This paper develops an Economic Order Quantity (EOQ) model that incorporates three realistic features of modern inventory systems: linear time-dependent demand, linear deterioration of stocked items, and a partial backlogging rate that varies with waiting time. Many traditional EOQ models assume constant demand and exponential deterioration, which limits their applicability to industries where consumption patterns grow steadily and items deteriorate at a proportional rate. To address this gap, the proposed model formulates a deterministic framework in which demand increases or decreases linearly over time, and deterioration is represented through a linear deterioration coefficient. Shortages are permitted, and the willingness of customers to wait is modelled as a decreasing function of the waiting time, leading to time-dependent partial backlogging. The total cost function is derived by combining ordering, holding, deterioration, and shortage-related costs and the optimal replenishment cycle and order quantity are obtained using analytical methods. A numerical example and sensitivity analysis highlight the influence of key parameters on the optimal policy. The findings demonstrate that time-dependent backlogging significantly affects shortage decisions, while linear demand and deterioration jointly shape replenishment frequency. The developed model offers practical insights for inventory managers dealing with gradually changing demand trends and products vulnerable to deterioration.
