chapter 12 book: inventory management Flashcards
independent demand
The demand is unknown and has to be forecasted
Demand for manufacturing parts is dependent demand, why?
Demand for manufacturing parts and components depends on the production schedule for the finished goods
we know how much we need
An inventory or stock
any material, part, or product sitting idle, not being used, usually in a warehouse or stockroom, and kept for use or sale in the future
stock keeping unit (SKU)
A warehousing item that is unique
it must be stored and accounted for separately from other items
what are the 5 main types of assets than companies hold in inventory?
raw materials
purchased manufacturing parts and components
work-in-process (WIP)
finished goods
Inventory management
concerned with planning and controlling inventories
A typical company has approximately how much of its current assets in inventory?
approximately 50%
return on assets (ROA)
widely used measure of business performance
profit after tax divided by total assets
what will happen to ROA if we manage to reduce our inventory?
a significant increase in ROA
Functions (Purposes) of Inventory
- To wait while being transported (in-transit inventory)
- To protect against stock-outs
–> lack of supplies basically
- To take adνantage of economic lot size or future price increase
- To smooth seasonαl demand or production
–> building up inventory during off season to meet high demand during the peak season
- To decouple operations
- To meet anticipated above-average demand
in-transit inventory
Items being transported
safety stock
stock in excess of average demand
to protect against stock-outs
cycle stock
inventory that is replenished cyclically and is gradually depleted as demand occurs and is met
seasonal inventory
Inventory produced during the off season to meet peak season demand, or inventory produced during a growing season kept for later sale
how to decouple operations?
Manufacturers use decoupling inventory between successive operations in order to create independence between the two operations in case one of them breaks down temporarily
made of WIP inventory
the average supply rate and the average demand rate should be equal
decoupling inventory`
Inventory between successive operations in order to create independence between the two operations in case one of them breaks down temporarily
anticipation inventory
Additional inventory to meet higher than average demand during a sales promotion or when customers expect a future price increase, and in anticipation of a plant shutdown
consequences of being a dumb ass in inventory management
Under-stocking results in missed deliveries, lost sales, dissatisfied customers, and production stoppage
overstocking unnecessarily ties up funds that might be more productive elsewhere and also ties up storage space
Inventory management’s two main concerns
the level of customer service (item availability or fiII rate)
the inventory costs
the level of customer service (item availability or fiII rate)
to have the right goods, in sufficient quantities, in the right place, at the right time
The overall objective of inventory management
to achieve satisfactory levels of customer service while minimizing inventory costs
a buyer or inventory analyst must make which two decisions for each item
the timing and size of orders
inventory turnover
performance measure to judge the effectiveness of their inventory management
the ratio of annual cost of goods sold (COGS) to average inventory investment
indicates how many times a year the inventory is sold or used
the ratio the better
days of inventory
performance measure to judge the effectiveness of their inventory management
a number that indicates the expected number of days of sales or usage that can be supplied from existing inventory
Effective inventory management requires:
- Safe storage and handling of inventories
- Tracking inventory levels and using inventory control models
- Forecasting demands and lead times
- Estimating inventory costs
- Performing A-B-C classification
A warehouse management system (WMS)
a computer software that controls the movement and storage of materials within a warehouse
processes the associated transactions
automated storage and retrieval system (ASRS)
A computer-controlled system
automatically places and retrieves loads from defined storage locations
The required warehouse capacity depends on?
depends on yearly volume and frequency of inventory movements
the inventory position for each item
Quantity on hand + On order - back-ordered
On order relates to an order that has been received by a supplier but the shipment has not arrived yet
back order is a shortage that the customer has agreed to wait for; it is a future inventory committed to a customer
the fixed-interval/order-up-to level model
An inventory control model that places orders at fixed time intervals to bring the inventory position up to the order-up-to level
a replenishment model that bases the order quantity on the difference between order-up-to level and inventory position
order-up-to level
estimate on how much of the item will be demanded from now until receipt of the next delivery
advantage of the fixed-interval/order-up-to level model
items from the same supplier are ordered at the same time
results in economies in ordering, shipping, receiving, and paying
disadvantage of the fixed-interval/order-up-to level model
the possibility of stock out between reviews
Perpetual or continual tracking
keeps track of removals from and additions to inventory on a continuous basis
allows the system to provide information on the current inventory position for each item at any time
economic order quantity/reorder point model (EOQ/ROP)
Another common inventory control model
works only with perpetual tracking
When the inventory position of an item drops down to or below a predetermined minimum called the reorder point (ROP), a fixed (economic) quantity of the item is ordered
advantages of the economic order quantity/reorder point model (EOQ/ROP)
the probability or expected number of shortage can be controlled
the order quantity is fixed
–> management can determine an optimal order quantity and use it for a few months, provided that demand does not vary seasonally or have a trend
disadvantage of the economic order quantity/reorder point model (EOQ/ROP)
this model is the added cost of individual ordering
the two bin system
A simple implementation of the economic order quantity/reorder point model
does not require perpetual inventory tracking
Items are withdrawn from the first bin until its contents are exhausted
–> It is then time to reorder
The second bin contains enough stock to satisfy expected demand until the order is filled plus safety stock
–> When the order arrives, the second bin is topped off and the remainder is placed in the first bin
A bar code
a unique number assigned to an item or a location
made of a group of vertical black and white bars that are read by a scanner
has increased the speed and accuracy of transactions significantly
main bar code type
universal product code (UPC)
universal product code (UPC)
The standard grocery bar code
has 12 digits
the purchase lead time
the time interval between ordering and receiving an order
the manufacturing lead time
the time it will take for a batch of a part/product to be manufactured
A point-of-sale (POS) system
electronically records actual sales at the time and location of sale
after accumulation into daily or weekly or monthly sales, these
the three basic costs, other than the purchase price, associated with inventories
holding costs
ordering costs
shortage costs
holding costs
relate to physically having items in storage
include warehousing costs, the opportunity cost associated with funds tied up in inventory, insurance, theft, etc
how are holding costs stated?
as a percentage of unit cost or as a dollar amount per unit
what are the typical annual holding cost rates?
20 to 40% of an item’s cost
ordering cost
the cost of placing an order, receiving it, and paying for it
generally expressed as a fixed dollar amount per order, regardless of order size
what are the ordering costs of a company that produces its own parts instead of ordering from a supplier?
the cost of machine setup
Machine setup
involves preparing the machine for the job by a司justing it, changing cutting tools, etc
Shortage cost
results when demand exceeds supply of inventory on hand
can include the opportunity cost of not making a sale
if it is an item used for production is what were missing, the shortage costs are what we have not produced but we could have
The A-B-C classification
groups inventory items into three classes according to some measure of importance, usually annual dollar value
it then allocates inventory control efforts accordingly
A: very important
B: moderately important (
C: least important
sometimes used to guide cycle counting
the A class items ratio
15-20 percent of the items in inventory
about 70-80 percent of the annual dollar value (ADV)
the C class items ratio
might account for about 50-60 percent of the items in inventory
only about 5-10 percent of the ADV
cycle counting
counting the items in inventory on a cyclic schedule (more frequently than annually)
we want to reduce discrepancies between inventory records and the actual quantities of inventory on hand
we want to investigate the causes of inaccuracy and fix them
physical inventory
Determination of inventory quantity by actual count
allowable error limits for A, B, and C classified items
+ or - 0.2 percent for
A items
+ or - 1 percent for B items
+ or - 5 percent for C items
A items should be counted more frequently than C items
The economic order quantity (EOQ)
the order size that minimizes the total annual inventory control cost
the four EOQ related models
- Basic economic order quantity (EOQ)
- Economic production quantity (EPQ)
- EOQ with quantity discount
- EOQ with planned shortage
the Basic economic order quantity (EOQ)
the basic one bruv
will minimize the sum of annual costs of holding and ordering inventory
The annual purchase price is not included because in the basic case it is assumed that unit purchase price is unaffected by the order size
based on a number of assumptions
the Basic economic order quantity (EOQ) assumptions
- Only one item is involved
- Annual demand is known.
- Demand is spread evenly throughout the year so that the demand rate is reasonably constant
- Purchase lead time does not vary
- Each order is received in a single delivery
- There are no quantity discounts
- Shortage is not allowed
how is annual holding cost calculated?
by multiplying the average amount of inventory on hand by the cost to hold one unit for one year
(Q/2) · H
Q = Order quantity (units per order)
H = Holding cost per unÎt per year
Annual holding cost is thus a linear function of Q: It increases in direct proportion to changes in the order quantity Q
annual ordering cost will increase decrease as order quantity increases? why?
annual ordering cost will decrease
because for a given annual demand, the larger the order quantity, the fewer the number of orders needed
annual ordering cost formula
(D/Q) · S
D = Demand (units per year)
S = Ordering cost per order
Q = Order quantity (units per order)
The total annual inventory cost of holding and ordering inventory, when Q units are ordered each time (formula)
TC = ((Q/2) · H) + ((D/Q) · S)
annual holding cost + annual ordering cost
Q = Order quantity (units per order)
H = Holding cost per unÎt per year
D = Demand (units per year)
S = Ordering cost per order
The total annual inventory cost of holding and ordering inventory curve
U-shaped
it reaches its minimum at the quantity where annual holding and annual ordering costs are equal
formula for the optimal order quantity?
EOQ = Q0 = ((2 · D · S) / H)^(1/2)
H = Holding cost per unÎt per year
D = Demand (units per year)
S = Ordering cost per order
Q0 = the optimal order quantity
The length of an order cycle (in years) formula
Q0/D
Q0 = the optimal order quantity
D = Demand (units per year)
formula to find how many times we will order per year using EOQ
D/Q0
Q0 = the optimal order quantity
D = Demand (units per year)
economic production quantity (EPQ)
to determine the optimal production lot size when we are producing an item in-house
the production lot size that minimizes total annual production setup and inventory holding cost
difference between EPQ and EOQ
instead of shipments being received in a single delivery, units are received incrementally
under the economic production quantity (EPQ), how do we find the inventory growth rate?
production - usage
ex: produced 20 units and the daily usage rate is 5 units, inventory will build up at the rate of 20 - 5 = 15 units per day
under the economic production quantity (EPQ), what is the point where the inventory on hand will be at max?
when production ceases
there, inventory starts to decrease
When the amount of inventory on hand is exhausted, production is resumed and the cycle repeats itself
the equivalent of ordering costs under the economic production quantity (EPQ)
setup costs
the cost to prepare the equipment for the job, such as cleaning，adjusting, and changing tools and fixtures
treated in exactly the same way, and we use the same symbol, S, to denote setup cost per production run
setup costs
the cost to prepare the equipment for the job, such as cleaning，adjusting, and changing tools and fixtures
analogous to ordering costs because they are independent of the lot (run) quantity
treated in exactly the same way as ordering costs, and we use the same symbol, S, to denote setup cost per production run
total cost under the economic production quantity (EPQ)
TC = Annual holding cost + Annual setup cost =
(Imax / 2) + (D/Q)S
Imax: Maximum inventory
D: Demand quantity
Q: Production run quantity
S: Setup cost per production run
how to calculate Imax under the economic production quantity (EPQ)?
Imax = Q - d(Q/p)
Q: Production run quantity
d: Production rate (e.g., units per day)
p: Usage or demand rate (e.g., units per day)
how to calculate cycle length under the economic production quantity (EPQ)?
Q/d
Q: Production run quantity
d: Production rate (e.g., units per day)
how to calculate production run length under the economic production quantity (EPQ)?
Q/p
Q: Production run quantity
p: Usage or demand rate (e.g., units per day)
how to calculate optimal production (Q0) under the economic production quantity (EPQ)?
Q0 = √(2DS/H) · √(p/(p - d))
D: Demand quantity
S: Setup cost per production run
H = Holding cost per unÎt per year
d: Production rate (e.g., units per day)
p: Usage or demand rate (e.g., units per day)
A quantity discount
a price reduction for large orders
offered to customers to induce them to buy in large quantities
Total Cost under EOQ With Quantity Discount
TC = Annual holding cost + Annual ordering cost + Annual purchase cost
(Q/2)H + (D/Q)S + RD
R = unit price
Q = Order quantity (units per order)
H = Holding cost per unÎt per year
D = Demand (units per year)
S = Ordering cost per order
the rationale of holding costs under EOQ With Quantity Discount
because holding cost is a percentage of price, lower prices will lead to lower holding cost
how to find the best purchase quantity under EOQ With Quantity Discount?
- Beginning with the lowest unit price, calculate the EOQ for each unit price until you find a feasible EOQ
–> until an EOQ falls in the quantity range for its unit price
- If the EOQ for the lowest unit price is feasible, it is the optimal order quantity
–> If not, compare the total cost at all the break quantities larger than the feasible EOQ with the total cost of the feasible EOQ. The quantity that yields the lowest total cost among these is optimum
a planned shortage
When holding cost per unit is large and the customer can wait
to intentionally allow shortage
We assume that all shorted demand will be back-ordered
the back-ordered demand will incur shortage cost proportional to the length of the time a unit is back-ordered
the average inventory on hand during the year under EOQ With Planned Shortage
((Q - Qb)^2) / 2Q
Qb = Quantity back-ordered per order cycle
Q = Quantity ordered
the average level of back-orders during the year under EOQ With Planned Shortage
(Qb^2)/2Q
Qb = Quantity back-ordered per order cycle
Q = Quantity ordered
the total annual inventory control cost under EOQ With Planned Shortage
TC = Annual ordering cost + Annual holding cost + Annual back-order cost
(D/Q)S + (((Q - Qb)^2)/2Q) · H + ((Q^2)/2Q) · B
Qb = Quantity back-ordered per order cycle
Q = Quantity ordered
H = Holding cost per unÎt per year
D = Demand (units per year)
S = Ordering cost per order
B = Back-order cost per unit per year
how to find the Qb (Quantity back-ordered per order cycle) under EOQ With Planned Shortage?
Qb = Q · (H/(H + B))
Q = Quantity ordered
H = Holding cost per unÎt per year
B = Back-order cost per unit per year
how to find the optimal quantity ordered under EOQ With Planned Shortage?
Q = √(((2DS)/H) · ((H + B)/B))
Q = Quantity ordered
H = Holding cost per unÎt per year
B = Back-order cost per unit per year
S = Ordering cost per order
The reorder point (ROP)
the inventory position at or below which an order should be issued
inventory position = On hand + On order 一 Back-ordered
The reorder point (ROP) formula with no safety stock
ROP = d · LT
d = Demand rate (units per day or week or month)
LT = Lead time (in days or weeks or months)
d and LT must have the same time units
The reorder point (ROP) formula with safety stock
Expected demand during a lead time + Safety stock
The amount of safety stock that is appropriate for an item depends on:
- Demand and lead time variability
2. The desired service level
the main ways we focus on to define the service level when finding the amount of safety stock that is appropriate for an item
- Lead time service level
2. Annual service level
Lead time service level
the probability that demand will not exceed inventory on hand during a lead time
the probability of no shortage during a cycle
equal to the fraction of cycles with no shortage
Annual service level
the proportion of annual demand filled from stocks on hand
fill rate
The formula commonly used to determine the safety stock, in the presence of demand and/or lead time variability
assumes that demand during a lead time is Normally distributed
Safety stock = z · σdLT
z = Safety factor; number of standard deviations above the expected demand
–> the smaller the desired stock-out risk, the greater the value of z
σdLT = Standard deviation of demand during a lead time
The reorder point (ROP) formula when only demand is available
ROP = d_ · LT + z · √LT · σd
d_: average daily or weekly or monthly demand
σd: standard deviation of daily or weekly or monthly demand
LT: Lead time in days or weeks or months
z = Safety factor; number of standard deviations above the expected demand
The reorder point (ROP) formula when both demand and lead time are available
ROP = d_ · LT + z · √(LT_ · (σd)^2 + (d_)^2 · (σLT)^2)
d_: average daily or weekly or monthly demand
σd: standard deviation of daily or weekly or monthly demand
LT: Lead time in days or weeks or months
z = Safety factor; number of standard deviations above the expected demand
LT_: Average lead time, in days or weeks or months
σLT: Standard deviation of the lead time, in days or weeks or months
reorder point ROP Using Annual Service Level steps
- Calculate E(z)
–> E(z) = Standardized expected number of units short during an order cycle
- determine the associated z value
- Use the z value in the following general ROP formula or a specific one
–> ROP = Expected demand during lead time + z · σdLT
E(z) formula in reorder point ROP Using Annual Service Level steps
E(z) = (Q(1 - SLannual)) / σdLT
σdLT = Standard deviation of demand during a lead time
SLannual = desired annual service level
Q = quantity ordered
ROP formula in reorder point ROP Using Annual Service Level steps
ROP = Expected demand during lead time + z · σdLT
σdLT = Standard deviation of demand during a lead time
Periodic reνiew (variation of the EOQ/ROP or Min7Max models)
inventory position is reviewed periodically
Min = d_ · (LT + RP) + z · σd · √(LT + RP)
Mαx = Min + EOQ
Cαn-order model (variation of the EOQ/ROP or Min7Max models)
In this model, when an item’s inventory position drops to or below its ROP, all related items re investigated to see if their inventory position is at or below their can-order level
–> If so, they are ordered too (to bring their inventory level up to their Max)
The fixed-interval / order-up-to level model
used when orders are placed at fixed time intervals (e.g., weekly, twice a month, etc.),
used also when inventory position is brought up to the order-up-to level
unlike the EOQIROP model, the order size tends to vary from interval to interval depending on demand during the previous interval
Two decisions needed to apply the fixed-interval / order-up-to level model for a group of items from the same supplier
(1) the order interval
(2) the order-up-to level for each item
in the fixed-interval / order-up-to level model, how can the order interval be determined
by minimizing the total annual holding and ordering costs of all the SKUs received from a particular supplier
OI = √((2 · (S + n · s)) / (i · E(Dj · Rj)))
S = purchase order ordering cost
s = line item ordering cost
n = Number of SKUs purchased from the supplier
Rj = Unit cost of SKU
i = Annual holding cost rate
Dj = Annual demand of SKUj
S = purchase order ordering cost
Fixed ordering cost per purchase order excluding line items
s = line item ordering cost
Variable ordering cost per SKU included in the purchase order
how do we determine the amount we will purchase enough to last until the next order time under the fixed-interval / order-up-to level model
Qj = Dj · OI
OI = Order interval (in fraction of a year)
Dj =Annual demand of SKUj
Total annual inventory control cost (TC) under the fixed-interval / order-up-to level model
TC = E(((Dj · OI)/2) · Rj) + i + (S + n · s) · (I/OI)
S = purchase order ordering cost
s = line item ordering cost
n =Number of SKUs purchased from the supplier
Rj=Unit cost of SKU
i = Annual holding cost rate
Dj =Annual demand of SKUj
OI =Order interval (in fraction of a year)
Therefore, order-up-to level or Imax formula under the fixed-interval / order-up-to level model
Imax = Expected demand during an order interval plus a lead time + Safety stock
Imax = d_ · (OI + LT) + z · σd · √(OI + LT)
d_: Average daily or weekly or monthly demand
OI = Order interval (length of time between orders); in days or weeks or months
LT = Lead time in days or weeks or months
z = Safety factor; number of standard deviations above the expected demand
σd = Standard deviation of daily or weekly or monthly demand
Order quantity Q formula under the fixed-interval / order-up-to level model
Q = Imax - inventory position
The coordinated periodic review model
A variation of fixed interval model where an item is ordered to meet demand
for a multiple m of a common orderinterval
steps to find the optimal amount in the coordinated periodic review model
- Find the SKU with largest annual dollar value DjRj
- For every other SKUj caluclate Mj
- calculate OI
fuck the formula im sick of writing them down
The single period model
used for ordering perishables and other items that have a limited useful life
generally focuses on two costs: shortage and excess
Cshortage = Cs = Revenue per unit - Purchase cost per unit
Excess cost in the single period model
pertains to items left over at the end of the period
the difference between purchase cost and salvage value
Cexcess = Ce = Purchase cost per unit - Salvage value per unit
multi-echelon supply chain
A supply chain with multiple levels or stages
methods used for coordinated control of inventories in a supply chain
Multi-echelon control
Distribution requirements planning
Inventory optimization
Multi-echelon control
A distribution network is usually like a tree on its side
The warehouse echelon (level) is the warehouse and all the retailers it feeds
retailers transmit their point of sale (POS) data to the warehouse
Distribution requirements planning
a planning method that determines time-phased replenishment schedules between a manufacturer’s facility and DCs
DRP requires:
- Forecast of demand at each DC (usually done by the DC itself).
- Current inventory on hand and on order.
- Order quantities/batch sizes.
- Lead times.
Inventory optimization
a method that determines the location and optimal level of inventory in the supply chain
given customer-promised LT
probability distribution of demand at each inventory location
cost of holding inventory at each location
processing time at each location
transport times
we have determine committed LT and amount of inventory to be kept at each location in order to minimize total inventory holding cost
