Chapter 6
Inventory Control Models
Presented by: Jeniel Pascual & Caleb Costales
Learning Objectives
After completing this chapter, students will be able to:
• Understand the importance of inventory control.
• Understand the various types of inventory related decisions.
• Use the economic order quantity (EOQ) to determine how much to order.
• Compute the reorder point (ROP) in determining when to order more inventory.
• Handle inventory problems that allow non-instantaneous receipt.
• Handle inventory problems that allow quantity discounts.
Learning Objectives
After completing this chapter, students will be able to:
• Understand the use of safety stock.
• Compute single period inventory quantities using marginal analysis.
• Understand the importance of ABC analysis.
• Describe the use of material requirements planning in solving dependent-demand
inventory problems.
• Discuss just-in-time inventory concepts to reduce inventory levels and costs.
• Discuss enterprise resource planning systems.
Inventory as an Important Asset
-Inventory is one of the most expensive and important assets to many companies..
Inventory
-Inventory is any stored resource that is used to satisfy a current or a future need.
Examples:
1.
2.
3.
Raw materials,
work-in-process, and
finished goods.
-Studying how organizations control their inventory is equivalent to studying how
they achieve their objectives by supplying goods and services to their customers.
-Inventory is the common thread that ties all the functions and departments of the
organization together.
Inventory
-Lower inventory levels
• Can reduce costs
• May result in stockouts (frequent inventory outages) and dissatisfied
customers
-Companies must make the balance between low and high inventory levels.
-Cost minimization is the major factor in obtaining this delicate balance.
Inventory Planning & Control (Figure 6.1)
Five Uses of Inventory
1. The decoupling function
o Reduces delays and improves efficiency
o A buffer between stages
2. Storing resources
o Seasonal products stored to satisfy off-season demand
o Materials stored as raw materials, work-in-process, or finished goods
o Labour can be stored as a component of partially completed subassemblies
3. Irregular supply and demand
o Not constant over time
o Inventory used to buffer the variability
Five Uses of Inventory
4. Quantity discounts
o Lower prices may be available for larger orders
o Higher storage and holding costs (spoilage, damaged stock, theft, insurance…)
o By investing in more inventory, you will have less cash to invest elsewhere!
5. Avoiding stockouts and shortages
o Stockouts may result in lost sales
o Dissatisfied customers may choose to buy from another supplier o Loss of
goodwill
Inventory Decisions
ECONOMIC ORDER QUANTITY (EOQ)
2 Fundamental Decisions
1. How much to order
2. When to order
REORDER POINT (ROP)
-A major objective in controlling inventory is to minimize total inventory costs.
1. Cost of the items- (purchase cost or material cost)
2. Cost of ordering- (often involves personnel time)
3. Cost of carrying, or holding, inventory- (taxes, insurance, cost of capital…)
4. Cost of stockouts- (lost sales and goodwill that result from not having the items
available for the customers)
Inventory Cost Factors
Inventory Cost Factors (Table 6.1)
• Ordering costs are generally independent of order quantity
o Many involve personnel time
o The amount of work is the same no matter the size of the order
• Holding costs generally vary with the amount of inventory or order size
o Labour, space, and other costs increase with order size
o Cost of items purchased can vary with quantity discounts
Economic Order Quantity
Economic order quantity (EOQ) model
o One of the oldest and most commonly known inventory control
techniques
o Easy to use
o Several important assumptions limits the applicability of this model
• Objective is to minimise total cost of inventory
*Lead time = the time between the placement of the order and the receipt of the order
Economic Order Quantity
Assumptions:
1. Demand is known and constant over time
2. Lead time* is known and constant
3. Receipt of inventory is instantaneous (arrives in one batch, at one point in
time!)
4. Purchase cost (= cost of the inventory!) per unit is constant throughout
the year (Quantity discounts are not possible!)
5. The only variable costs are ordering cost and holding or carrying cost, and
these are constant throughout the year
6. Orders are placed so that stockouts or shortages are avoided completely
If this amount is 1,000 bananas, all 1,000 bananas arrive at one time when an order is received. The inventory
level jumps from 0 to 1,000 bananas (Q).
Inventory Usage Over Time
Inventory Costs in the EOQ Situation
Based on our assumptions - if we minimise the sum of the ordering and
carrying costs we are minimising the total costs
• Annual ordering cost is number of orders per year times cost of placing
each order
• Annual carrying cost is the average inventory times carrying cost per unit
per year
Inventory Costs in the EOQ Situation
Inventory Costs in the EOQ Situation
Inventory Costs in the EOQ Situation
Inventory Costs in the EOQ Situation
Total Cost as a Function of Order Quantity:
Finding the EOQ
When the EOQ assumptions are met, total cost is minimised when:
Annual ordering cost = Annual holding cost
Economic Order Quantity (EOQ) Model
Equation summary:
Sumco Pump Company Example
Sumco, a company that sells pump housings to other manufacturers, would
like to reduce its inventory cost by determining the optimal number of
pump housings to obtain per order. The annual demand is 1,000 units, the
ordering cost is $10 per order, and the average carrying cost per unit per
year is $0.50. Using these figures, if the EOQ assumptions are met, we can
Calculate the optimal number of units per order:
Sumco Pump Company Example
Reduce inventory costs by finding optimal order quantity
Sumco Pump Company Example
The total annual inventory cost is the sum of the ordering costs and the
carrying costs:
Number of orders per year = (D÷Q) = 5
Average inventory (Q÷2) = 100
Sumco Pump Company Example
Sensitivity Analysis with the EOQ Model
• The EOQ model assumes that all input values are fixed and known with
certainty.
• Values are estimated or may change
• Sensitivity analysis determines the effects of these changes
• Because the EOQ is a square root, changes in the inputs (D; Co; Ch) result
in relatively minor changes in the optimal order quantity
Sensitivity Analysis with the EOQ Model
For example, if Co were to increase by a factor of 4, the EOQ would only increase by a
factor of 2.
Consider the Sumco example just presented. The EOQ for this company is as follows:
In general, the EOQ changes by the square root of the change to any of the inputs!
Reorder Point: Determining When To Order
• Next decision is “When to order”
• The time between placing an order and its receipt is called the lead time (L) or
delivery time
• “On hand” and “on order” inventory must be available to meet demand during
lead the total of these is called “inventory position”
• Generally the “when to order” decision is usually expressed in terms of a
reorder point (ROP; inventory position at which an order should be placed)
d = Demand per day L = Lead time for a new order in days
Procomp’s Computer Chips Example
D = Annual demand = 8,000
d = Daily demand = 40 units
L = Delivery in 3 working days
An order for the EOQ (400) is placed when the inventory reaches 120 units
The order arrives 3 days later just as the inventory is depleted to 0!
Reorder Point Graphs
Q = 400 d; = 40 units; L = Delivery in 3 working days; ROP = d * L = 120
ROP < Q 120 < 400
d = Demand per day L = Lead time for a new order in days
Procomp’s Computer Chips Example
Suppose the lead time for Procomp Computer Chips was 12 days instead of
3 days. How would this affect the “reorder point”?
Annual demand = 8,000
Daily demand = 40 units
Delivery in three twelve working days
d = Demand per day L = Lead time for a new order in days
Procomp’s Computer Chips Example
Annual demand = 8,000
Daily demand = 40 units
Delivery in three twelve working days
New order placed when inventory = 80 and one order is in transit!
Reorder Point Graphs
Q = 400; d = 40 units; L = Delivery in 12 working days; ROP = d * L = 480
ROP > Q 480 > 400
Reorder Point Graphs
EOQ Without Instantaneous Receipt
• When a firm receives its inventory over a period of time, a new model is
needed that does not require the “instantaneous inventory receipt
assumption”!
• This new model is applicable when inventory continuously flows or builds
up over a period of time after an order has been placed or when units are
produced and sold simultaneously.
•Under these circumstances, the daily demand rate (d) must be taken into
account.
EOQ Without Instantaneous Receipt
The production run model eliminates the instantaneous receipt assumption.
Production run model: This graph shows inventory levels as a function of time. Model
especially suited to the production environment!
Annual Carrying Cost for Production Run Model
• In the production process, instead of having an ordering cost, there will be a setup
cost
-Cost of setting up the production facility to manufacture the desired product!
• Salaries and wages of employees responsible for setting up the equipment
• Engineering and design costs of making the setup
• Paperwork, supplies, utilities …
Annual Carrying Cost for Production Run Model
So how can we derive the optimal production quantity?
• We need to set our “setup costs” equal to “carrying costs” and then solve for the
“order quantity”.
• Let’s start by developing the expression for carrying cost!
Annual Carrying Cost for Production Run Model
As with the EOQ model, the carrying costs of the production run model are based on
the average inventory, and the average inventory is one-half the maximum inventory
level.
p = daily production rate d = daily demand rate t = length of production run in days
Annual Carrying Cost for Production Run Model
Annual Carrying Cost for Production Run Model
Annual Carrying Cost for Production Run Model
When a product is produced over time, setup cost replaces ordering cost:
Both of these are independent of the size of the order and the size of the production
run! This cost is simply the number of orders (or production runs) times the ordering
cost (setup cost).
Annual Carrying Cost for Production Run Model
Production Run Model
Brown Manufacturing Example
Brown Manufacturing produces commercial refrigeration units in batches. The firm’s
estimated demand for the year is 10,000 units. It costs about $100 to set up the
manufacturing process, and the carrying cost is about 50 cents per unit per year.
When the production process has been set up, 80 refrigeration units can be
manufactured daily. The demand during the production period has traditionally been
60 units each day. Brown operates its refrigeration unit production area 167 days per
year.
How many units should Brown produce in each batch?
How long should the production part of the cycle last?
Brown Manufacturing Example
Produces commercial refrigeration units in batches:
How many units should Brown produce in each batch?
How long should the production part of the cycle last?
Brown Manufacturing Example
Brown Manufacturing Example
Brown Manufacturing Example
If Q* = 4,000 units and we know that 80 units can be produced daily, the length of
each production cycle will be days. When Brown decides to produce refrigeration
units, the equipment will be set up to manufacture the units for a 50-day time span.
-The number of production runs per year will be D/Q = 10,000/4,000 = 2.5.
-The average number of production runs per year is 2.5.
-There will be 3 production runs in one year with some inventory carried to the next
year
-Therefore only 2 production runs are needed in the second year.
Quantity Discount Models
In developing the EOQ model, we assumed that quantity discounts were not
available.
-However, many companies do offer quantity discounts.
-If such a discount is possible, but all of the other EOQ assumptions are met, it is
possible to find the quantity that minimises the total inventory cost by using the EOQ
model and making some adjustments
Quantity Discount Models
• When quantity discounts are available the basic EOQ model is adjusted by adding in
the “purchase or materials cost”
Quantity Discount Models
Quantity Discount Models
Quantity Discount Models
•Overall our objective is to minimise the total cost.
• Because the unit cost (4.75) for the third discount is lowest, we might be tempted to
order 2,000 units or more to take advantage of the lower material cost.
• Placing an order for that quantity with the greatest discount cost might not
minimise the total inventory cost.
• As the discount quantity goes up, the material cost goes down, but the carrying cost
increases because the orders are large.
• Key trade-off when considering quantity discounts is between the reduced material
cost and the increased carrying cost!
Quantity Discount Models
Brass Department Store Example
Brass Department Store stocks toy race cars. Recently, the store was given a quantity
discount schedule for the cars. The ordering cost is $49 per order, the annual demand
is 5,000 race cars, and the inventory carrying charge as a percentage of cost, I, is 20%.
Brass Department Store Example
Toy race cars: Quantity discounts available
Brass Department Store Example
Brass Department Store Example
Brass Department Store Example
Brass Department Store stocks toy race cars. Recently, the store was given a quantity
discount schedule for the cars. The ordering cost is $49 per order, the annual demand
is 5,000 race cars, and the inventory carrying charge as a percentage of cost, I, is 20%.
Brass Department Store Example
Brass Department Store Example
Brass Department Store Example