A two-warehouse inventory model for non-instantaneous deteriorating items over stochastic planning horizon

This paper deals with a two-warehouse inventory control problem for non-instantaneous deteriorating items in stochastic framework, wherein shortages are permissible and are mixture of partially backlog and lost sales. The paper tackles a situation in which the retailer procures more quantity than his/her own warehouse (OW) storage capacity. In such a situation, a rented warehouse (RW) is needed to keep the over purchasing. The stochastic framework captures the situation of random planning horizon of trading. The multifariousness of the random planning horizon is discussed by considering two special cases, namely, uniform and truncated normal distributions. Depending upon the consumption times to and tr of OW and RW inventories, respectively, and preserve time tp after that product starts to deteriorate, we formulate mathematical models for three cases: (i) tp ≤ tr ≤ to, (ii) tr ≤ tp ≤ to, and (iii) tr ≤ to ≤ tp. The discussion is further elongated by presenting some numerical illustrations with comprehensive sensitivity analysis for changes in the value of parameters.