Inventory Control Models

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Inventory Control Models

• Session 7
• MHA 6350

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Inventory Planning and Control
Planning on What Inventory to Stockand How to
Acquire It.
Forecasting Parts/ProductDemand.
Controlling InventoryLevels.
Feedback Measurements to Revise Plans
andForecasts.
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Importance of Inventory Control

• Decoupling Function
• (buffers)
• Storing Resources
• (work-in-process)
• Irregular Supply and Demand
• Quantity Discounts
• Avoiding Stockouts and Shortages

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Inventory Decision

• How much to order
• When to order
• For the purpose of minimizing inventory costs of
• items
• ordering
• carrying or holding inventory
• safety stock
• stockouts

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Economic Order Quantity(EOQ)Important
Assumptions

• Demand is known and constant
• Lead time is known and constant
• Receipt of inventory is instantaneous
• Quantity discounts are not possible
• Only variable costs are ordering and holding or
  carrying costs
• If orders are placed at right time stockouts and
  shortages are completely avoided.

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Finding EOQ

• Q optimal number of pieces per order
• k Fixed cost per order
• A annual demand
• h Annual cost per dollar value of holding items
  in inventory.
• T Time between orders

2Ak hc
Q
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Objective
Choose the number of items to order Q Order
quantity such that Total annual cost Ordering
cost Holding cost Procurement cost is
minimized. INVENTORY CYCLE Each cycle has a
duration of T years (some fraction of one year).
Q
Inventory level
Slope - A
T
A
Q
Time (years)
Q
T
Order points
A
Source Lapin, 1994
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Example
The local convenience store sells 5,200 cases of
root beer each year. The keep it simple we will
assume that the beverage is sold at a constant
rate throughout the year. The net cost of each
case is 2. The wholesale supplier charges 10
for each delivery regardless of the order
quantity and is delivered within 24 hours of the
time the order is placed. The store owners
working capital is tied up in inventory and these
funds are borrowed at a simple interest rate of
10. In addition, the owner must pay state
franchise tax of 5 of annual inventory value and
another 5 for theft insurance. All other
operating costs are either fixed or are not
dependent on the amount of root beer sold.
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Problem Solution
k 10 per order A 5,200 cases per year c 2
per case h .20 annual cost per dollar value of
root beer held in inventory
Present policy Order every week Order
quantity Q 100 cases
5,200 52
Total annual relevant cost of this policy is
TC(Q) ( )k hc ( ) ( )
10 .20(2) ( ) 520 20 540 dollars per
year
A Q
Q 2
100 2
5,200 100
Annual cost of 520 is much larger than annual
20 holding cost. The two cost components should
be the same to achieve an optimal inventory
policy.
Q
2Ak hc
2(5,200)10 .20(2)


260,000
509.9, or 510 cases of root beer Optimal
inventory policy
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Problem solution Cont
Optimal time between orders is T
.098 years Converted to days 365
(.098) 35.8 or 36 days. The optimal inventory
policy is order 510 cases every 36 days. Total
Annual Relevant cost TC(510) (5,200/510)10
.20(2)(510/2) 101.96 102.00 203.96
dollars per year The two cost components differ
by .04 because the value of Q was rounded to
the nearest whole number.) More than 300 in
annual costs can be saved by switching to the
optimal inventory policy.
510
5,200
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Reorder Point

• ROP (demand per day) x (lead time for a new
  order in days) d x L
• If the average daily usage rate of a material is
  25 units and the lead-time is 4 days, then
  Reorder level Average daily usage rate x Lead
  time in days 25 units x 4 days 100 units
• Safety Stock
• SWAG
• Formula
• ROP d x L SS

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Re-order Point (ROP)Using Excel
Formula for ROP with Optimal SSRe-order
pointAverage Lead TimeAverage Demand
ZSQRT(Avg. Lead TimeStandard Deviation of
Demand2 Avg. Demand2Standard Deviation of
Lead Time2) Note A value followed
by the (caret symbol) and number is the
exponent of the value e.g. 32 is three squared.
1. What is the average lead time for the
part/finished good that you need? 2. What is the
standard deviation of that lead time? It is very
important to track how long shipments take from
you suppliers. If you are not doing this, start.
It should be your top priority. Assuming you have
tracked the data, excel can very easily help you
determine your standard deviation. In excel, go
to the toolbar and click on Insert, then click on
Function, and choose STDEV and click ok. Then,
enter in as much lead time data you have and
presto, you have your standard deviation.
http//www.inventorymanagementreview.org/2005/06/s
afety_stock.html
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Re-order Point (ROP) Cont
3. What is the expected demand you are working
with? 4. What is the standard deviation on this
demand?  Perhaps this is something you will be
familiar with from experience, however, if not,
this is something you should be able to squeeze
out of Ted from the marketing department.  One
way to find it is to look at historical demand
and use the STDEV function in excel to determine
it. 5. How sure do you want to be that you arent
going to run out? 90, 95, 98, 99? Whatever
you decide, this will become your service level.
Using this percentage, a statistical z-table
should be used to get the corresponding
z-value. A good z-value webpage can be found at
http//www.inventoryops.com/safety_stock.htm. So,
for example, if you want a 98 service level, you
would use 2.05 as your z-value.
3. What is the expected demand you are working
with? 4. What is the standard deviation on this
demand?  Perhaps this is something you will be
familiar with from experience, however, if not,
this is something you should be able to squeeze
out of Ted from the marketing department.  One
way to find it is to look at historical demand
and use the STDEV function in excel to determine
it. 5. How sure do you want to be that you arent
going to run out? 90, 95, 98, 99? Whatever
you decide, this will become your service level.
Using this percentage, a statistical z-table
should be used to get the corresponding
z-value. A good z-value webpage can be found at
http//www.inventoryops.com/safety_stock.htm. So,
for example, if you want a 98 service level, you
would use 2.05 as your z-value.
http//www.inventorymanagementreview.org/2005/06/s
afety_stock.html
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Just in TimeInventory Control

• Kanban signal card
• Kanban and Container

Producer Area
Storage Area
User Area
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1
3
2
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Theory of Constraints cost accounting
Eliyahu M. Goldratt developed the Theory of
Constraints in part to address the
cost-accounting problems in what he calls the
"cost world". He offers a substitute, called
throughput accounting, that uses throughput
(money for goods sold to customers) in place of
output (goods produced that may sell or may boost
inventory) and considers labor as a fixed rather
than as a variable cost. He defines inventory
simply as everything the organization owns that
it plans to sell, including buildings, machinery,
and many other things in addition to the
categories listed here. Throughput accounting
recognizes only one class of variable costs the
operating expenses like materials and components
that vary directly with the quantity
produced. Finished goods inventories remain
balance-sheet assets, but labor efficiency ratios
no longer evaluate managers and workers. Instead
of an incentive to reduce labor cost, throughput
accounting focuses attention on the relationships
between throughput (revenue or income) on one
hand and controllable operating expenses and
changes in inventory on the other. Those
relationships direct attention to the constraints
or bottlenecks that prevent the system from
producing more throughput, rather than to people
- who have little or no control over their
situations.
http//en.wikipedia.org/wiki/Inventory
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Theory of ConstraintsThe key steps in
implementing an effective TOC approach are

• Step zero Articulate the goal of the
  organization. Frequently, this is something like,
  "Make money now and in the future."
• Identify the constraint (the thing that prevents
  the organization from obtaining more of the goal)
  
• Decide how to exploit the constraint (make sure
  the constraint is doing things that the
  constraint uniquely does, and not doing things
  that it should not do)
• Subordinate all other processes to above decision
  (align all other processes to the decision made
  above)
• Elevate the constraint (if required, permanently
  increase capacity of the constraint "buy more")
• If, as a result of these steps, the constraint
  has moved, return to Step 1. Don't let inertia
  become the constraint.

http//en.wikipedia.org/wiki/Theory_of_Constraints