A partial backlogging production-inventory lot-size model with time-varying holding cost and Weibull deterioration

Abstract

This paper presents an economic production model with time varying holding cost. The demand and backlogging rates are assumed to be continuous and varying with time. While the production rate is assumed to be stock dependent with unknown time horizon. Shortages are allowed with partial backlogging of demand. Deterioration is taken into consideration and the deterioration rate follows the Weibull distribution pattern. The models generate optimal values of initial production run time, onset of shortages, and production recommencement time that minimises the total relevant costs of production and inventory for any given set of system parameters. A numerical example and sensitivity analysis are given to validate the proposed models.