Inventory Periodic Review Model (nq, R, T) With Quadratic Backorder Costs

At each review, the quantity ordered is a multiple of Q, nQ and the reorder level is R. The backorder cost CB(t)
is taken as a question function of t, the length of time of the backorder. CB(t) is b1+b2+b3t
3
.
The paper firstly gives the basic mathematics required for the analysis. The demand for, is assumed to follow a
normal distribution.
The expected backorder cost is derived.
The inventory costs are derived superlatively for the factors b1, b2, and b3 of the quadratic costs. By setting the
b1, b2 and b3 to zero we have the inventory cost that is not time dependent.
Setting b3 alone to zero, we obtain the inventory costs when the backorder cost is a linear function of the time
of backorder.