Continuous review substitutable inventory system with partial backlogging

This paper deals with a two‐commodity substitutable (two way) inventory control system. A continuous review strategy is implemented to maintain the system for transaction reporting and reorders are placed jointly whenever necessary. The substitutable nature of the commodities gives an added advantage to balance the inventory levels and consequently a joint reorder. Backlogging is allowed for both commodities up to a certain level say Ni,(i = 1,2), whenever substitution is not possible due to non‐availability of items. The demand points are assumed to follow independent Poisson processes with parameter λi > 0, i = 1,2, and the lead time for each joint reorder is exponentially distributed with parameter μ> 0. The steady state probability distribution of the Markov process with ergodic property is computed and the various system performance measures are established. By imposing proper cost structure, total expected cost per unit time is obtained to illustrate optimal parameters via suitable numerical examples.