Salvage Value from Deterioration (SVD): A Three-Parameter Weibull Distribution Inventory Model Approach

Abstract

Maintaining inventory systems with deteriorating items is one of the major problems in inventory management. This study aimed to develop an inventory model for deteriorating items with a prior focus on stochastic demand, salvage value, and shortages during which partial backlogging occurred. To achieve this, we derived an innovative approach of a single-item inventory model for deteriorating items having a time-dependent deterioration rate that follows a three-parameter Weibull distribution. While the demand pattern follows a negative exponential distribution with partial backlogging and salvage value. In a real market situation, salvage value is crucial to minimize the cost of the seller on deteriorating items. To validate our model on a real market inventory problem that incurred deteriorating items, we collected numerical data from the Ose poultry store and used the Maple mathematical software package to analyze the situation. An analytical procedure for deriving the optimal inventory solutions was provided. In addition, the necessary and sufficient conditions for the optimal policy of the inventory model were confirmed. A sensitivity analysis of the optimal solution concerning various parameters of the model was carried out to evaluate the model's responsiveness to changes in the inventory parameters. The findings from our study showed that the optimal inventory policy is best achieved when the seller places an order for 50 crates of eggs approximately every 2 weeks. In conclusion, this study can be adapted to complex situations, especially during the phase of the COVID-19 pandemic when supply chains and inventories experienced risks of disruptions.