臺灣博碩士論文加值系統

傳統的存貨模式通常假設物品可以永久保存以滿足未來的需求，以及企業擁有單一且無容量限制的倉庫。實際上，大多數的物品於正常的儲存過程中，會有退化的現象發生，例如生鮮食品的腐敗、酒精的揮發和藥物的變質，致使存貨水準因需求而減少外，也因為退化而降低。因此，在決定這類物品的最適存貨策略時，退化現象所造成的額外損失就不可被忽視。另一方面，當企業訂購大量的物品時，受限於自有倉庫的容量，可能需要外租倉庫以存放額外的數量。

本研究在存貨系統中考慮允許缺貨的情況下，建構三個不同的退化性物品存貨模式。第二章在物品退化率隨時間變動的情況下提出一個需求與售價有關的存貨模式。此存貨系統允許發生缺貨，並假設欠撥率為等候下一次補貨的時間長度之函數，而且以指數的方式遞減。第三章則延續第二章對退化率和需求率的一般化假設，另外考慮貨幣的時間價值，利用現金流量法建立一個允許完全欠撥的存貨模式，決定最適的售價和訂購週期，使得總利潤的淨現值為最大。 第二章和第三章均假設自有倉庫的容量不受限制，第四章則將自有倉庫的容量限制納入存貨模式中，並假設與等候時間有關的欠撥率。當訂購數量超過自有倉庫容量時，可向外租借倉庫儲存超額的數量。以上所建立的存貨模式，均被證明最適解不僅存在而且唯一，並於相關章節之後以數值範例來說明其求解過程。第五章為結論，並對本文各章所建構的存貨模式作一總結，同時提出未來的研究方向。

The general assumptions in classical inventory models are that items can be stored indefinitely to meet future demand and the business owns a single warehouse without
capacity limitation. In practice, it is well known that certain products such as medicine, volatile liquids, blood bank, food stuff and many others, decrease under deterioration (vaporization, damage, spoilage, dryness and so on) during their normal storage period. As a result, while determining the optimal inventory policy of that type of products, the loss due to deterioration can not be neglected. On the other hand, while a large stock is
to be held, due to the limited capacity of the own warehouse, one extra warehouse may be required.

In this thesis, three deterministic inventory models for deteriorating items have been formulated with backorders considerations. In Chapter 2, a deterministic inventory model for deteriorating items with price-dependent demand is developed. The demand and deterioration rates are continuous and differentiable functions of price and time, respectively. In particular, we allow for shortages and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. Following the assumptions about deterioration and demand rates, in Chapter 3, an infinite time horizon inventory model with time-value of money is discussed. In addition, we allow for shortages and completely backlogged. The objective is to find the optimal replenishment and pricing strategies
maximizing the net present value of total profit over the infinite horizon. It is assumed that the capacity of the own warehouse is unlimited in Chapter 2 and Chapter 3. In
Chapter 4, a deterministic inventory model is developed for deteriorating items with capacity constraint and time-proportional backlogging rate. A rented warehouse is used
when the ordering quantity exceeds the limited capacity of the own warehouse. In all inventory models, the existence and uniqueness of the optimal solution are proved and numerical examples are provided to illustrate the proposed models. Finally, in Chapter 5, we provide some conclusions of this thesis and future research topics.

目錄 i
表目錄 iv
圖目錄 v
使用符號一覽表 vi
基本假設 vii
第一章緒論 1
1.1 研究動機與目的 1
1.2 文獻探討 3
1.3 本文結構 9
第二章需求率與售價有關且允許部分欠撥的退化性物品存貨模式 12
2.1 前言 12
2.2 符號說明與假設 12
2.3 模式的建立. 13
2.4 模式的求解 16
2.5 數值範例 21
2.6 小結 23
第三章考慮貨幣的時間價值下需求率與售價有關且允許完全欠撥的退化性物品存貨模式 26
3.1 前言 26
3.2 符號說明與假設 27
3.3 模式的建立 27
3.4 模式的求解 30
3.5 數值範例 33
3.6 小結 35
第四章需求率為固定常數且允許部分欠撥的兩倉庫退化性物品存貨模式 36
4.1 前言 36
4.2 符號說明與假設 37
4.3 模式的建立 38
4.4 模式的求解 43
4.5 自有倉庫無容量限制的存貨模式 51
4.6 一些特殊的情況 54
4.7 數值範例 58
4.8 小結 59
第五章結論63
5.1 主要研究成果 63
5.2 未來研究方向 66
參考文獻 68
附錄A 77
附錄B 80
附錄C 81
附錄D 86
附錄E 87
附錄F 88
附錄G 89
附錄H 90

表目錄
1.1 主要參考文獻之存貨模式比較表 10
2.1 例題一的求解程序列表 22
2.2 例題二的求解程序列表 23
4.1 例題五在不同的W 和δ 值下最適解彙整表 60


圖目錄
1.1 本文結構流程圖 11
2.1 部分欠撥下存貨水準與時間之關係圖 13
2.2 例題一當p* = 30.36569 時, AR(p*, to, ts) 的立體圖 24
2.3 例題一AR(p, to*, ts* ) 的平面圖 24
2.4 例題二當p*= 59.19363 時, AR(p*, to, ts) 的立體圖 25
2.5 例題二AR(p, to*, ts* ) 的平面圖 25
3.1 完全欠撥下存貨水準與時間之關係圖 28
4.1 部分欠撥下存貨水準與時間之關係圖 39
4.2 例題五不同的W 和δ 值對最適的每單位時間總利潤之關係圖 61
4.3 例題五不同的W 和δ 值對最適的訂購數量之關係圖 61
4.4 例題五不同的W 和δ 值對最大的存貨量之關係圖 62

[1] 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. 6, pp. 603-607.

[2] 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.

[3] Abad, P. L. (2001), “Optimal price and order size for a reseller under partial backordering”, Computers & Operations Research, Vol. 28, No. 1, pp. 53-65.

[4] Benkherouf, L. (1997), “A deterministic order level inventory model for deteriorating items with two storage facilities”, International Journal of Production Economics, Vol. 48, No. 2, pp. 167-175.

[5] Bhunia, A. K. and Maiti, M. (1994), “A two warehouse inventory model for a linear trend in demand”, Opsearch, Vol. 31, pp. 318-329.

[6] Bhunia, A. K. and Maiti, M. (1998), “A two-warehouse inventory model for deteriorating items with a linear trend in demand and shortages”, Journal of the Operational
Research Society, Vol. 49, No. 3, pp. 287-292.

[7] Chakrabarty, T., Giri, B. C. and Chaudhuri, K. S. (1998), “An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: an extension
of Philip’s model”, Computers & Operations Research, Vol. 25, No. 7-8, pp. 649-657.

[8] Chang, H. J. and Dye, C. Y. (1999), “An EOQ model for deteriorating items with time varying demand and partial backlogging”, Journal of the Operational Research
Society, Vol. 50, No. 11, pp. 1176-1182.

[9] Chang, H. J., Hung, C. H. and Dye, C. Y. (2002), “A finite time horizon inventory model with deterioration and time-value of money under the conditions of permissible
delay in payments”, International Journal of Systems Science, Vol. 33, No. 2, pp. 141-151.

[10] Chang, C. T. and Teng, J. T. (2004), “Retailer’s optimal ordering policy under supplier credits”, Mathematical Methods of Operations Research, Vol. 60, No. 3, pp. 471-483.

[11] Chang, H. J., Teng, J. T., Ouyang, L. Y. and Dye, C. Y. (2006), “Retailer’s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging”, European Journal of Operational Research, Vol. 168, No. 1, pp. 51-64.

[12] Chung, K. J. and Huang, T. S. (2007), “The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing”,
International Journal of Production Economics, Vol. 106, No. 1, pp. 127-145.

[13] Cohen, M. A. (1977), “Joint pricing and ordering policy for exponentially decaying inventory with known demand”, Naval Research Logistics Quarterly, Vol. 24, No. 2, pp. 257-268.

[14] Covert, R. P. and Philip, G. C. (1973), “An EOQ model with Weibull distribution deterioration”, AIIE Transactions, Vol. 5, No. 4, pp. 323-326.

[15] Dave, U. (1988), “On the EOQ models with two levels of storage”, Opsearch, Vol. 25, pp. 190-196.

[16] Dave, U. and Patel, L. K. (1981), “(T,Si) policy inventory model for deteriorating items with time proportional demand”, Journal of the Operational Research Society, Vol. 32, No. 2, pp. 137-142.

[17] Dye, C. Y. (2007), “Joint pricing and ordering policy for a deteriorating inventory with partial backlogging”, Omega, Vol. 35, No. 2, pp. 184-189.
[18] Eilon, S. and Mallaya, R. V. (1966), “Issuing and pricing policy of semi-perishables”, Proceedings of the 4th International Conference on Operational Research, Wiley-Interscience, New York.

[19] Erlenkotter, D. (1989), “Notes: An early classic misplaced: Ford W. Harris’s Economic Order Quantity Model of 1913”, Management Science, Vol. 35, No. 7, pp. 898-900.

[20] Erlenkotter, D. (1990), “Ford Whitman Harris and the economic order quantity model”, Management Science, Vol. 38, No. 6, pp. 937-946.

[21] Ghare, P. M. and Schrader, G. H. (1963), “A model for an exponentially decaying inventory”, Journal of Industrial Engineering, Vol. 14, pp. 238-243.

[22] Goswami, A. and Chaudhuri, K. S. (1992), “An economic order quantity model for items with two levels of storage for a linear trend in demand”, Journal of the Operational Research Society, Vol. 43, No. 2, pp. 157-167.
[23] Goyal, S. K. and Giri, B. C. (2001), “Recent trends in modeling of deteriorating inventory”, European Journal of Operational Research, Vol. 34, No. 1, pp. 1-16.

[24] Hadley, G. (1964), “A comparison of order quantities computed using the average annual cost and the discounted cost”, Management Science, Vol. 10, No. 3, pp. 472-
476.

[25] Harris, F. W. (1913), “How many parts to make at once”, Factory, The Magazine of Management, Vol. 10, No. 2, pp. 135-136.

[26] Harris, F. W. (1915), “What quantity to make at once”, The Library of Factory Management, Vol. 5, Operations and costs, A. W. Shaw Company, Chicago, pp. 47-
52.

[27] Hartley, R. V. (1976), Operations Research−A Managerial Emphasis, Good Year Publishing Company, California, pp. 315-317.

[28] Huang, Y. F. (2006), “An inventory model under two levels of trade credit and limited storage space derived without derivatives”, Applied Mathematical Modelling, Vol. 30, No. 5, pp. 418-436.

[29] Hwang, H. and Shinn, S. W. (1997), “Retailer’s pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments”, Computers & Operations Research, Vol. 24, No. 6, pp. 539-547.

[30] Kang, S. and Kim, I. (1983), “A study on the price and production level of the deteriorating inventory system”, International Journal of Production Research, Vol. 21, No. 6, pp. 899-908.

[31] Kar, S., Bhunia, A. K. and Maiti, M. (2001), “Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon”, Computers & Operations Research, Vol. 28, No. 13, pp. 1315-1331.

[32] Lee, C. C. and Ma, C. Y. (2000), “Optimal inventory policy for deteriorating items with two-warehouse and time-dependent demands”, Production Planning & Control, Vol. 11, No. 7, pp. 689-696.

[33] Leung, K.-N. F. (2007), “A generalized geometric-programming solution to “An economic production quantity model with flexibility and reliability considerations””, European Journal of Operational Research, Vol. 176, No. 1, pp. 240-251.

[34] Misra, R. B. (1975), “Optimum production lot size model for a system with deteriorating inventory”, International Journal of Production Research, Vol. 13, No. 5, pp. 495-505.

[35] Mukhopadhyay, S., Mukherjee, R. N. and Chaudhuri, K. S. (2004), “Joint pricing and ordering policy for a deteriorating inventory”, Computers & Industrial Engineering, Vol. 47, No. 4, pp. 339-349.

[36] Mukhopadhyay, S., Mukherjee, R. N. and Chaudhuri, K. S. (2005), “An EOQ model with two-parameter Weibull distribution deterioration and price-dependent demand”,
International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 1, pp. 25-33.

[37] Murdeshwar, T. M. and Sathe, Y. S. (1985), “Some aspects of lot size model with two levels of storage”, Opsearch, Vol. 22, No. 4, pp. 255-262.

[38] Ouyang, L. Y., Wu, K. S. and Ho, C. H. (2006), “The single-vendor single-buyer integrated inventory problem with quality improvement and lead time reduction -
Minimax distribution-free approach”, Asia-Pacific Journal of Operational Research, Vol. 23, No. 3, pp. 407-424.

[39] 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.

[40] Pakkala, T. P. M. and Achary, K. K. (1992), “A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate”, European
Journal of Operational Research, Vol. 57, No. 1, pp. 71-76.

[41] Papachristos, P. and Skouri, K. (2000), “An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type-backlogging”,
Operations Research Letters, Vol. 27, No. 4, pp. 175-184.

[42] Papachristos, P. 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.

[43] Park, K. S. (1982), “Inventory models with partial backorders”, International Journal of Systems Science, Vol. 13, No. 12, pp. 1313-1317.

[44] Philip, G. C. (1974), “A generalized EOQ model for items with Weibull distribution deterioration”, AIIE Transactions, Vol. 6, No. 2, pp. 159-162.

[45] Raafat, F. (1991), “Survey of literature on continuously deteriorating inventory”, Journal of Operational Research Society, Vol. 42, No. 1, pp. 27-37.

[46] Rachamadugu, R. (1988), “Error bounds for EOQ”, Naval Research Logistics, Vol. 35, pp. 419-435.

[47] 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, No. 3, pp. 249-254.

[48] Roach, B. (2005) “Origin of the economic order quantity formula; transcription or transformation?”, Management Decision, Vol. 43, No. 9, pp. 1262-1268.

[49] Sarma, K. V. S. (1983), “A deterministic inventory model with two level of storage and an optimum release rule”, Opsearch, Vol. 20, pp. 175-180.

[50] Sarma, K. V. S. (1987), “A deterministic order level inventory model for deteriorating items with two storage facilities”, European Journal of Operational Research, Vol. 29, No. 1, pp. 70-73.

[51] Silver, E. A., Pyke, D. F. and Peterson, R. (1998), Inventory Management and Production Planning and Scheduling (3rd edition), John Wiley & Sons.

[52] Sun, D. and Queyranne, M. (2002), “Production and inventory model using net present value”, Operations Research, Vol. 50, No. 3, pp. 528-537.

[53] Tadikamalla, P. R. (1978), “An EOQ inventory model for items with Gamma distribution”, AIIE Transactions, Vol. 10, pp. 100-103.

[54] Teng, J. T. and Chang, C. T. (2005), “Economic production quantity models for deteriorating items with price- and stock-dependent demand”, Computers & Operations
Research, Vol. 32, No. 2, pp. 297-308.

[55] Teng, J. T., Chang, H. J., Dye, C. Y. and Hung, C. H. (2002), “An optimal replenishment policyfor deteriorating items with time-varying demand and partial backlogging”,
Operations Research Letters, Vol. 30, No. 6, pp. 387-393.

[56] Teng, J. T. and Yang, H. L. (2004), “Deterministic economic order quantity models with partial backlogging when demand and cost are fluctuating with time”, Journal
of the Operational Research Society, Vol. 55, No. 5, pp. 495-503.

[57] Wee, H. M. (1995), “A deterministic lot-size inventory model for deteriorating items with shortages and a declining market”, Computers & Operations Research, Vol. 22, No. 3, pp. 345-356.

[58] Wee, H. M. (1997), “A replenishment policy for items with a price-dependent demand and a varying rate of deterioration”, Production Planning & Control, Vol. 8, No. 5, pp. 494-499.

[59] Wee, H. M. (1999), “Deteriorating inventory model with quantity discount, pricing and partial backordering”, International Journal of Production Economics, Vol. 59, No. 1, pp. 511-518.

[60] Wee, H. M. and Law, S. T. (2001), “Replenishment and pricing policy for deteriorating items taking into account the time-value of money”, International Journal of
Production Economics, Vol. 71, No. 1-3, pp. 213-220.

[61] Wilson, R. H. (1934), “A scientific route for stock control”, Harvard Business Review, Vol. 13, pp. 116-128.
[62] Yang, H. L. (2004), “Two-warehouse inventory models for deteriorating items with shortages under inflation”, European Journal of Operational Research, Vol. 157, No.
2, pp. 344-356.

[63] Yang, H. L. (2006), “Two-warehouse partial backlogging inventory models for deteriorating items under inflation”, International Journal of Production Economics, Vol. 103, No. 1, pp. 362-370.

[64] Zhou, Y.W. (2003), “A multi-warehouse inventory model for items with time-varying demand and shortages”, Computers & Operations Research, Vol. 30, No. 14, pp. 2115-
2134.

[65] Zhou, Y. W. and Yang, S. L. (2005), “A two-warehouse inventory model for items with stock-level-dependent demand rate”, International Journal of Production Economics, Vol. 95, No. 2, pp. 215-228.