EPQ for an unreliable production system with endogenous reliability and product deterioration

In this paper, we study an economic production quantity problem for a production line subject to random shift from the in-control state (with high production rate) to out-of-control state (with low production rate). Different from previous research, we model the expected shift time as a controllable variable, based on the fact that, by investment in resources, the reliability of the production line can be improved. In the mathematical model, we consider three possible scenarios: no shift, shift without demand shortage, and shift with demand shortage, which are determined by the values of actual shift time and shifted production rate. Combining the three possible scenarios, the goal is to minimize the expected total cost per unit time by finding the optimal production time, as well as the optimal expected shift time. In addition, we extend the model to deterioration products and study the influence of product deterioration to the optimal decisions. Numerical examples are presented to illustrate the optimal solutions, followed by the sensitive analysis on important parameters. Comparing the optimal solutions under no reliability investment, reliability investment can help companies save more cost. Some other managerial insights are also proposed based on the numerical tests.

[1]  Shib Sankar Sana,et al.  An economic production lot size model in an imperfect production system , 2010, Eur. J. Oper. Res..

[2]  K. S. Chaudhuri,et al.  Production lot sizing with process deterioration and machine breakdown , 2008, Eur. J. Oper. Res..

[3]  Kun-Jen Chung,et al.  Optimal inventory replenishment models for deteriorating items taking account of time discounting , 2000, Comput. Oper. Res..

[4]  Stephen C. Graves,et al.  Production/inventory systems with a stochastic production rate under a continuous review policy , 1981, Comput. Oper. Res..

[5]  Yong He,et al.  A Production Model for Deteriorating Inventory Items with Production Disruptions , 2010 .

[6]  Nadim E. Abboud.  A simple approximation of the EMQ model with Poisson machine failures , 1997 .

[7]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

[8]  Xiang Fang,et al.  Supply chain performance under pull or push contracts in the presence of a market disruption , 2017, Int. Trans. Oper. Res..

[9]  Tsu-Pang Hsieh,et al.  An optimal replenishment policy for deteriorating items with effective investment in preservation technology , 2012, Eur. J. Oper. Res..

[10]  A. K. Pal,et al.  Order level inventory system with ramp type demand rate for deteriorating items , 1998 .

[11]  C. Chung,et al.  Economic production quantity model for deteriorating inventory with random machine unavailability and shortage , 2011 .

[12]  Divya Jain,et al.  The effect of inflation-induced demand and trade credit on ordering policy of exponentially deteriorating and imperfect quality items , 2012, Int. Trans. Oper. Res..

[13]  Ali Gharbi,et al.  Optimal safety stocks and preventive maintenance periods in unreliable manufacturing systems , 2007 .

[14]  Izak Duenyas,et al.  Integrated maintenance and production control of a deteriorating production system , 2002 .

[15]  Christoph H. Glock.  The machine breakdown paradox: How random shifts in the production rate may increase company profits , 2013, Comput. Ind. Eng..

[16]  Soo Y. Chang,et al.  Optimal production run length and inspection schedules in a deteriorating production process , 2001 .

[17]  Gede Agus Widyadana,et al.  An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown , 2012, Int. J. Syst. Sci..

[18]  Wansheng Tang,et al.  Dynamic joint pricing and production policy for perishable products , 2018, Int. Trans. Oper. Res..

[19]  H. Wee,et al.  Preservation technology investment for deteriorating inventory , 2010 .

[20]  Angus Jeang.  Simultaneous determination of production lot size and process parameters under process deterioration and process breakdown , 2012 .

[21]  Mohamed Ben-Daya,et al.  Economic production quantity model with a shifting production rate , 2008, Int. Trans. Oper. Res..

[22]  K. S. Chaudhuri,et al.  Two-echelon manufacturer-retailer supply chain strategies with price, quality, and promotional effort sensitive demand , 2015, Int. Trans. Oper. Res..

[23]  M. A. Rahim,et al.  An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate , 2006 .

[24]  Hardik N. Soni,et al.  Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates , 2013 .

[25]  H. Wee,et al.  Economic production quantity models for deteriorating items with rework and stochastic preventive maintenance time , 2012 .

[26]  Tadashi Dohi,et al.  Optimal design of unreliable production-inventory systems with variable production rate , 2005, Eur. J. Oper. Res..

[27]  Lawrence V. Snyder,et al.  EOQ Models with Supply Disruptions , 2014 .

[28]  Hui-Ming Wee,et al.  Economic production lot size for deteriorating items taking account of the time-value of money , 1999, Comput. Oper. Res..

[29]  Lin Wang,et al.  Modeling and Optimization of Stochastic Joint Replenishment and Delivery Scheduling Problem with Uncertain Costs , 2013 .

[30]  S. Goyal,et al.  An imperfect production process in a volume flexible inventory model , 2007 .

[31]  Mohamad Y. Jaber,et al.  Economic lot sizing with the consideration of random machine unavailability time , 2000, Comput. Oper. Res..

[32]  Kin Keung Lai,et al.  An optimal production-inventory model for deteriorating items with multiple-market demand , 2010, Eur. J. Oper. Res..

[33]  Shib Sankar Sana,et al.  A production-inventory model in an imperfect production process , 2010, Eur. J. Oper. Res..

[34]  P. M. Ghare.  A model for an exponentially decaying inventory , 1963 .

[35]  Yong He,et al.  Two-Level Credit Financing for Noninstantaneous Deterioration Items in a Supply Chain with Downstream Credit-Linked Demand , 2013 .

[36]  L. Ouyang,et al.  An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging , 2006 .

[37]  Kuo-Lung Hou,et al.  An optimal production run time with imperfect production processes and allowable shortages , 2003, Comput. Oper. Res..

[38]  K. S. Chaudhuri,et al.  A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage , 2009, Int. Trans. Oper. Res..

[39]  Lotfi Tadj,et al.  A generalized economic order quantity model with deteriorating items and time varying demand, deterioration, and costs , 2008, Int. Trans. Oper. Res..

[40]  Biswajit Sarkar,et al.  An inventory model with reliability in an imperfect production process , 2012, Appl. Math. Comput..

[41]  Fengjian Yang,et al.  Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems , 2010 .

[42]  Biswajit Sarkar,et al.  Product inspection policy for an imperfect production system with inspection errors and warranty cost , 2016, Eur. J. Oper. Res..