A partial back-ordering inventory model for log-gamma degenerating items with quadratic demand and shortages

Abstract

In this paper, an inventory model for deteriorating items with quadratic demand is developed. Deterioration is permitted on inventory that follows two-parameter of log-gamma distributions. In the inventory system, shortages are taken as fully and partially back-ordered. The goal is to find the optimal cycle times in order to minimise total costs. First, the problem formulation and procedure are explained to find the most favourable solution. The solution process is also found to minimise the overall cost. Various principles are used to calculate the total costs. A solution process is developed and numerical examples are presented to demonstrate the outcome of the proposed model in order to find the optimal solution. Sensitivity analysis of the most favourable solution with respect to system parameters is performed and recommendations are provided for further research.