# American Institute of Mathematical Sciences

April  2010, 6(2): 425-433. doi: 10.3934/jimo.2010.6.425

## On the optimal replenishment in a finite planning horizon with learning effect of setup costs

 1 Department of Information Technology and Management, Shih Chien University, Taipei, Taiwan 2 Department of Accounting, Tamkang University, Taipei, Taiwan

Received  August 2009 Revised  January 2010 Published  March 2010

The traditional economic order quantity (EOQ) and/or economic production quantity (EPQ) have been extensively examined and continually modified so as to accommodate specific business needs and market environments. In this paper, the learning effect of setup costs is incorporated into an inventory replenishment system where the demand is assumed to be deterministically constant in a finite planning horizon. The inventory replenishment system with learning considerations of setup costs is formulated as a mixed-integer cost minimization problem in which the number of replenishments and the replenishment time points in the planning horizon are regarded as decision variables. We first show that the time interval between any two successive replenishments should be equal. Then, the conditions of the optimal solution for the proposed problem are derived. Finally, numerical examples are provided to illustrate the features of the proposed problem.
Citation: Ta-Wei Hung, Ping-Ting Chen. On the optimal replenishment in a finite planning horizon with learning effect of setup costs. Journal of Industrial & Management Optimization, 2010, 6 (2) : 425-433. doi: 10.3934/jimo.2010.6.425
 [1] Jun Li, Hairong Feng, Mingchao Wang. A replenishment policy with defective products, backlog and delay of payments. Journal of Industrial & Management Optimization, 2009, 5 (4) : 867-880. doi: 10.3934/jimo.2009.5.867 [2] Guodong Yi, Xiaohong Chen, Chunqiao Tan. Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1579-1597. doi: 10.3934/jimo.2018112 [3] Jun Li, Hairong Feng, Kun-Jen Chung. Using the algebraic approach to determine the replenishment optimal policy with defective products, backlog and delay of payments in the supply chain management. Journal of Industrial & Management Optimization, 2012, 8 (1) : 263-269. doi: 10.3934/jimo.2012.8.263 [4] Alexander O. Brown, Christopher S. Tang. The impact of alternative performance measures on single-period inventory policy. Journal of Industrial & Management Optimization, 2006, 2 (3) : 297-318. doi: 10.3934/jimo.2006.2.297 [5] Jingzhen Liu, Ka Fai Cedric Yiu, Alain Bensoussan. Ergodic control for a mean reverting inventory model. Journal of Industrial & Management Optimization, 2018, 14 (3) : 857-876. doi: 10.3934/jimo.2017079 [6] Jui-Jung Liao, Wei-Chun Lee, Kuo-Nan Huang, Yung-Fu Huang. Optimal ordering policy for a two-warehouse inventory model use of two-level trade credit. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1661-1683. doi: 10.3934/jimo.2017012 [7] Jing Shi, Tiaojun Xiao. Service investment and consumer returns policy in a vendor-managed inventory supply chain. Journal of Industrial & Management Optimization, 2015, 11 (2) : 439-459. doi: 10.3934/jimo.2015.11.439 [8] Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. An integrated inventory model with variable holding cost under two levels of trade-credit policy. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 169-191. doi: 10.3934/naco.2018010 [9] Kun-Jen Chung, Pin-Shou Ting. The inventory model under supplier's partial trade credit policy in a supply chain system. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1175-1183. doi: 10.3934/jimo.2015.11.1175 [10] Qi Feng, Suresh P. Sethi, Houmin Yan, Hanqin Zhang. Optimality and nonoptimality of the base-stock policy in inventory problems with multiple delivery modes. Journal of Industrial & Management Optimization, 2006, 2 (1) : 19-42. doi: 10.3934/jimo.2006.2.19 [11] Yiju Wang, Wei Xing, Hengxia Gao. Optimal ordering policy for inventory mechanism with a stochastic short-term price discount. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2018199 [12] Sankar Kumar Roy, Magfura Pervin, Gerhard Wilhelm Weber. Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2019032 [13] Jianbin Li, Mengcheng Guan, Zhiyuan Chen. Optimal inventory policy for fast-moving consumer goods under e-commerce environment. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2019028 [14] John Leventides, Iraklis Kollias. Optimal control indicators for the assessment of the influence of government policy to business cycle shocks. Journal of Dynamics & Games, 2014, 1 (1) : 79-104. doi: 10.3934/jdg.2014.1.79 [15] C.E.M. Pearce, J. Piantadosi, P.G. Howlett. On an optimal control policy for stormwater management in two connected dams. Journal of Industrial & Management Optimization, 2007, 3 (2) : 313-320. doi: 10.3934/jimo.2007.3.313 [16] Sung-Seok Ko. A nonhomogeneous quasi-birth-death process approach for an $(s, S)$ policy for a perishable inventory system with retrial demands. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-19. doi: 10.3934/jimo.2019009 [17] Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Multi-item deteriorating two-echelon inventory model with price- and stock-dependent demand: A trade-credit policy. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1345-1373. doi: 10.3934/jimo.2018098 [18] Shuren Liu, Qiying Hu, Yifan Xu. Optimal inventory control with fixed ordering cost for selling by internet auctions. Journal of Industrial & Management Optimization, 2012, 8 (1) : 19-40. doi: 10.3934/jimo.2012.8.19 [19] Yanqing Hu, Zaiming Liu, Jinbiao Wu. Optimal impulse control of a mean-reverting inventory with quadratic costs. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1685-1700. doi: 10.3934/jimo.2018027 [20] Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk, H. M. Mulder. On EOQ cost models with arbitrary purchase and transportation costs. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1211-1245. doi: 10.3934/jimo.2015.11.1211

2018 Impact Factor: 1.025

## Metrics

• PDF downloads (4)
• HTML views (0)
• Cited by (1)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]