On a Production-Inventory Model for Deteriorating Items Subject to an Imperfect Process

不完美製程下劣化產品的生產存量模式

10.29977/JCIIE.200707.0007

Gary C. Lin；宮大川(Dah-Chuan Gong)

存量 ； 劣化產品 ； 不完美製程 ； inventory ； deteriorating item ； imperfect process

工業工程學刊

24卷4期（2007 / 07 / 01）

319 - 326

英文

本文考量一個不完美製程下劣化產品的生產存量模式。在產品的生產週期中，假設前期處於管制狀態，且需求平穩、已知，縱使產品本身有劣化現象，但在固定的劣化率下，生產策略仍為在一定的時間內生產一定的庫存量，以因應所需。由於不允許缺貨，因此，至所有庫存耗盡，新生產即開始。然而在生產過程中，生產系統可能隨機偏移至非管制狀態，造成所生產的產品會出現較高的劣化率。本文所發展模式之目的，在於求解符合單位時間期望總成本最小化的生產期，所涵蓋的成本項目有設置成本、持有成本、劣化成本，而系統至非管制狀態的時間和產品至劣化的時間均假設呈指數分配。本文並提供一個近似最佳解的式子，以利快速求解。

This paper considers a production-inventory model for deteriorating items subject to an imperfect production process. A product is to be manufactured in cycles on a system that is assumed to be in an in-control state at the beginning of a production run. The demand rate of the product is assumed to be fairly stable and known. For each production cycle, the production is run for a predetermined amount of time during which items produced are used to meet the demand and to build inventories. Items produced in this state are subject to a constant rate of deterioration. After a production run is completed, the system will be kept idle until all on-hand inventories are depleted. Since no shortages are allowed, a new production run will begin only when the inventory level reaches to zero. During a production run, the production system may shift at random from an in-control state to an out-of-control state. Subsequently, items produced in the out-of-control state are subject to a higher deterioration rate than those units produced during the in-control state. The objective of the model is to determine a production uptime so as to minimize the expected total cost per unit time including the setup, the inventory holding, and the deterioration cost. The time-to-shift of the productions system and the time-to-deterioration of an item are assumed to be exponentially distributed. A closed-form solution of a near optimal production uptime is derived.

1. Bazaraa, M. S.,H. D. Sherali,C. M. Shetty(2006).Nonlinear Programming: Theory and Algorithms.New York:John Wiley & Sons.
2. Chiu, S. W.,D. C. Gong,H. M. Wee(2004).Effects of random defective rate and imperfect rework process on economic production quality model.Japan Journal of Industrial and Applied Mathematics,21,375-389.
3. Ghare, P. M.,G. F. Schrader(1963).A model for exponential decaying inventory.Journal of Industrial Engineering,14,238-243.
4. Goyal, S. K.,B. C. Giri(2001).Recent trends in modeling of deteriorating inventory.European Journal of Operational Research,134,1-16.
5. Hwang H.,H. S. Hwang(1982).Optimal issuing policy in production lot size system for items with Weibull deterioration.International Journal of Production Research,20,87-94.
6. Lin, G. C.(1999).Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials.Mathematical and Computer Modeling,29,81-89.
7. Lin, G. C.,E. K. Dennis,C. J. Lin(2005).Determining a common production cycle time for an economic lot scheduling problem with deteriorating items.European Journal of Operational Research
8. Mak, K. L.(1982).A production lot size inventory model for deteriorating items.Computers & industrial engineering,6,309-317.
9. Misra, R. B.(1975).Optimum production lot size model for a system with deteriorating inventory.International Journal of Production Research,13,495-505.
10. Osteryoung, J. S.,E. Nosari,D. E. McCarty,W. J. Reinhart(1986).Use of EOQ model for inventory analysis.Production and Inventory Management Journal,27,39-45.
11. Raafat, F.(1991).Survey of literature on continuously deteriorating inventory models.Journal of the Operational Research Society,42,27-37.
12. Rosenblatt, M. J.,H. L. Lee(1986).Economic production cycles with imperfect production process.IIE Transactions,18,48-55.
13. Ross, S. M.(2002).Introduction to Probability Models.New York:Academic Press.

1. Sung, June-Chun,Lin, Chen-Sin,Gong, Dah-Chuan(2009).Extended Research on an Imperfect Process Production-inventory Model with Deteriorating Items under Two Dispatching Policies.管理與系統,16(3),415-438.