Probabilistic Inventory Model for Deteriorating Items with Variable Production Rate under Trade Credit
Charles Chibuike Christopher
Department of Statistics, University of Nigeria, Nsukka, Nigeria and Department of Management Information Systems, Edith Cowan University, Perth, Western Australia, Australia.
Abimibola Victoria Oladugba *
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Managing deteriorating items requires a strategic inventory model to minimize stocking duration and associated costs. This study develops a probabilistic economic production quantity (EPQ) model for a deteriorating item inventory system with a variable production rate. The model accounts for production rate variations during uptime and incorporates a trade credit policy extended by manufacturers to retailers, as well as partially backlogged shortages. The deterioration rate is assumed to be constant, while the demand rate follows a uniform distribution. Based on these conditions, the study’s cost functions were formulated for two scenarios: when the customer cannot pay the manufacturer before the expiration of the trade credit period, M (i.e., Scenario 1: t4 ≤ M ≤ T), and when the customer can pay before the expiration (i.e., Scenario 2: M ≥ T). It was observed from the result of the numerical example that the cost function for Scenario 2 is equivalent to a model without a trade credit policy. Sensitivity analysis showed that offering a moderately extended trade credit period in a production inventory system with partially backlogged shortages is more cost-effective for optimization.
Keywords: Production rate, EPQ model, deterioration rate, trade credit policy, probabilistic demand, partially backlogged shortages