INVENTORY MODEL
Inventory control serves several important functions and adds a great deal of flexibility to the
operation of the firm. Consider the following five uses of inventory:
https://youtu.be/xmC_dRzghqk
1. The decoupling function
2. Storing resources
3. Irregular supply and demand
4. Quantity discounts
5. Avoiding stockouts and shortages
INVENTORY MODELS
Management Science
Inventory represents the goods or material that must be held by a company for
use sometime in the future. The usual examples of inventories are:
• raw material
• finished goods
• semi-finished products
• spare parts
TWO MAJOR QUESTIONS RELATED TO INVENTORY
How much to order? When to order?
NOTE: To answer these questions, management should be able to understand and
identify the costs associated with acquiring inventory.
Inventory Terminology and Models Classification
The most important types of partial inventory cost:
Ordering and setup cost are all the necessary expenses of placing an order. This item
represents the fixed charge that includes e.g. the cost of paper work, billing cost and
supplier’s fixed cost associated with the order. This cost is associated with ordering or
receiving inventory. Include cost of labor & materials used in setting up machinery for
the production run (Expressed as a peso amount per order, regardless of order size).
More frequent ordering of smaller quantities results in a higher cost during the period
than less frequent ordering of larger quantities.
Unit purchasing cost is the variable cost associated with purchasing a single unit. This
item becomes an important factor in case the price of the single unit depends on the
size of the order (quantity discount – unit price decreases with increasing order quantity).
Holding and carrying cost is the opportunity cost associated with owing the inventory
(Specified as a percentage of unit price or peso amount)
Holding or carrying cost includes:
• storage cost (maintaining the storage space),
• store keeping operations (taking physical inventory),
• insurance and taxes on inventory,
• interest (paid on the capital invested in inventories),
• the opportunity cost (e.g., the interest gained
from money saved in the bank, the return from money invested in shares or
bonds, or the yield gained by possible alternative use of funds),
• cost due to the possibility of spoilage or
obsolescence.
Shortage (or stockout) cost is significant if shortage of items affects the company’s
activities, revenue, profit, employment inside the company etc. In general, shortage
leads to unsatisfied demand for the required items. Following examples of such cost
can be considered:
• cost o f i d l e d p r o d u c t i o n , c o s t o f i d l e d machines (in case of the spare-parts
storage),
• cost of placing special expensive expediting order to restore the inventory,
• loss of customers due to late deliveries of
the finished goods,
• other cost, often incalculable (the shortage of blood or ambulance in garage)
Inventory Level
This is the available size of the inventory,
i.e. the number of stocked items (the number of units) or the amount of stocked material
(in kilograms, liters, meters, etc.).
Demand and Depletion
The purpose of making inventory corresponds to specific demand. In production
process, for example, the production technology determines amount of items required
within specific period. The rate of demand then determines the inventory depletion rate
(and hence, the inventory level). The higher the rate of demand is, the quicker the
inventory level is being reduced. The rate of demand can be constant throughout time
or can fluctuate.
Reordering, Reorder Point, and Lead Time
Since the inventory is being depleted, stocked items must be replenished
periodically. When the inventory level is reduced to a signal level called the reorder
point, the replenishment order must be placed to restore the inventory on time. The
time period between placing the order and receiving the shipment is called the lead
time. This period can be constant or variable.
Shortages, Surpluses, and Safety Stock
In an ideal case, the shipment arrives at the moment when the last unit of
inventory has been depleted. Wrong timing of real replenishment order may cause the
future unexpected shortage of the inventory (if we make the order after the optimal
reorder date) or surplus of units in the warehouse (if we make the order before the
optimal reorder date). To prevent the shortage (its full elimination or partial reduction)
company’s management can keep a buffer in the form of safety stock that is used in
case where shortage event would occur. This issue is the most significant in the models
with probabilistic demand or lead time.
Average Inventory
Concept of an average inventory is used in almost all the inventory models. As a
short illustration of this very important term of inventory management, we introduce the
following example:
Monitoring the inventory level during a five-day period, we get the following numbers:
The average inventory level is 100 units computed as follows:
Average Inventory = (200+150+100+50+0) / 5 days
Figure 4.1 shows the depletion of the inventory in time (decrease of the inventory level
occurs at the beginning of each day). Since demand is constant in time, the average
inventory can be also computed as (200+0)/2 = 100 units.
HOW MUCH TO ORDER-THE ECONOMIC ORDER QUANTITY (EOQ) MODEL
- Applicable only when demand for the item has a constant or nearly constant rate and
when the entire quantity ordered arrives in the inventory at one time.
- The objective of most inventory models is to minimize the total costs.
2𝑎𝐷
EOQ = √
𝑘
a = Ordering cost or set up cost
k = Carrying cost or holding cost
D = Demand
𝐸𝑂𝑄 𝐷
Average Inventory = Number of orders =
2 𝐸𝑂𝑄
𝐸𝑂𝑄 𝐷
Annual Carrying cost = (𝑘) Annual ordering cost = (𝑎)
2 𝐸𝑂𝑄
Total annual cost = Annual carrying cost + Annual ordering cost
Example
Suppose R & C Beverages Company has a beverage product that has a constant annual
demand rate of 7200 cases. A case of soft drink costs R & C P288. Ordering cost is P200 per
order and inventory carrying cost is charged @ 25% of the cost per case. Identify the following:
a. EOQ
b. Average inventory
c. Annual carrying cost
d. Number of orders
e. Annual ordering cost
f. total annual cost
D = 7200 cases
Purchase price = 288/case
a = 200/order
k = 288 (25%) = 72
Solution:
2𝑎𝐷 2 (200(7200)
a. EOQ = √ =√ = 200 cases
𝑘 72
𝐸𝑂𝑄 200
b. Average = = = 100 cases
2 2
𝐸𝑂𝑄
c. Annual Carrying cost = (𝑘) = 100 (72) = P7,200
2
𝐷 7200
d. Number of orders = = = 36 orders
𝐸𝑂𝑄 200
𝐷
e. Annual ordering cost = (𝑎) = 36 (200) = P7, 200
𝐸𝑂𝑄
f. Total annual cost = Annual carrying cost + Annual ordering cost
= 7,200 + 7,200 = 14, 400
