An Ordering Policy with Generalized Deterioration, Ramp-Type Demand Under Complete Backlogging

Abstract

In this paper, a deteriorating inventory model is proposed by considering the followed assumptions: (i) Shortages are permitted at the beginning of the model. (ii) Demand rate is deterministic and ramp-type. (iii) Deteriorating items chase a two-parameter Weibull distribution. The mathematical model is derived under the circumstance when the fixed shortage time point is less than procurement time point, and it is also valid for newly launched high-tech products like android mobiles, 4G SIM cards, and automobiles, and seasonal items, etc. The primary aim of the developed model is to determine the optimum value of the procurement time point and the cycle time to calculate the ordering quantity and the average total cost. Furthermore, the algorithm, numerical examples, and sensitivity analysis for different parameters are provided.

Appendix

$$ \frac{{\partial^{2} {\mathbf{\mathbb{Z}}}\left( {t_{b} } \right)}}{{\partial t_{b}^{2} }} = \frac{{a_{0} \mu }}{T}\left[ {\alpha \beta c_{d} t_{b}^{\beta - 2} \left[ {\left( {\beta - 1} \right)\left( {t_{b} - T} \right) + t_{b} } \right] + h\left[ {1 + \alpha \beta t_{b}^{\beta - 1} \left( {T - t_{b} } \right)} \right] + c_{b} } \right]. $$