This paper modifies Paknejad et al.'s inventory model by relaxing the assumption that the stochastic demand during lead time follows a specific probability distribution, and by considering that the unsatisfied demands are partially backordered. Also, instead of having a stockout cost in the objective function, a service level constraint is employed. In this new model, we investigate the feasibility of setup cost reduction and derive the closed-form expression of the optimal policy. The critical points of some interested parameters for which investment on setup cost reduction is warranted are included, and some numerical examples are given to illustrate the results derived.
