Article ID: | iaor20133566 |
Volume: | 144 |
Issue: | 1 |
Start Page Number: | 180 |
End Page Number: | 188 |
Publication Date: | Jul 2013 |
Journal: | International Journal of Production Economics |
Authors: | Maiti Manoranjan, Kumar Maiti Manas, Guchhait Partha |
Keywords: | inventory, optimization, control, combinatorial optimization |
In this paper, economic production quantity (EPQ) models for breakable or deteriorating item are developed with variable demands, being dependent on time or on‐hand stock. Here rate of production and holding cost are time dependent, unit production cost is a function of both production reliability indicator and production rate. Set‐up cost is also partially production rate dependent. The production process produces some imperfect quantities which are instantly reworked at a cost to bring back those units to the perfect ones. The production process ultimately depends on both time and reliability indicator. The models are formulated as optimal control problems and the total profit functions with effect of inflation and time‐value of money are expressed as finite integrals over the finite planning horizon. The problems are solved using Euler–Lagrange function based on variational calculus and Newton–Raphson method to determine the optimal production reliability indicator (