BA 301
Operations Management
Spring 2003
Inventory Management
Chapter 12
Continued
Calculating Order Size
When material is ordered from a
supplier outside the firm, use the EOQ
model and extend this with “quantity
discount” information when appropriate.
 When sub-assemblies are fabricate
within the firm, use the Production
Order Quantity (POQ) model

EOQ Model
How Much to Order?
Annual Cost
Order (Setup) Cost Curve
Optimal
Order Quantity (Q*)
Order Quantity
EOQ Model
When To Order
Inventory Level
Average
Inventory
(Q*/2)
Optimal
Order
Quantity
(Q*)
Reorder
Point
(ROP)
Lead Time
Time
Production Order Quantity
Part A-60 is a “sub-assembly”. It is a
platform for the computer “motherboard”. The
company requires 3000 of these per year.
This part is fabricated in the production
facility.
 The machine that fabricates the platform
(A-60) can make 30 per day.
 Two hours of labor time are required to do the
set-up for the fabricating machine.
 Labor time costs $100 per hour

POQ Model Inventory Levels
Inventory Level
Production portion of cycle
Demand portion of cycle with no
supply
Supply
Begins
Supply
Ends
Time
POQ continued
The item cost of the platform (A-60) is
$20.
 The holding cost is 25% of the item
cost.
 What is the “Order Quantity”?

Inventory Costs for
Production Order Quantity
Holding costs - associated with holding
or “carrying” inventory over time
 Setup costs - cost to prepare a
machine or process for
manufacturing an order

Setup Costs
Clean-up costs
 Re-tooling costs
 Adjustment costs
 These costs are primarily determined by
the labor time necessary to perform the
tasks.

POQ continued

We need to derive a formula that minimizes the
Total Cost (Annual Holding Cost + Annual Setup Cost).
 Differences between POQ situation for the A60 platform and the EOQ situation for the A-61
microprocessor:
We fabricate the item rather than purchase
it from a supplier.
We use the item while it is being made.
 This results in a difference in the maximum
inventory.
POQ continued

In the EOQ model, maximum inventory was
equal to the Order Size.
 In the POQ model, maximum inventory is less
than the Order Size.
 Why? Because we make the item and use
it while it is being made.
 Assume that the Order Size is 300.
– How long would it take to make this order?
– What would the inventory level be at the end of
the first day?
– What would the inventory level be when we had
finished the order?
– How can we use this information to derive a
general formula for Production Order Quantity?
EOQ Model
When To Order
Inventory Level
Average
Inventory
(Q*/2)
Optimal
Order
Quantity
(Q*)
Reorder
Point
(ROP)
Lead Time
Time
POQ continued

Maximum Inventory = (p-d)(# days production)
This is the inventory build-up rate (p-d) times the
number of days the fabrication machine makes the
part.





Let “# days production” = t (for “time”)
Maximum Inventory = (p-d)t = pt-dt
Order Size = Q = pt; t = Q/p
Max Inv Level = (p-d)(Q/p) = p(Q/p) – d(Q/p)
= Q – Q(d/p) = Q(1 - d/p)
Ave Inv Level = Q(1 – d/p)/2
POQ continued
The Production Order Quantity formula:
Q* = POQ = sq.rt.(2DS/(H(1-d/p))
See formula 12.7 on page 491
 For part A-60:
 POQ = sq.rt.(2x3000x200/(5(1-10/30))
 POQ = 600 (rounded)
 Calculate AHC, ASC, & Total Annual Cost
