Inventory Costs
Overview
Inventory management refers to the process that a company uses to determine the optimal amount of inventory to hold at any given time.
In general, a firm must evaluate the trade off between holding inventory to meet customer demand (and in particular unexpected demand) and
the cost of holding that inventory. Inventory management models estimate the relevant values and probabilities and runs an optimization to
determine the best level.
Holding Costs
Holding costs can be categorized as
fixed and variable.
-
Fixed Costs - fixed costs do not change with the level of inventory (at least locally, meaning within
a given range). Fixed Costs are important in understanding total firm profitability
(see modeling the firm)
However, because they are fixed (cannot change),
they dont really impact the solution of optimizing an inventory policy.
-
Variable Costs - these are what are normally referred to as holding costs, and will
be denoted as {% h %}, expressed as the dollar cost of holding one unit of inventory for one unit of time.
Define the total units of inventory held as {% Q %}. Then the total variable holding costs are
{% Holding\: Costs = h \times Average\: Q %}
Somemtimes h is assumed to be expressed as a fraction of the product cost, {% c %}, in which case we should have
{% Holding\: Costs = h \times c \times Average\: Q %}
Transaction Costs
Transacation costs can likewise be categorized as
fixed and variable.
{% k %} is usually defined as the fixed cost per transaction and {% c_T %} is the variable transaction cost.
If we assume a simple model of constant product demand of {% D %} per period, where we reorder {% Q %} units everytime
inventory goes to zero, then our per period transaction costs are
{% k (D/Q) + c_T D %}
This assumes that once an inventory order is issued, it is fulfilled instantaneously (so that the constant demand
is continuously fulfilled). The cost curve mapped against {% Q %} is given below.
Total Costs
Adding the fixed and variable costs, we get
{% Total\: Costs = h \times Average\: Q + k (D/Q) + c_T D %}
Note that if demand is constant, the average Q is just Q/2. Also note that the last term in the formula is independent of Q, so when optimizing
for Q, we can just ignore this term.
