A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints

Abstract This paper develops a mathematical model for a single period multi-product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints. After calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness, particular expressions for those density functions are considered. Here the constraints are of three types: (i) both are stochastic, (ii) one stochastic and other one imprecise (fuzzy) and (iii) both imprecise. The stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility/necessity constraints. Stochastic and fuzzy constraints are transformed to equivalent deterministic ones using ‘here and now’ approach and fuzzy relations respectively. The deterministic problems are solved using a non-linear optimization technique-Generalized Reduced Gradient Method. The model is illustrated through numerical examples. Sensitivity analyses on profit functions due to different permitted ‘aspiration’ and ‘confidence’ levels are presented.

[1]  M. K. Salameh,et al.  Economic production quantity model for items with imperfect quality , 2000 .

[2]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[3]  D. Dubois,et al.  The mean value of a fuzzy number , 1987 .

[4]  Jing-Shing Yao,et al.  Consumer surplus and producer surplus for fuzzy demand and fuzzy supply , 1999, Fuzzy Sets Syst..

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

[6]  M. D. S. Aliyu,et al.  Multi-item-multi-plant inventory control of production systems with shortages/backorders , 1999, Int. J. Syst. Sci..

[7]  Moutaz Khouja,et al.  The economic production lot size model under volume flexibility , 1995, Comput. Oper. Res..

[8]  D. Dubois,et al.  Systems of linear fuzzy constraints , 1980 .

[9]  Abdul Raouf,et al.  On the Constrained Multi‐item Single‐period Inventory Problem , 1993 .

[10]  Edward A. Silver,et al.  Operations Research in Inventory Management: A Review and Critique , 1981, Oper. Res..

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

[12]  Jack C. Hayya,et al.  On production policies for a linearly increasing demand and finite, uniform production rate , 1990 .

[13]  Manoranjan Maiti,et al.  Production , Manufacturing and Logistics Possibility and necessity constraints and their defuzzification — A multi-item production-inventory scenario via optimal control theory , 2006 .

[14]  J. Teghem,et al.  STRANGE: an interactive method for multi-objective linear programming under uncertainty , 1986 .

[15]  Huey-Ming Lee,et al.  Economic production quantity for fuzzy demand quantity, and fuzzy production quantity , 1998, Eur. J. Oper. Res..

[16]  PradeHenri,et al.  The mean value of a fuzzy number , 1987 .

[17]  L. Cárdenas-Barrón,et al.  Note on: Economic production quantity model for items with imperfect quality – a practical approach , 2002 .

[18]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

[19]  Shan-Huo Chen,et al.  A Model and Algorithm of Fuzzy Product Positioning , 1999, Inf. Sci..

[20]  Adrijit Goswami,et al.  EOQ model for an inventory with a linear trend in demand and finite rate of replenishment considering shortages , 1991 .

[21]  Mohamed Ben-Daya,et al.  The economic production lot-sizing problem with imperfect production processes and imperfect maintenance , 2002 .

[22]  Masahiro Inuiguchi,et al.  The usefulness of possibilistic programming in production planning problems , 1994 .

[23]  Juite Wang,et al.  Fuzzy decision modeling for supply chain management , 2005, Fuzzy Sets Syst..

[24]  Chih-Hsun Hsieh,et al.  Optimization of fuzzy production inventory models , 2002, Inf. Sci..

[25]  J. Leclercq Stochastic programming: An interactive multicriteria approach , 1982 .

[26]  Baoding Liu,et al.  A note on chance constrained programming with fuzzy coefficients , 1998, Fuzzy Sets Syst..

[27]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[28]  Juite Wang,et al.  A fuzzy set approach for R&D portfolio selection using a real options valuation model , 2007 .

[29]  San-Chyi Chang,et al.  Fuzzy production inventory for fuzzy product quantity with triangular fuzzy number , 1999, Fuzzy Sets Syst..

[30]  Didier Dubois,et al.  Fuzzy constraints in job-shop scheduling , 1995, J. Intell. Manuf..

[31]  Nikos Tsourveloudis,et al.  Fuzzy work-in-process inventory control of unreliable manufacturing systems , 2000, Inf. Sci..

[32]  K. S. Chaudhuri,et al.  An economic production lot-size model with shortages and time-dependent demand , 1999 .

[33]  S. Kalpakam,et al.  (S - 1,S) Perishable systems with stochastic leadtimes , 1995 .

[34]  Uday S. Karmarkar,et al.  Lot Sizes, Lead Times and In-Process Inventories , 1987 .

[35]  Robert S. Sullivan,et al.  A goal programming model for readiness and the optimal redeployment of resources , 1978 .

[36]  Didier Dubois,et al.  Ranking fuzzy numbers in the setting of possibility theory , 1983, Inf. Sci..

[37]  N. Shah Probabilistic time-scheduling model for an exponentially decaying inventory when delays in payments are permissible , 1993 .

[38]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

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

[40]  Didier Dubois,et al.  Qualitative possibility theory and its applications to constraint satisfaction and decision under uncertainty , 1999, Int. J. Intell. Syst..

[41]  Yong-Wu Zhou,et al.  Optimal Production Policy for an Item with Shortages and Increasing Time-varying Demand , 1996 .

[42]  Bruno Contini,et al.  A Stochastic Approach to Goal Programming , 1968, Oper. Res..

[43]  S. Goyal,et al.  A simple integrated production policy of an imperfect item for vendor and buyer , 2003 .

[44]  Baoding Liu,et al.  Chance constrained programming with fuzzy parameters , 1998, Fuzzy Sets Syst..