A production-inventory model in an imperfect production process

The paper develops a model to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process. The basic assumption of the classical Economic Manufacturing Quantity (EMQ) model is that all manufacturing items are of perfect quality. The assumption is not true in practice. Most of the production system produces perfect and imperfect quality items. In some cases the imperfect quality (non conforming) items are reworked at a cost to restore its quality to the original one. Rework cost may be reduced by improvements in product reliability (i.e., decreasing in product reliability parameter). Lower value of product reliability parameter results in increase development cost of production and also smaller quantity of nonconforming products. The unit production cost is a function of product reliability parameter and production rate. As a result, higher development cost increases unit production cost. The problem of optimal planning work and rework processes belongs to the broad field of production-inventory model which deals with all kinds of reuse processes in supply chains. These processes aim to recover defective product items in such a way that they meet the quality level of 'good item'. The benefits from imperfect quality items are: regaining the material and value added on defective items and improving the environment protection. In this point of view, a model is introduced here to guide a firm/industry in addressing variable product reliability factor, variable unit production cost and dynamic production rate for time-varying demand. The paper provides an optimal control formulation of the problem and develops necessary and sufficient conditions for optimality of the dynamic variables. In this purpose, the Euler-Lagrange method is used to obtain optimal solutions for product reliability parameter and dynamic production rate. Finally, numerical examples are given to illustrate the proposed model.

[1]  Ranga V. Ramasesh,et al.  Measurement of manufacturing flexibility: A value based approach , 1991 .

[2]  Jan Olhager,et al.  Valuation of product-mix flexibility using real options , 2002 .

[3]  Yash P. Gupta,et al.  Flexibility of manufacturing systems: Concepts and measurements , 1989 .

[4]  Timothy L. Urban.  Production , Manufacturing and Logistics Inventory models with inventory-level-dependent demand : A comprehensive review and unifying theory , 2004 .

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

[6]  R. R. Jesse,et al.  A Note on Determining Order Quantities with a Linear Trend in Demand , 1984 .

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

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

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

[10]  E. Ritchie,et al.  The E.O.Q. for Linear Increasing Demand: A Simple Optimal Solution , 1984 .

[11]  T.C.E. Cheng,et al.  Optimal production stopping and restarting times for an EOQ model with deteriorating items , 1998, J. Oper. Res. Soc..

[12]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting , 1995 .

[13]  Manoranjan Maiti,et al.  A Fuzzy Inventory Model of Deteriorating Items with Stock-dependent Demand under Limited Storage Space , 1998 .

[14]  A. Goswami,et al.  A deterministic inventory model for deteriorating items with stock-dependent demand rate , 1993 .

[15]  Hui-Ming Wee,et al.  A deterministic lot-size inventory model for deteriorating items with shortages and a declining market , 1995, Comput. Oper. Res..

[16]  A. Goswami,et al.  An inventory model for deteriorating items with stock-dependent demand rate , 1996 .

[17]  Adamantios Mettas,et al.  Reliability allocation and optimization for complex systems , 2000, Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No.00CH37055).

[18]  Jinn-Tsair Teng,et al.  A deterministic inventory replenishment model with a linear trend in demand , 1996, Oper. Res. Lett..

[19]  M. Maiti,et al.  Inventory Model for Damagable Items with Stock-Dependent Demand and Shortages , 1997 .

[20]  Suresh Kumar Goyal.  A Heuristic for Replenishment of Trended Inventories Considering Shortages , 1988 .

[21]  Timothy L. Urban,et al.  A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate , 1988 .

[22]  Moncer Hariga,et al.  A lot sizing heuristic for deteriorating items with shortages in growing and declining markets , 1997, Comput. Oper. Res..

[23]  Suresh P. Sethi,et al.  Flexibility in manufacturing: A survey , 1990 .

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

[25]  Upendra Dave,et al.  A deterministic lot-size inventory model with shortages and a linear trend in demand , 1989 .

[26]  Timothy L. Urban.  An Inventory Model with an Inventory-Level-Dependent Demand Rate and Relaxed Terminal Conditions , 1992 .

[27]  M. Maiti,et al.  Inventory of damagable items with variable replenishment rate, stock-dependent demand and some units in hand , 1999 .

[28]  T. Datta,et al.  Demand promotion by upgradation under stock-dependent demand situation – a model , 1998 .

[29]  Shib Sankar Sana,et al.  On a volume flexible inventory model for items with an imperfect production system , 2007 .

[30]  B. Sarker,et al.  Effects of inflation and the time value of money on order quantity and allowable shortage , 1994 .

[31]  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..

[32]  Toni M. Somers,et al.  The measurement of manufacturing flexibility , 1992 .

[33]  D. Aranda.  Service operations strategy, flexibility and performance in engineering consulting firms , 2003 .

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

[35]  S.-L. Yang,et al.  An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy , 2003, J. Oper. Res. Soc..

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

[37]  T. M. Murdeshwar.  Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages-An Optimal Solution , 1988 .

[38]  R. Levin.  Production/Operations Management: Contemporary Policy for Managing Operating Systems , 1983 .

[39]  K. Skouri,et al.  Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging , 2003 .

[40]  Timothy L. Urban.  Inventory models with the demand rate dependent on stock and shortage levels , 1995 .

[41]  Manoranjan Maiti,et al.  Multi-objective Inventory Model of Deteriorating Items with Space Constraint in a Fuzzy Environment , 2008 .

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

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

[44]  K. Sarma,et al.  A Periodic Review Inventory Problem with Variable Stock Dependent Demand , 2001 .

[45]  Stanisław Bylka,et al.  Heuristics for impulse replenishment with continuous periodic demand , 2004 .

[46]  T. Datta,et al.  A Note on an Inventory Model with Inventory-level-dependent Demand Rate , 1990 .

[47]  K. S. Chaudhuri,et al.  AN EOQ MODEL WITH TIME-DEPENDENT DEMAND, INFLATION AND MONEY VALUE FOR A WARE-HOUSE ENTERPRISER , 2003 .

[48]  Lakdere Benkherouf,et al.  Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand , 1994 .

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

[50]  S. Goyal,et al.  The Finite Horizon Trended Inventory Replenishment Problem With Shortages , 1992 .

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

[52]  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..

[53]  Upendra Dave.  On a Heuristic Inventory-replenishment Rule for Items with a Linearly Increasing Demand Incorporating Shortages , 1989 .

[54]  Emmanuel Thanassoulis,et al.  Applied data envelopment analysis , 1991 .

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

[56]  T. Datta,et al.  Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages , 1991 .

[57]  M. Hariga.  An EOQ Model for Deteriorating Items with Shortages and Time-Varying Demand , 1995 .

[58]  Abraham Mehrez,et al.  Economic Production Lot Size Model with Variable Production Rate and Imperfect Quality , 1994 .

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

[60]  S. Sana,et al.  ON A VOLUME FLEXIBLE PRODUCTION POLICY FOR A DETERIORATING ITEM WITH TIME-DEPENDENT DEMAND AND SHORTAGES , 2004 .