Imperfect production policy of a breakable item with variable breakability and demand in random planning horizon

Abstract

Production inventory model of a breakable item, i.e., item made of glass, ceramic, etc. is developed where, above a certain stock level breakability increases with time and stock level. Demand of the item is stock and selling price dependent. Production process is not 100% perfect, i.e., not all produced units are of perfect quality. Defective units are sold at a reduced price. Duration of demand of the item in the market is assumed as stochastic in nature and follows normal distribution with a known mean and standard deviation. Here, the unit production cost depends on production rate and is derived from the particular production function under which it is being produced. Here selling price, reliability of production process, set-up cost and duration of each cycle are decision variables. Model is illustrated with numerical data and some sensitivity analyses have been presented.