An imperfect production process for time varying demand with inflation and time value of money - An EMQ model

Abstract The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.

[1]  Maurice Bonney,et al.  Economic manufacture quantity (EMQ) model with lot-size dependent learning and forgetting rates , 2007 .

[2]  Chih-Chung Lo,et al.  Optimal production run length for products sold with warranty in an imperfect production system with allowable shortages , 2006, Math. Comput. Model..

[3]  Philip M. Wolfe,et al.  An inventory model for deteriorating items , 1991 .

[4]  K. S. Chaudhuri,et al.  A deterministic EOQ model with delays in payments and price-discount offers , 2008, Eur. J. Oper. Res..

[5]  J. Buchanan.  Alternative Solution Methods for the Inventory Replenishment Problem under Increasing Demand , 1980, The Journal of the Operational Research Society.

[6]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[7]  C. H. Kim,et al.  An optimal production run length in deteriorating production processes , 1999 .

[8]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand , 1991 .

[9]  Evan L. Porteus.  Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction , 1986, Oper. Res..

[10]  K. S. Chaudhuri,et al.  A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand , 2003, Comput. Oper. Res..

[11]  Hui-Ling Yang,et al.  Two-warehouse inventory models for deteriorating items with shortages under inflation , 2004, Eur. J. Oper. Res..

[12]  Shyamal Kumar Mondal,et al.  Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money , 2008, Eur. J. Oper. Res..

[13]  Shib Sankar Sana,et al.  Optimal reliability, production lotsize and safety stock: an economic manufacturing quantity model , 2010 .

[14]  Suresh Kumar Goyal,et al.  Short communicationA note on the economic replenishment interval for an item with a linear trend in demand , 1986 .

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

[16]  J. Buzacott.  Economic Order Quantities with Inflation , 1975 .

[17]  K. S. Chaudhuri,et al.  A note on a lot sizing heuristic for deteriorating items with time-varying demands and shortages , 2000, Comput. Oper. Res..

[18]  Gerald L. Thompson,et al.  Optimal strategies for general price-quality decision models of new products with learning production costs , 1996 .

[19]  S. Aggarwal.  Purchase-Inventory Decision Models for Inflationary Conditions , 1981 .

[20]  M. Hariga.  Optimal EOQ Models for Deteriorating Items with Time-Varying Demand , 1996 .

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

[22]  Hong-Dar Lin,et al.  A note on optimal replenishment policy for imperfect quality EMQ model with rework and backlogging , 2008, Comput. Math. Appl..

[23]  Biswajit Sarkar,et al.  A finite replenishment model with increasing demand under inflation , 2010, Int. J. Math. Oper. Res..

[24]  Yuan-Shyi Peter Chiu,et al.  Optimization of the finite production rate model with scrap, rework and stochastic machine breakdown , 2010, Comput. Math. Appl..

[25]  M. Chandra,et al.  The effects of inflation and the time value of money on some inventory systems , 1985 .

[26]  H. Bierman,et al.  INVENTORY DECISIONS UNDER INFLATIONARY CONDITIONS , 1977 .

[27]  K. Chaudhuri,et al.  An EOQ model with stock-dependent demand, shortage, inflation and time discounting , 1997 .

[28]  Panganamala Ramana Kumar,et al.  Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems , 1988, Oper. Res..

[29]  K. S. Chaudhuri,et al.  A production-inventory model for a deteriorating item with trended demand and shortages , 2004, Eur. J. Oper. Res..

[30]  W. A. Donaldson.  Inventory Replenishment Policy for a Linear Trend in Demand An Analytical Solution , 1977 .

[31]  Jinn-Tsair Teng,et al.  Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation , 2008, Eur. J. Oper. Res..

[32]  K. S. Chaudhuri,et al.  Optimal reliability, production lot size and safety stock in an imperfect production system , 2010, Int. J. Math. Oper. Res..

[33]  K. Chaudhuri,et al.  A Note on the Heuristic for Replenishment of Trended Inventories Considering Shortages , 1987 .

[34]  Ilkyeong Moon,et al.  An EPQ model with inflation in an imperfect production system , 2011, Appl. Math. Comput..

[35]  R. Misra.  A note on optimal inventory management under inflation , 1979 .

[36]  Tadashi Dohi,et al.  Exact formulation of stochastic EMQ model for an unreliable production system , 2004, J. Oper. Res. Soc..

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