A probabilistic inventory model without trade credits with linear random component demand

Abstract

This paper develops a probabilistic inventory model without trade credits in which demand
follows a linear trend with a random component. The holding cost is assumed to be time
dependent, and shortages are permitted to meet unexpected demand fluctuations. The model
is formulated to minimize the expected total cost, which consists of ordering cost, holding
cost, and shortage cost. A numerical example is provided to demonstrate the applicability of
the proposed model. The results show that the optimal order quantity is obtained as the sum
of expected demand and a safety stock component determined by the variability in demand.
Sensitivity analysis reveals that demand variability has the greatest impact on total cost,
followed by holding cost, service level, and ordering cost. The findings highlight the importance
of incorporating demand uncertainty into inventory policies, especially in situations where
immediate payment is required and trade credits are not available. This research provides
valuable insights for decision-makers in designing inventory strategies under uncertainty