problem with variable stock dependent demand. Opsearch, Vol. 38, No. 3, pp. 332–341.
Rosenberg, D., (1979). A new analysis of a lot-size model with partial backlogging. Naval Research Logistics, Vol. 26, No. 2, pp. 349-353.
Roy, T. K. and Maiti, M., (1998). Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment. Computers and Operations Research, Vol. 25, No. 12, pp. 1085-1095.
Roy, T.K.and Maiti, M., (2000). A multi-item fuzzy displayed inventory model under limited shelf-space. Journal of Fuzzy Mathematics, Vol. 8, No. 4, pp. 789-796.
Sana, S. and Chaudhuri, K. S., (2003). On a volume flexible stock-dependent inventory model. Advanced Modeling and Optimization, Vol. 5, No. 3, pp. 197-210.
Sarker, B. R., Mukherjee, S. and Balan, C. V., (1997). An order-level lot size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, Vol. 48, No. 3, pp. 227-236.
Shah, Y. K., (1977). An order-level lot-size inventory model for deteriorating items. AIIE Transactions, Vol. 9, pp. 108-112.
Shiue, Y. N., (1990). An inventory model for perishable items in a lot size system with quantity discount. European Journal of Operational Research, Vol. 45, No. 2-3, pp. 260-264.
Su, C. T., Tong, L. I. and Liao, H. C., (1996). An inventory model under inflation for stock dependent consumption rate and exponential decay. Opsearch Vol. 33, No. 2, pp. 71-82.
Teng, J. T., Chang, H. J., Dye, C. Y. and Hung, C. H., (2002). An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging. Operations Research Letters, Vol. 30, No. 6, pp. 387-393.
Tersine, R. J. and Toelle, R. A., (1985). Lot size determination with quantity discounts. Production and Management, Vol.26, No.3, pp.1-23.
Urban, T L. and Baker, R. C., (1997). Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns. European Journal of Operational Research, Vol. 103, No. 3, pp. 573-583.
Urban, T. L., (1992). An inventory model with an inventory-level dependent demand rate and relaxed terminal conditions. Journal of the Operational Research Society, Vol. 43, No. 7, pp. 721-724.
Urban, T. L., (1995). Inventory models with the demand rate dependent on stock and shortage levels. International Journal of Production Economics, Vol. 40, No. 1, pp. 21-28.
Urban, T. L., (1998). An inventory-theoretic approach to product assortment and shelf-space allocation. Journal of Retailing, Vol. 74, No. 1, pp. 15-35.
Urban, T. L., (2002). The interdependence of inventory management and retail shelf management. International Journal of Physical Distribution and Logistics Management, Vol. 32, No. 1, pp. 41-58.
Urban, T. L., (2005). Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory. European Journal of Operational Research, Vol. 162, No. 3, pp. 792-804.
Vrat, P. and Padmanabhan, G., (1990). An inventory model under inflation for stock dependent consumption rate items. Engineering Costs and Production Economics, Vol. 19, No. 1-3, pp. 379-383.
Wang, S. P., (2002). An inventory replenishment policy for deteriorating items with shortages and partial backlogging. Computers and Operations Research, Vol. 29, No. 14, pp. 2043-2051.
Wang, Y. and Gerchak, Y., (2001). Supply chain coordination when demand is shelf-space dependent. Manufacturing and Service Operations Management, Vol. 3, No. 1, pp. 82-87.
Wee, H. M., (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, Vol. 59, No. 1-3, pp. 511-518.
Weng, Z. K., (1995). Channel coordination and quantity discounts. Management Science, Vol. 41, No. 9, pp. 1509-1522.
Whitin, T. M., (1957). The Theory of Inventory Management. Princeton University Press, Princeton, NJ.
Wu, K. S. and Liu, H. A., (1998). A production lot size inventory model for deteriorating items with inventory-level-dependent demand and partial backordering. Tamsui Oxford Journal of Mathematical Sciences, Vol. 14, pp. 113-123.
Wu, K. S., Ouyang L.Y. and Yang C.T., (2006). An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. International Journal of Production Economics, Vol. 101, No. 2, pp. 369-384.
Yang, P. C., (2004). Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. European Journal of Operational Research, Vol. 157, No. 2, pp. 389-397.
Zhou, Y. W. and Yang, S. L., (2003). An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy. Journal of the Operational Research Society, Vol. 54, No. 6, pp. 585-593.