Three echelon supply chain inventory model for deteriorating items with limited storage facility and lead‐time under inflation

In this study, we have explored a three echelon supply chain inventory model with limited storage facility under inflation. The supplier experiences the problem of lead‐time at his end. So even though the retailer has placed the order, he has to wait for the supplier to deliver. The lead‐time of the supplier is a probability density function of his managing cost. The more the supplier is ready to spend as managing expenses, smaller will be the lead time and vice versa. However, there is a constraint upon the amount the supplier can afford to spend; hence there involved capital constraint also. For the retailer, we have considered the two situations according to rented and own warehouse used. Due to the life time in RW, the product has no deterioration but in OW, the product has deterioration. The setup has been explored numerically and the sensitivity has also been analysed.