1. Inventory Management
Chapter 13

2. MIS 373: Basic Operations Management
Inventory Costs
Purchase cost
The amount paid to buy the inventory
Holding (carrying) costs
Cost to carry an item in inventory for a length of time, usually a year
Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security).
Ordering costs
Costs of ordering and receiving inventory
determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage.
Shortage costs
Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit
MIS 373: Basic Operations Management

3. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time
MIS 373: Basic Operations Management

4. MIS 373: Basic Operations Management
Total Annual Cost
Total Cost = Annual Holding Cost + Annual Ordering Cost
(TC)
where
Q = order quantity in units
H = holding (carrying) cost per unit, usually per year
D = demand, usually in units per year
S = ordering cost per order = Q H + D S 2
Average number of units in inventory
Number of orders
MIS 373: Basic Operations Management

5. MIS 373: Basic Operations Management
Deriving EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
𝑇 𝐶 ′ = 𝐻 2 + −1 𝐷𝑆 𝑄 2 =0 → 𝐷𝑆 𝑄 2 = 𝐻 → 𝐷𝑆 𝑄 = 𝐻𝑄 2
𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
MIS 373: Basic Operations Management

6. EPQ: Inventory Cycle Q Qp Imax 13-6 Time Production and usage Usage
only
Cumulative
production
Amount
on hand
Time
13-6
Instructor Slides

7. Time Cycle time Run time The time between setups of consecutive runs
The production phase of the cycle

8. EPQ – Total Cost
13-8
Instructor Slides

9. EPQ Optimal Batch size a.k.a Economic Produciton Quantity (EPQ) 13-9
Instructor Slides

10. Quantity Discount Model
Price reduction for larger orders offered to customers to induce them to buy in large quantities
13-10
Instructor Slides

11. MIS 373: Basic Operations Management
Reorder-Point
ROP = (Demand per day) * (Lead time for a new order in days)
= d * L
where
d = (Demand per year) / (Number of working days in a year)
Example:
Demand = 12,000 iPads per year
300 working day year
Lead time for orders is 3 working days
In other words, the manager should place the order when only 120 units left in the inventory.
d = 12,000 / 300 = 40 units
ROP = d * L = 40 units per day * 3 days of leading time = 120 units
MIS 373: Basic Operations Management