Antti Salonen
KPP227 - HT 2015
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Inventory management
Inventory management concerns
short-range decisions about
supplies, inventories, production
levels, staffing patterns, schedules
and distribution.
The decisions are often of a tactical
(rather than strategic) character.
Strategic Tac+c Opera+onal KPP227
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What is inventory?
An inventory is a stock or store of
goods.
Goods inventory management is
essential to the successful
operation of most organizations for
a number of reasons, like:
•  the amount of money inventory
represents (capital investment)
•  The impact on daily operations
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What is inventory?
Inventory is a stock of anything, held
to meet future demand.
Manufacturing companies (for
example) carry supplies of:
Firms typically stock a large amount
of items, ranging from small items
(such as screws and nuts) to large items
(such as machines and castings), depending
on the kind of business.
•  raw material
•  purchased parts
•  sub assemblies/partially completed
items (Work in Process – WIP)
•  finished goods
•  spare parts for machines, tools and
other supplies.
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Accounting categories
Inventories for a manufacturing plant exist in three forms (so
called accounting categories):
•
•
•
Raw material
Work in process (WIP)
Finished goods
1.
Raw material at the plant passes through one or more processes, which
transforms them into various levels of WIP inventory.
When this inventory is processed at the final operation, it becomes
finished goods inventory.
Finished goods can be held at a plant, a distribution center (DC), and
retail locations.
2.
3.
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Nature and importance of inventory
Inventories are not only necessary for operations, but also for customer
satisfaction. Hence, a typical firm can have about 30 % of it´s current assets
and 90 % of it´s working capital invested in inventory.
Question:
What can be possible benefits
and drawbacks of inventory?
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Functions of Inventory
1.  To meet anticipated customer demand
Anticipation stock: Inventories are held to satisfy an expected
average demand.
2.  To smooth production requirements
Seasonal inventories: Inventories are built during off-season to
satisfy the demand during high season.
3.  To decouple operations
Buffers: Inventories are held between successive operations to
maintain continuity of production despite e.g. breakdowns.
4.  To protect against stock outs
Safety stocks: Inventories are held to cover for late deliveries
and unexpected increases in demand.
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Functions of Inventory
5.  To take advantage of order cycles
Cycle stock: Inventories are held to minimize purchasing cost
resulting in order cycles.
6.  To hedge against price increases
Inventories are held to avoid a substantial price increase.
7.  To permit operations
Pipeline inventory: Inventories are held in order to avoid
shortages of e.g. raw material which can result in production
stops (work in process).
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Types of inventory
1.  Cycle inventory
Increased inventory and lower cost by ordering larger quantities.
Lot sizing principles:
•  The lot size Q must equal the demand during the time between orders
•  The longer the time between orders, the greater the cycle inventory.
2.  Safety stock inventory
Protects against uncertainties in demand, lead time and supply.
3.  Anticipation inventory
Used to absorb uneven rates of demand or supply.
4.  Pipeline inventory
Inventory that is created when an order for an item is issued but not yet
placed in inventory. (Inventory moving from point to point in the material flow
process)
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Inventory levels
Inadequate control of inventories can result in both under- and overstocking of items.
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Inventory levels
Inadequate control of inventories can result in both under- and overstocking of items.
•
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Under-stocking
Results in missed deliveries, lost sales, dissatisfied customers and
production bottle necks.
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Inventory levels
Inadequate control of inventories can result in both under- and overstocking of items.
•
•
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Under-stocking
Results in missed deliveries, lost sales, dissatisfied customers and
production bottle necks.
Over-stocking
Results in unnecessary capital being tied up, that could have been
used for something more productive.
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Inventory levels
Inadequate control of inventories can result in both under- and overstocking of items.
•
•
Under-stocking
Results in missed deliveries, lost sales, dissatisfied customers and
production bottle necks.
Over-stocking
Results in unnecessary capital being tied up, that could have been
used for something more productive.
Although overstocking may appear to be the lesser of the two evils,
excessive overstocking can be staggering where holding costs are high.
This is one factor dealt with by e.g. lean production (JIT, reduced waste
etc).
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Cost information
The costs associated with inventories are:
•
Holding costs
Relates to physically having items in storage (see next slide).
•
Ordering cost (or setup costs)
Relates to ordering and receiving inventory, which vary with the actual placement
of an order. These costs include e.g. determining how much is needed, preparing
the invoice, shipping, goods inspection, moving the goods to temporary storages
etc.
•
Shortage costs
Relates to the case when demand exceeds supply. These costs include e.g.
opportunity cost of making the sale, loss of customer goodwill or even cost of lost
production (if the customer is internal)
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Holding or carrying cost
Inventory holding (or carrying) cost is the cost of keeping items on hand.
These cost components change with inventory level.
The components of holding cost
•  Cost of capital
To finance an investment (often up to 15 %)
•  Storage and handling costs
Inventory needs space and must be moved in and out of storage
•  Taxes, insurance and shrinkage
Shrinkage can take three forms:
•  Pilferage/Theft
•  Obsolescence due to e.g. model changes
•  Deterioration implies a lower value
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Pressures for low inventory
•
Inventory represents a temporary monetary investment =>
firm must pay (rather than receive) interest.
•
Inventory hides quality problems.
•
Inventory takes up space that could be used for a more
profitable activity.
•
Inventory needs to be handled => increased materials
handling requirements.
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Pressures for high inventory
•
Customer service
Inventory can speed up delivery and avoids stock outs and
backlogs.
•
Ordering cost
Minimize the cost of preparing purchase order.
•
Setup cost
Producing inventory reduces the amount of setups
between different items.
•
Labor and equipment utilization
Increased productivity
•
Transportation cost
Inventory on hands allows the possibility to optimize
transportation.
•
Quantity discounts
The more you buy at one time, the cheaper the price/item
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However…
It is not unusual for managers to discover that their firm has a
10 year supply of some items => a balance is needed!
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Inventory concerns
•  Level of customer service
To have the right goods, in sufficient quantities, in the
right place at the right time
•  Cost of ordering and carrying inventory
Overall objective
To achieve satisfactory customer service levels while
keeping inventory costs within reasonable bounds.
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Inventory measures
The average aggregate inventory value is the total value of all items held in
inventory and represents the inventory investments over a period of time.
Average aggregate inventory value = ∑i (No of unit Xi* Value of unit Xi)
However, it is also important to consider weeks of supply (how many weeks of
demand the average inventory can cover) and inventory turnover (how many times the
whole inventory is replaced per year).
Weeks of supply = Average aggregate inventory/Weekly sales (at cost)
Inventory turnover = Annual sales (at cost)/ Average aggregate inventory
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EXAMPLE
1
Inventory measures
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Problem to solve
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Solution
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The Pareto principle
The Pareto Principle (also
called 80/20 rule)
The 80/20 rule means that in
anything, a few (20 percent)
are vital and many (80
percent) are trivial.
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ABC analysis
The product line of a typical firm is
made up of individual products at
different stages of their respective life
cycles and with different degrees of
sales success.
E.g. 80 % of a firm’s sales are
generated by 20 % of the product line
items.
=> important to primarily control these
(and not the other 80 %).
Percentage of items
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ABC Analysis
Classification of articles in regards to e.g. item value.
•
Class “A” items constitute the most important class of inventories so far as the
proportion in the total value of inventory. The “A” items consists of ~20% of the
total items and accounts for ~80% of the total material usage. This items need a
tightly controlled inventory system with constant attention.
•
Class “B” items constitute an intermediate position, which constitute ~30% of the
total items, accounts for ~15% of the total material consumption. These items
need a formalized inventory system and periodic attention.
•
Class “C” items are quite negligible. It consists of the remaining ~50% items,
accounting for only ~5% of the monetary value of total material usage . Quite
relaxed inventory procedures are used.
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Now that we have identified the inventory
items deserving the most attention, we devote
the remainder of the lecture to the decisions of
how much to order and when.
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Inventory Control Systems
•  Independent demand
Items for which demand is influenced by market conditions and is not
related to the inventory decisions for any other item held in stock or
produced.
•  Dependent demand
Items required as components or inputs to a service or product.
Dependent demand exhibits a pattern very different from that of
independent demand and must be managed with different techniques.
(will be covered in upcoming lectures)
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Independent demand
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•
Wholesale and retail merchandise
Service support inventory (e.g. office supplies)
•
•
Product and replacement-part distribution inventories
Maintenance, repair, and operating (MRO) supplies
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Demand forecast and lead time information
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Inventories are used to satisfy order demand requirements, so it is essential to
have reliable estimates of the amount and timing of demand.
•
Similarly, it is essential to know how long it will take for orders to be delivered.
•
Managers also need to know the extent to which demand and lead time (the time
between submitting an order and receiving it) might vary. The greater the
variability, the greater the need for additional stock to reduce the risk of a
shortage between deliveries.
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Definitions: A reminder
•
Inventory holding cost is the sum of the cost of capital and the
variable costs of keeping items on hand, such as storage and
handling, taxes, insurance, and shrinkage.
•
Ordering cost is the cost of preparing a purchase order for a supplier
or a production order for the shop.
•
Setup cost is the cost of changing over a machine to produce a
different item.
Cycle inventory is the portion of total inventory that varies directly with lot size.
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Economic Order Quantity (EOQ)
The lot size, Q, that minimizes total annual
inventory holding and ordering costs.
When to use EOQ:
•  Constant and certain demand
•  No lot size constraints
•  Inventory holding cost and fixed cost per lot
are the only costs
•  Decisions for an item can be made
independently
•  Constant and certain lead time
EOQ is a reasonable approximation, not
an optimization tool!
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EOQ calculation
Q = Lot size (units)
H = Holding cost for one unit during one year (SEK)
D = annual demand (units/year)
S = Ordering cost/Set up cost (SEK/lot)
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EOQ calculation
Total annual cycle-inventory cost = Annual holding cost + Annual ordering or setup cost
Economic order quantity:
C = total annual cycle-inventory cost
Q = lot size, in units
H = cost of holding one unit in inventory for a year, often expressed as
a percentage of the item’s value
D = annual demand, in units per year
S = cost of ordering or setting up one lot
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EOQ
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Time Between Orders (TBOEOQ)
Sometimes, inventory policies are based on the time between
replenishment orders, rather than on the number of units in the lot size.
The Time Between Orders (TBO) for a particular lot size is the average
elapsed time between receiving (or placing) replenishment orders of Q
units.
=> TBO gives a hint on how often an order should be placed.
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EXAMPLE
3
EOQ, Cost, TBO
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a)
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a)
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b)
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Problem to solve
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Solution
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EOQ sensitivity analysis
TABLE 12.1
Parameter
|
SENSITIVITY ANALYSIS OF THE EOQ
EOQ
Demand
2DS
H
Order/Setup
Costs
2DS
H
Holding
Costs
2DS
H
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Parameter
Change
EOQ
Change
Comments
↑
Increase in lot size is in proportion to the
square root of D.
↓
↓
Weeks of supply decreases and inventory
turnover increases because the lot size
decreases.
↓
↑
Larger lots are justified when holding
costs decrease.
↑
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The EOQ and other lot-sizing methods
answer the important question:
How much should we order?
Another important question that needs
an answer is:
When should we place the
order?
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Continuous review (Q) system
A continuous review (Q) system, sometimes called a reorder
point (ROP) system or fixed order-quantity system, tracks the
remaining inventory of a SKU each time a withdrawal is made to
determine whether it is time to reorder.
A Q system means that whenever the inventory position reaches a certain point, a new order is
placed!
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Continuous review (Q) system
Q system when demand and lead time are constant and certain
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Continuous review (Q) system
Q system when demand and lead time are constant and certain
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Continuous review (Q) system
Q system when demand and lead time are constant and certain
Inventory position = On-hand inventory +
Scheduled Receipts – Back Orders
IP = OH + SR – BO
If IP ≤ Reorder point
=> An order should be placed!
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Problem to solve
Inventory position = On-hand inventory + Scheduled receipts – Backorders
IP = OH + SR – BO
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Solution
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Continuous review (Q) system
Q system when demand is uncertain
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Continuous review (Q) system
Calculation of reorder point (ROP) when demand is uncertain:
1.  Choose an appropriate service-level policy.
E.g. choosing a 90 percent cycle service level means that the probability is 90
percent that the demand will not exceed the supply during the lead time.
2.  Determine the demand during lead time probability distribution
3.  Determine the safety stock and reorder point levels
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Continuous review (Q) system
The size of the safety stock depends on the variability, which is measured
with probability distributions.
Normal distribution
Cycle-service level = 85%
Probability of stockout
(1.0 – 0.85 = 0.15)
Average demand
during lead time
R
zσdLT
Finding Safety Stock with a Normal Probability Distribution for an 85 Percent Cycle-Service Level
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Continuous review (Q) system
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EXAMPLE 4
Reorder point (ROP) & safety stock
(normal distribution)
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a) Normal distribution
vv
v
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a)
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b) Normal distribution
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b) Normal distribution
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Problem to solve
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Solution
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Continuous review (Q) system
The size of the safety stock depends on the variability, which is measured
with probability distributions.
Discrete distribution
•
•
•
Data are unavailable
Each possible demand during lead time, along with it’s probability is listed.
R is selected from the list of demand levels.
Find the smallest value of R that meets the desired service level.
E.g. if the desired cycle-service level is 95% and R is set at 500 units the
probabilities of all demands ≤500 must equal or exceed 0.95, and R is the smallest
such quantity.
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EXAMPLE 5
Reorder point (ROP) & Safety stock
(discrete distribution)
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Periodic review (P) system
A periodic review (P) system, sometimes called a periodic
reorder system or fixed interval reorder system, reviews an item’s
inventory position periodically rather than continuously (=> TBO is
fixed). The lot size, Q, may change from one order to the next
(demand is uncertain).
Essential assumptions:
•  item is delivered in lots
•  inventory holding cost is not affected by lot sizing decisions
•  decisions for one item are independent of decisions for other items
•  amount received is exactly amount ordered
A P system means that on a regular basis, a new order is
placed.
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Periodic review (P) system
P system when demand is uncertain and lead time is certain
Inventory position = On-hand inventory +
Scheduled Receipts – Back Orders
IP = OH + SR – BO
An order is placed every period P
and the amount to order = T-IP !
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EXAMPLE 6
Order quantity
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Periodic review (P) system
Two decisions must be made:
•
P: Length of time between reviews
Could e.g. be based on the cost trade-offs of the EOQ,
average time between orders of the EOQ (= TBO).
•
T: Target inventory level
Must equal to the expected demand during protection
interval (P + L) plus enough safety stock to protect against
demand and lead time uncertainties.
T = average demand during the protection interval
+ safety stock for protection interval
! = ! ! + ! + !! !!! = ! ! + ! + !!!! ! + !!
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EXAMPLE 7
P system
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Demand for a bird feeder is normally distributed with a mean of
18 units per week and a standard deviation in weekly demand
of 5 units. The lead time is 2 weeks, and the business
operates 52 weeks per year. EOQ is 75 units and the safety
stock is 9 units for a cycle-service level of 90 percent.
What is the equivalent P system? Find P and T!
Answers are to be rounded to the nearest integer.
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Q system vs. P system
Primary advantages of Q systems
•  Review frequency may be individualized
•  Fixed lot sizes can result in quantity discounts
•  Lower safety stocks
Primary advantages of P systems
•  Convenient
•  Orders can be combined
•  Only need to know IP when review is made
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Hybrid systems
Optional replenishment systems
•  Optimal review, min-max, or (s,S) system, like the P system
•  Reviews IP at fixed time intervals and places a variable-sized order to
cover expected needs
•  Ensures that a reasonable large order is placed
Base-stock system
•  Replenishment order is issued each time a withdrawal is made
•  Order quantities vary to keep the inventory position at R
•  Minimizes cycle inventory, but increases ordering costs
•  Appropriate for expensive items
Visual systems
•  Allows employees to place orders when inventory visibly reaches a
certain marker. (E.g. Kanban)
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Non-instantaneous replenishment
If an item is being produced
internally (rather than purchased)
finished units may be used or
sold as soon as they are
completed, without waiting until
a full lot is completed!
Usually production rate, p,
exceeds the demand rate, d, so
there is a build-up of (p – d)
units for Q/p days!
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Non-instantaneous replenishment
Maximum cycle inventory (Imax):
I max
Q
⎛ p − d ⎞
= ( p − d ) = Q⎜
⎟
p
⎝ p ⎠
where
p = production rate
d = demand rate
Q = lot size
Average cycle inventory is no longer Q/2 (as in
EOQ). Instead it is Imax /2
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Non-instantaneous replenishment
Total annual cost = Annual holding cost + Annual ordering or setup cost
I max
(H ) + D (S ) =>
C=
2
Q
I = inventory
D = annual demand
p = production rate
d = demand rate
Q = lot size
H = holding cost
S = ordering/setup cost
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Q ⎛ p − d
C = ⎜⎜
2 ⎝ p
⎞
D
⎟⎟(H ) + (S )
Q
⎠
=> Economic production lot size:
2 DS
ELS =
H
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p−d
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EOQ vs. ELS
Do NOT mix up
Economic order size
EOQ =
2DS
H
Economic production lot size
ELS =
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EXAMPLE 8
Non-instantaneous replenishment
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Solution
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Skärmurklipp gjort: 2010-11-21; 13:18
Problem to solve
A toy manufacturer uses 48000 rubber wheels per year for its popular dump truck series.
The firm makes its own wheels, which it can produce at a rate of 8 per day. The toy trucks
are assembled uniformly over the entire year. Carrying cost is €1 per wheel a year. Setup
cost for a production run of wheels is €45. The firm operates 240 days per year.
Determine the:
a.  Optimal run size
b.  Minimum total annual cost for carrying and setup
c.  Cycle time for the optimum run size
d.  Run time
D = 48000 wheels per year
S = €45
H = €1 per wheel per year
p = 800 wheels per day
d = 48000 wheels per 240 days, or 200 wheels per day
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Skärmurklipp gjort: 2010-11-21; 13:18
Solution
a: ELS =
b:
√
√
p
p-d
=
√
Cmin = Carrying cost + Setup cost =
Imax =
Cmin =
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2DS
H
ELS
(p – d) =
p
(
1800
2
2x48000x45
1
(
Imax
2
√
) (
H+
800
800 - 200
D
ELS
)
= 2400 wheels
S
2400
(800 – 200) = 1800 wheels
800
) (
1+
48000
2400
)
45 = 900 + 900 = €1800
c:
Cycle time =
(
ELS
d
)
=
2400
200 = 12 days
d:
Run time =
(
ELS
p
)
=
2400
800 = 3 days
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Quantity discounts
Price incentives to purchase large quantities, create pressure to maintain
a large inventory. Hence, a new approach is needed to find the best lot
size - one that balances the advantages of lower prices for purchased
materials and fewer orders (which are benefits of large order quantities)
against the disadvantage of the increased cost of holding more inventory.
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Quantity discounts
Total annual cost =Annual holding cost + Annual ordering or
setup cost + Annual cost of materials
Q
D
C = ( H ) + ( S ) + PD
2
Q
where
Q = lot size
H = holding cost
D = annual demand
d = demand rate
S = ordering and/or setup cost
P = price/unit
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Quantity discounts
Step 1.
Beginning with lowest price, calculate the EOQ
for each price level until a feasible EOQ is found.
It is feasible if it lies in the range corresponding
to its price. Each subsequent EOQ is smaller than
the previous one, because P, and thus H, gets
larger and because the larger H is in the
denominator of the EOQ formula.
Step 2.
If the first feasible EOQ found is for the lowest
price level, this quantity is the best lot size.
Otherwise, calculate the total cost for the first
feasible EOQ and for the larger price break
quantity at each lower price level. The quantity
with the lowest total cost is optimal.
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EXAMPLE 9
Quantity discounts
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One period decisions
One of the dilemmas facing many retailers is how to handle seasonal
goods. Often, they cannot be sold at full markup the next year because of
changes in styles. This type of situation is often called the newsboy
problem.
Step 1: List different demand levels and probabilities.
Step 2: Develop a payoff table that shows the profit for each
purchase quantity, Q, at each assumed demand level, D.
Each row represents a different order quantity and each
column represents a different demand.
The payoff depends on whether all units are sold at the
regular profit margin which results in two possible cases.
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One period decisions
Case 1.
Case 2.
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One period decisions
Step 3: Calculate the expected payoff of each Q by using the
expected value decision rule: For a specific Q, first
multiply each payoff by its demand probability, and then
add the products.
Step 4: Choose the order quantity Q with the highest expected
payoff.
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EXAMPLE 10
One period decisions
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Demand
exceeds
supply =>
Case 1
Supply
exceeds
demand
=> Case 2
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Relevant book chapters
•  Chapter: Managing inventories
•  Supplement C: Special inventory models
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Questions?
antti.salonen@mdh.se
Next lecture on Tuesday 2015-12-08
Scheduling, Assignment
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