Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

•We analyze an EOQ model where the unit holding cost has two significant components.•Shortages are allowed and partially backordered.•We develop a solution procedure for determining the optimal inventory policy.•We present a sensitivity analysis on the optimal policy.

In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.