Production Quantity Model for Deteriorating Items under Inventory Dependent Demand and Time-Dependent Production with Shortages

Abstract

This paper develops a Production Quantity Model for deteriorating items with time-dependent
production rates and inventory-dependent demand. Demand is assumed to depend on on-hand
inventory, while production varies over time and deterioration occurs at a constant rate. Using
differential equations, the inventory level at any point in time is determined. The model
calculates the total production cost under fully backlogged shortages, and the optimal production
schedule is derived by minimizing this cost. A sensitivity analysis is conducted to investigate the
impact of costs and system parameters on the optimal policy. The model is further extended to
the no-shortage case, offering a flexible framework for production planning of perishable or
deteriorating items.