This paper aims to investigate the inventory policy for non-instantaneously deteriorating items. A generalized inventory replenishment model is formulated by maximizing the average profit of the system. In the model, it is assumed that the demand rate is influenced by the instantaneous inventory level with different influence coefficients in the deterioration period and non-deterioration period, the deterioration rate in the deterioration period and the holding cost are time-varying, shortage is allowed and the unmet demand is partially backlogged in the shortage period. The sufficient condition for the existence of the unique optimal solution to the model is presented. Finally, some numerical examples and the sensitivity analyses on the main parameters are given using the Newton's method. The results indicate that, to prolong the non-deterioration period of items will be helpful to the increase of the system's average profit. The increase of the demand in the deterioration period is more beneficial to the increase of the system's average profit than that in the non-deterioration period. For deteriorating items with high deterioration rate, the influence of the disposal cost of the deterioration items on the optimal policy and the average profit is significant. Besides, the model formulated in this paper is generalized, so it has a wide range of application.
LI Gui-ping, DUAN Yong-rui, HUO Jia-zhen, XIONG De-ping
. Inventory Policy for Non-instantaneously Deteriorating Items with Time-varying Holding Cost and Deterioration Rate[J]. Chinese Journal of Management Science, 2015
, 23(8)
: 122
-131
.
DOI: 10.16381/j.cnki.issn1003-207x.2015.08.014
[1] Goyal S K, Giri B C. Recent trends in modeling of deteriorating inventory [J]. European Journal of Operational Research, 2001, 134(1): 1-16.
[2] Bakker M, Riezebos J, Teunter R H. Review of inventory systems with deterioration since 2001 [J]. European Journal of Operational Research, 2012, 221(2): 275-284.
[3] Ghare P M, Schrader G F. A model for an exponentially decaying inventory [J]. Journal of Industrial Engineering, 1963, 14: 238-243.
[4] Covert R P, Philip G C. An EOQ model for items with Weibull distribution deterioration [J]. AIIE Transactions, 1973, 5(4): 323-326.
[5] Philip G C. A generalized EOQ model for items with Weibull distribution deterioration [J]. AIIE Transactions, 1974, 6(2): 159-162.
[6] Tadikamalla P R. An EOQ inventory model for items with gamma distribution [J]. AIIE Transactions,1978, 10(1): 100-103.
[7] Begum R, Sahoo R R, Sahu S K. A replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages [J]. International Journal of System Science, 2012, 43(5): 903-910.
[8] Sarkar B. An EOQ model with delay in payments and time varying deterioration rate [J]. Mathematical and Computer Modelling, 2012, 218(17): 8295-8308.
[9] Ahmed M A, Al-Khamis T A, Benkherouf L. Inventory models with ramp type demand rate, partial backlogging and general deterioration rate [J]. Applied Mathematics and Computation, 2013, 219(9): 4288-4307.
[10] Wu Kunshan, 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.
[11] Chang Chuntao, Teng J T, Goyal S K. Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand [J]. International Journal of Production Economics 2010, 123(1): 62-68.
[12] 闵杰, 周永务. 存货影响销售率的非立即变质物品的库存模型[J]. 系统工程学报, 2009, 24(2): 198-204.
[13] Ouyang L Y, Wu Kunshan, 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.
[14] Musa A, Sani B. Inventory ordering policies of delayed deteriorating items under permissible delay in payments [J]. International Journal of Production Economics, 2012, 136(1): 75-83.
[15] Maihami R, Abadi N K. Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging[J]. Mathematical and Computer Modelling, 2012, 55(5-6): 1722-1733.
[16] Maihami R, Kamalabadi I N. Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand [J]. International Journal of Production Economics, 2012, 136(1): 116-122.
[17] Shah N H, Soni H N, Patel K A. Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates [J]. Omega, 2013, 41(2): 421-430.
[18] Dye C Y. The effect of preservation technology investment on a non-instantaneous deteriorating inventory model [J]. Omega, 2013, 41(5): 872-880.
[19] Alfares H K. Inventory model with stock-level dependent demand rate and variable holding cost [J]. International Journal of Production Economics, 2007, 108(1-2):259-65.
[20] Pando V, García-Lagunaa J, San-José L A, et al. Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level [J]. Computers and Industrial Engineering, 2012, 62(2): 599-608.
[21] Roy A. An inventory model for deteriorating items with price dependent demand and time-varying holding cost [J]. Advanced Modeling and Optimization, 2008, 10(1): 25-37.
[22] Abad P L. Optimal pricing and lot-sizing under conditions of perishability and partial backlogging [J]. Management Science, 1996, 42(8): 1039-1104.
