A Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item

In this paper, some realistic multi-period production-inventory models are formulated for deteriorating items with known dynamic demands for optimal productions. Here, the rates of production are time dependent (quadratic/linear) or constant expressed by a Chebyshev polynomial and considered as a control variable. The models are solved using Chebyshev spectral approximations, the El-Hawary technique and a genetic algorithm (GA). The models have been illustrated by numerical data. The optimum results for different production functions are presented in both tabular and graphical forms.

[1]  M. A. Hall,et al.  The analysis of an inventory control model using posynomial geometric programming , 1982 .

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

[3]  Zaid T. Balkhi,et al.  An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money , 2004, Int. J. Syst. Sci..

[4]  S. K. Goyal,et al.  Recent trends in modeling of deteriorating inventory , 2001, Eur. J. Oper. Res..

[5]  Shanlin Yang,et al.  A new variable production scheduling strategy for deteriorating items with time-varying demand and partial lost sale , 2003, Comput. Oper. Res..

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

[7]  Manoranjan Maiti,et al.  Inventory of Deteriorating Complementary and Substitute Items with Stock Dependent Demand , 2005 .

[8]  G. Padmanabhan,et al.  Analysis of multi-item inventory systems under resource constraints: A non-linear goal programming approach , 1990 .

[9]  Kin Keung Lai,et al.  A fuzzy approach to the multiobjective transportation problem , 2000, Comput. Oper. Res..

[10]  Manoranjan Maiti,et al.  Numerical Approach of Multi-Objective Optimal Control Problem in Imprecise Environment , 2005, Fuzzy Optim. Decis. Mak..

[11]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[12]  M. S. Salim,et al.  A Chebyshev approximation for solving optimal control problems , 1995 .

[13]  Lakdere Benkherouf,et al.  A diffusion inventory model for deteriorating items , 2003, Appl. Math. Comput..

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

[15]  S. E. El-gendi,et al.  Chebyshev Solution of Differential, Integral and Integro-Differential Equations , 1969, Comput. J..

[16]  Zaid T. Balkhi,et al.  On a finite horizon production lot size inventory model for deteriorating items: An optimal solution , 2001, Eur. J. Oper. Res..

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