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Office Hours: MWF 11:30-12:20,
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Homework is due next Thursday,
September 3

HW : Read Chapter 1 in your book, do the
problem on the handout.
Calculators/Software
Evening Study Sessions
Models and Decision Making
Quantitative Decision Making with
Spreadsheet Applications 7th ed.
By Lapin and Whisler
Section 1-4
Inventory Problem
Total annual cost =
ordering cost + holding cost + procurement cost
Minimize:
 A
Q 
TC   k  hc    Ac
Q 
2
Where A = annual number of items demanded
k = cost of placing an order
h = annual cost per dollar value for holding
items in inventory
c = unit cost of procuring an item
Q = order quantity ← this is a variable
And TC is a variable, everything else is a parameter
Constraints and Feasible Solutions
Constraints place special limitations on the
problem variables.
Ex: Q ≤ 300
Feasible Solutions: values of Q less than
or equal to 300.
Infeasible Solutions: values of Q bigger
than 300.
Optimal Solution
Use quantitative methods to find an optimal
solution.
We find the optimal solution by setting the
formula for the holding cost equal to the formula
for the ordering cost and solving for Q.
Set holding cost equal to
 A
Q 
ordering cost
 k  hc  
Q 
2
2 Ak
Q
hc
Solve for Q. This is
Wilson’s Formula
Suppose each order costs $4 to place, the
annual demand is 1000 units, it costs $.20 per
year for each dollar value of items held in
inventory, and these items can be procured from
the supplier for $1 each.
k=4
2 Ak
A=1000
Q
h=.20
hc
c=1
2(1000)4
Q
 40,000  200
.20(1)
Wilson’s Formula
The Wilson formula is a method for determining
the optimal quantity to order and the time
between any two orders for a given entity.
Assumption: The only costs entailed are a
warehousing cost per stock keeping unit and a
one-time cost every time an order is placed.
Goal: Find an optimal balance between the two
costs to minimize the total cost, which is known
as the economic order quantity (EOQ).
<http://www.masystem.com/o.o.i.s/1360>
<http://www.free-logistics.com/index.php/Spec-Sheets/Forecasts-Supply-andInventory/Wilson-Formula-Economic-Order-Quantity.html>
Algorithms and Model Types
An algorithm is the procedure used to
solve a problem.
Deterministic models are models that
contain known and fixed constants
throughout their formulation.
Stochastic models are models that involve
one or more uncertain quantities and
probability must be considered to find a
solution.
Discussion Question
Analee Mark owns a tea shop. The demand for
gourmet teas is roughly constant over the year.
Past data indicate that the annual demand for
Assam Tea is 5200 cases per year. Ordering
costs are $10/order. The procurement cost is
$1.50 per case for the tea and $.50 for shipping.
The holding cost (storage and theft insurance) is
$.20 per dollar value of the tea held in inventory.
She wants to place orders at regular time
intervals for the same amount of tea each time.
Discussion Question
 A
Q 
TC   k  hc    Ac
Q 
2
A = annual number of items demanded
= 5200
k = cost of placing an order
= 10
h = annual cost per dollar value for holding
items in inventory
= .20
c = unit cost of procuring an item
= 1.50 + .50 = 2.00
Q = order quantity
this varies depending how frequently she orders
Discussion Question
What would be the cost if she were to
order the total inventory once a year?
 A
Q 
TC   k  hc    Ac
Q 
2
Q=5200
 5200 
 5200 
TC  
10  .20  2
  5200  2
 5200 
 2 
= $11,450
Discussion Question
What would be the cost if she were to
order the total inventory once a week?
 A
Q 
TC   k  hc    Ac
Q 
2
Q=5200/52=100
 5200 
 100 
TC  
10  .20  2
  5200  2
 100 
 2 
= $10,940