This paper used an algebraic approach to
examine the EOQ model with two backorder
costs. The analysis identified two cases: when the
size of the fixed backorder cost is relatively large
(pX
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2kh=rD
p
), there should optimally be no
backordering, and the basic EOQ applies. When
p is smaller than
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2kh=rD
p
; there should optimally
be some backorders. The linear backorder p cost
plays no role in this dichotomy: that component is
never too large itself to make backordering too
expensive. The optimal values of all variables were
obtained without calculus, and some new results
developed and some special cases considered. It
was also shown that the EPQ model is basically