Handout3 3 .docx - Handout 3: Inventory Control Inventory...

Handout
3: Inventory Control
Inventory level is controlled through ordering policy. The ordering policy needs to be
optimized by minimizing costs while fulfilling demands. Each inventory control model has some
assumptions and it is important to validate these assumptions when applying a model to a real-life
system.
1. Economic Order Quantity (EOQ) Model
Assumptions:
 Production (purchase) is instantaneous.
 Demand is deterministic and constant over time.
 A production (purchase) run incurs a fixed setup cost. Regardless of the size of the lot or the
status of the factory, the setup cost is the same.
 Backorders are not allowed.
Notations:
D = demand rate (in units per year)
c = unit production (purchase) cost, not counting setup or inventory costs (in dollars per
unit)
A = fixed setup cost to produce (purchase) a lot
h = inventory holding cost (in dollars per unit per year); if the holding cost consists entirely of
interest on money tied up in inventory, then h=ic, where i is the annual interest rate
Q = lot size (in units); this is the decision variable
Inventory behavior of EOQ model in an optimal ordering policy:
Total cost per year, which we denote by Y(Q), can be expressed as
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The lot size that minimizes annual cost is
This square root formula is the well-known economic order quantity (EOQ), also referred to
as the economic lot size. And, optimal order interval is
Example) Consider a shop that produces metal racks. The demand for metal racks is fairly steady
and predictable at D=1,000 units per year. The unit cost of the racks is c=$250, but the
metalworking shop also charges a fixed cost of A=$500 per order, to cover the cost of shutting down
the shop to set up. The shop estimates its opportunity cost for money at 10 percent per year. It also
estimates that the floor space required to store a rack costs roughly $10 per year in annualized costs.
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2. Economic Production Lot (EPL) Model
One extension of EOQ model is to the case in which replenishment is not instantaneous;
instead, there is a finite, but constant and deterministic, production rate. This model is sometimes
called the economic production lot (EPL) model. If we let P represent the production rate (and
assume that P > D so that the system has capacity to keep up with demand), then the EPL model
results in the following lot size to minimize the sum of setup and holding costs:
Note that if P=∞, then, this formula reduces to the regular EOQ. Otherwise, it results in a
larger lot size to cover for the fact that replenishment items take time to produce. Other variants of
the basic EOQ include backorders (i.e., orders that are not filled immediately, but have to wait until