Supply Chain Chapter 11 : Inventory
2. How many times per year will an order be placed?
(hint: use EOQ for Q in these calculations) D/EOQ = 10,800 / 240 = 45 yrs
Practice Problem for chapter 11 Daily demand for a product is 60 units. The review period is 10 days, and the lead time is 2 days. Standard deviation over the 12-day period is 34.64 units At the time of review there are 100 units in stock. If 98% service probability is desired, how many units should be ordered?
** fixed-time interval model** q = R- I R= d(T+L) +zσ d(daily demand)=60 t(review interval)= 10 days l(lead time)= 2 days z-score= go to normal table and find 98% for a z-score of 2.06 σ= SD of 34.64 R=60(10+2) (2.06)(34.64) R= 791.36 round to 792 now: 792-100= 692 units !
Inventory Turn Calculations Explanation
***Average Inventory***: expected amount of inventory over time ***Inventory turn***: number of times inventory is replaced over a year- a measure of how efficiently inventory is used
Overview of chapter 11:
- EOQ model is used to balance holding costs and ordering costs of your most critical inventory items - Use the Price-Break model when the supplier offers varying prices for order quantities - the fixed time period model is for your less critical inventory items. Set the restocking level to order the appropriate amount each time - the single period model is for specific items that last a selling season. we need to balance the overage and underage costs incurred
Fixed Order Quantity: How MUCH to order
- Economic Order Quantity (EOQ): the order quantity that minimizes annual holding and ordering costs for an item
Recap of 4 Inventory Control Systems
- Fixed-Order Quantity: 1. Basic EOQ model 2. Price-break model -Fixed-Time Period 1. P Model 2. Single-period model only looking at inventory
Basic Inventory management Questions
- How much to order -When to order
Fixed- Time Period P-Model
- Inventory levels are checked at regular intervals (e.g. once a week) - replenishment orders are issued at this time - the size of a replenishment order is based on the desired restocking level minus the current on hand
Classification of Inventory
- Manufacturing Inventory: raw materials, component parts, work-in-process (WIP), finished products, supplies -Distribution Inventory: in-transit, warehouse - Service Inventory: Supplies necessary to administer the service, may also include some tangible goods
P-Model Service Level (z-score)
- Service level is the amount of demand to be met under conditions of demand and supply uncertainty **Service Level & Z-Values** - 90%= 1.29 z-value -95%=1.65 z-value - 99%= 2.33 z-value -99.9%= 3.09 z-value the higher the z-score, forces restocking point higher, and to order more units each time
Fixed-Order Quantity: if demand rate (d) or lead time(L) varies:
- add safety stock units to account for this uncertainty R= dL +SS Where: SS= safety stock units ; provides additional buffer to have additional inventory on hand
Setup (production change) costs
- costs for obtaining the necessary materials, arranging specific equipment setups, filling out the required papers and so on
Basic EOQ Model
- fixed-order quantity basic EOQ model - inventory levels are monitored constantly - replenishment order is issued only when the reorder point (R) is reached - the reorder point is "X units remaining in inventory" - the size of a replenishment order is based on the trade-off between inventory holding costs and ordering costs
Economic Order Quantity (EOQ)Model Assumptions
- holding and ordering costs are known and fixed - price of each unit is fixed - only one product is involved - ordering in batch from the supplier - single delivery for each order
Slimstock video on economic order quantity
- the EOQ quantity is the link between all supply chain costs when selling products from stock - order quantities have a big effect on transportation, inventory carrying, warehouse operations, and order processing - when applying EOQ method, important to consider: 1. demand seasonality 2. promotion demand 3. irregular demand 4. allocation of different costs 5. synergy effects of clustering products 6. product lifecycle status 7. product obsolescence - Needs to be reviewed continuously because of demand, logistic units, discounts, and costs
Single Period Example #2 A coffee shop owner buys sesame bagels from a bakery for 75 cents early in the morning each day and sells them for 120 cents during the day. The owner is paid 60 cents back for each unsold bagel - Underestimating demand cost (shortage cost): the marginal cost of under-stocking one unit - Overestimating demand cost (excess cost): the marginal cost of over-stocking one unit
- underestimating: Cu= 120-75= 45 cents per bagel -overestimating Co=75+0-.60= 15 cents per bagel (no disposal cost) 45/ 45+15= 75% -75% we will have enough bagels for customers - but we will run out 25% of the time
Inventory Costs
-Holding (or carrying) costs -Setup (or production change) costs -Ordering costs -Shortage costs
Holding (carrying) costs
-costs for storage, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes, and the opportunity cost of capita1
Step 1: single period model
-determine cost of underestimating demand (lost sales) Cu= price-item cost (just do unit price-not bulk price) - determine cost of overestimating demand (excess units) Co= item cost+disposal cost - salvage value ************* Target Service Level= Cu / (Cu +Co)
Qualities of Inventory Management
-often largest asset on the balance sheet - can be difficult to convert back into cash - average cost of inventory in the US is 30 to35 percent of its value
Single-Period Model (special case of the fixed-time period model)
-only the first interval is considered - no opportunity to re-order products - sometimes called the "Newsboy Problem": how many papers should the newsboy grab to maximize his profit - when excess inventory cannot be held in the future, firms must weight the cost of being short against cost of holding excess units -examples: donuts, magazines, newspapers, Christmas trees
Price-Break Inventory Model
-use this model if the price varies with your order size - example: cereal is $3/box, but if you buy 5 boxes it's only $2.50/box
Fixed-Order Quantity: When to Order
-when the demand rate and lead time are constant: - Reorder Point= average demand x lead time R=d x L - units per day x Lead time = Reorder Point
Basic Equations Needed for Inventory Turn Calculations: COGS Average Inventory Average Inventory Value
1) COGS= D x C D=yearly demand C= cost per unit 2) Average inventory= Q/2 +SS Q=order quantity SS= safety stock 3)Average Inventory Value= [Q/2 + SS] x C Q= order quantity C= cost per unit
Inventory Turn Calculations
1) Inventory Turn= COGS / Average Inventory Value = D / (Q/2 + SS) D= annual demand Q= order quantity SS= safety stock
Single-Period Model 2 Step Process
1. Calculate the Target(optimal) service level: - the level at which the expected cost of understanding demand equals the expected cost of overestimating demand 2. Calculate the Target Stocking Point - the number of units that should be ordered
Purposes of Inventory
1. Customer Service: product is available immediately for the customer 2. Account for variability: - customers: variation in product demand -suppliers: variation in raw material delivery time 3. Allow flexibility in production scheduling: - a stock of finished goods gives production options of what to produce next 4. Maintain Independence of operations: - downstream operation doesn't have to wait for an upstream operation to finish if there's inventory to process 5. Take advantage of economic order sizes: - larger orders may reduce shipping costs for some products 6. Take advantage of quantity discounts
Price-Break 2 Step Process
1. Sort prices from lowest to highest and calculate the EOQ (estimated order quantity ; EOQ= √ 2DS /H) for each price starting with the lowest price until a feasible order quantity is found 2. If the first feasible order quantity is for the lowest price, this quantity is best. Otherwise, calculate the total cost for the first feasible quantity & calculate the total cost at each price lower than the price associated with the first feasible order quantity.
Fixed Time Period P-Model Example 2 Given: - daily demand is d=10 units/day - review period, T= 30 days - lead time, L= 14 days - current on hand inventory, I=150 -Standard deviation over a 44 day period (T+L time period) = 23 units - 98% of demand should be met from items in stock 1. What is the inventory policy? 2. How many units should be ordered?
1. q=R-I find R: R=d(T+L) + zσ t+l R= 10(30+14) + (2.06)(23) R= 487.4 Inventory policy: order (488-I) units every 30 days since there are currently 150 on hand, we order (488-150) = 338
Fixed-Time Period Model
An inventory system where the inventory level for an item is checked at regular intervals and restocked to some predetermined level - for less critical and low value items - P-Model -Single-Period Model
Fixed-Order Quantity Model
An inventory system where the inventory level for an item is constantly monitored and when the reorder point is reached, an order is released - for critical and high-value items - Basic EOQ Model -Price-Break Model
6. What is the reorder point (R)?
Annual demand D= 10,800 units/yr Leadtime: L = 6 days d must be in days because lead time is in days so : 10,800/365= 29.6 units/day R=d x L = 29.6 units/day x 6 days = 177.5 units Round up to 178 units
Fixed-Order Quantity Metrics from EOQ Equation
Annual orders = Annual demand/order quantity Time between orders = order quantity/annual demand Total Annual Cost: DC+D/Q (S) + Q/2 (H)
Step 1 example: single-period model
Cu= 8.50-2.50= $6.00 /pound Co= 2.50 + .50 - 1.50 = $1.50 / pound 6/(6+1.50) = 6/7.50 = 80% target service level 80% of the days, they should have enough fish - but 20% of the days, they will run out so, how often should the fish stand expect to be out of fish at the end of the day? 20%
4. How much does the company spend annually on ordering costs?
D / EOQ x (S) = 10,800/240 (60) = $2,700
EOQ Example Problem: Use to answer next 7 Questions Demand for a certain type of blu-ray players at a retail store is 900 units per month. Each blu-ray player costs the company $90. Ordering costs are $60, and holding costs are 25 percent of the purchase price. Lead time is 6 days and assume the store operates 365 days a year. the store holds no safety stock of blue-ray players
D(Demand per year)= 900 per month x 12 months = $10,800/yr S(ordering cost)= $60/order C(cost per unit)= $90, i= 0.25 H(holding cost)= .25 X 90 = $22.50 per one unit per year
5. How much does the company spend annually on holding (carrying) costs?
EOQ / 2 x (H) = 240/2 (22.5) = $2,700
3. How often will an order be placed (length of order cycle)
EOQ / D = 240 / 10,800 = 0.22222(yr) x 365 = 8.1 days
Fixed-Order Quantity Metrics Example
Given: -Annual demand (D) of 10,000 units per year -Order quantity (Q) of 1,000 units per year Solution: Annual Orders=D/Q= 10,000/1,000=10 orders/year Time between orders: 1,000/10,000= 0.1 years x 365 days per year = 36.5 days
7. What is the final inventory policy? (how much (EOQ)& when(reorder point-R)?)
Order however much you calculated for EOQ: 240 units when inventory drops to the reorder point which was 178 units
How much to order equation:
Qopt= EOQ= √ 2DS /H
Fixed-Order Quantity EOQ Equation
Qoptimal= EOQ= √ 2DS /H Q= order quantity H= annual holding cost per unit D=annual demand (needs to be converted to annual demand units) S=ordering cost
When to order equation is:
R= d L + SS
Formula for restocking level
R= d(T+L) + zσ d=average demand per day (units per day) T=number of days between reviews L= lead time in days z=z-score for the desired service level σ= standard deviation over the review + lead time zσ= safety stock
Price-Break Model- Example Annual demand = 10,000 Ordering cost= $20 per order Interest/Carrying cost= i=20% Cost per unit, C, depends on the quantity ordered - Order 1-499 ; cost is $5.00 per unit - Order 500- 999 ; cost is $4.50 per unit - Order 1000 or more ; cost is $3.90 per unit
Step 1: use Q= √ 2DS /iC D=annual demand i=interest/carrying cost S= ordering cost C=cost per unit starting with lowest price... calculate Q for 3.90 price: Q1000+ = √ 2(10,000) 20 / 0.20 (3.90) = 716 =not feasible since 716 is not in the 1000+ range then, calculate Q for the $4.50 price: Q500-999= √ 2(10,000)20 / .20(4.50) =667 (feasible 667 is in the 500-999 range) ***if the Q for a $4.50 price was not feasible, we would calculate the Q for the $5 price **** Step 2: since we didn't get the lowest price use TC= DC + D/Q (S) + Q/2 iC starting with the feasible Q... Use Q= 667 for the $4.50 price: TC= (10,000)(4.50) + 10,000/667 (20) + 667/2 (.20) (4.50) = $45,600 Now, check all lower prices for a better total cost (use the minimum Q in the range): Use Q=1,000 for the $3.90 price: TC=(10,000)(3.90) + 10,000/1000(20)+1000/2(20%)(3.90)= $39,590 ***Result: Lowest total cost at Q=1000 so order 1000 units each time
Step 2: single period model
Target Stocking Point = μ + zσ - use target service level (step one) to get the z-score from the Normal Table μ = mean demand per time period z= s-score to meet target service level σ= standard deviation of demand per time period
example #2 continued: More information about daily demand, determine the Target Stocking Point - the demand is approximately normal with a mean of 100 bagels per day (μ =100) and a standard deviation of 10 bagels per day (σ=10)
Target stocking point= μ +zσ =100+ (0.68)(10)= 106.8 ***round to 107 bagels find z-score in normal table 75% is a z-score of 0.68
Ordering Costs
costs of placing an order and associated with maintaining the system
Shortage costs
costs of stock-out
Reading the Normal Table for z-scores
don't stop short of the service value: example: 90% service level you have to hit .9, don't pick any number lower than that
Fixed Time Period Inventory Policy
example: "Order (R-I) units every 2 weeks" you need a restocking level subtracted from amount on hand and a constant time interval (ex: 2 weeks)
Pareto Principle
few items have significant importance (mostly A items)
Example Restocking problem: R= d(T+L) +zσ Assume we review inventory every money. so T=7 days Lead time is 3 days: L=3 days if today is Monday and there's 100 units in inventory, how long does that inventory have to last?
has to last 10 days because of lead time (7+3)
Cycle Counting
inventory is counted on a frequent basis - "A" items cycle counted more frequently than "C" items - More costly to the company it the count of "A" items is off than if the count of "C" items is
How to get a higher/more service level?
move restocking order higher
Fixed-Time Period P-Model Example The Pepsi delivery driver stops into the grocery store one morning and notes there are only 16 bottles of soda on the shelves. Consulting his route sheet, he discovers the restocking level is 60. What is the order quantity for the day? How was the restocking level of 60 created?
q= 60-16 q=44 bottles formula for restocking level: R= d (T+L) +zσ
Calculating the order quantity (q) for P-Model
q= R-I R= restocking level I= inventory level at the time of review
Manufacturing inventory
refers to items that contribute to or become part of a firm's product
ABC inventory Classification
scheme that divides inventory items into three groupings - high dollar volume (A) - moderate dollar volume (B) - low dollar volume (C) dollar volume = measure of importance to the company
Definition of Inventory
the stock of any item or resource used in an organization: raw materials, finished products, component parts, and work-in-process - MRO: maintenance, repair,. and operating supplies
Where is the optimal order quantity (Qopt)
where holding cost=ordering cost
Practice Problem 2 Chapter 11: A particular raw material is available to a company at three different prices, depending on the size of the order: Less than 100 lbs = $20 per pound 100 lbs to 1,000 lbs = $19 per pound More than 1,000 lbs = $18 per pound the cost to place an order is $40. Annual demand is 3,000 lbs. Holding (carrying) cost is 25% of the material price. What is the economic order quantity (EOQ) to buy each time?
EOQ= Qopt= √ 2DS / iC D= 3000 lbs S (ordering cost)= $40/order i= .25 C= start with $18/lb cost now calculate first EOQ: √ 2(3000)(40) / (.25)(18) = 231 lbs - not feasible next, calculate second lowest cost of $19 per lb: D=3000 lbs S(ordering cost)= $40/prder i=.25 C= $19/lb cost EOQ= √ 2(3000)(40)/.25 x 19 = 225 lbs - yes, it is feasible Step 2: now that you found a feasible EOQ: Find lowest total annual cost= DC + D/Q(S) + Q/2 (iC) 3000(19) + 3000/225(40) + 225/2 (.25x19) = $58,068 now plug in $18: 3000(18) + 3000/1001 x 40 + 1001/2 (.25x18) =$56,372 order quantity of 1001 lbs because that is the lowest total annual cost
Practice Problem Chapter 11: A local service station is open 7 days a week, 365 days per year. Sales of 10W40 grade premium oil average 20 cans per day. Inventory holding costs are $0.50 per can per year. ordering costs are $10 per order. Lead time is two weeks. Backorders are not practical-the motorist drives away. a. based on this data, choose the appropriate inventory model and calculate the economic order quantity and reorder point. b. use a safety stock of 59 cans. Determine a new inventory plan based on this information and the data in part (a). Use Qopt from part (a)
EOQ= √ 2DS / H D= annual demand (20 x 365= 7300 cans per year) S= ordering cost (10 per order) H=holding cost (.50 per can per year) EOQ= √ 2(7300x10) / .50 = 540 cans R(reorder)= d x L lead time = 2 weeks demand in cans has to be per week: so, 20 cans per day x 7 days a week = 140 cans per week Reorder point= 140 x 2= 280 cans order 540 cans when inventory drops to 280 cans b. R= d x L + SS 140 x 2 +59 = 339 cans order 540 cans when inventory drops to 339 cans
1. how many blu-ray players should the manager order in each lot?
EOQ= √ 2DS /H = √ 2(10,800)(60) / 22.5 = 240 units
Fixed-Order Quantity : Total Annual Cost Breakdown
Equation: DC+D/Q (S) + Q/2 (H) TC= Total annual cost D= Annual demand C= Cost per unit Q= order quantity S= cost of placing an order (setup cost) H= Annual cost of holding / storing one unit in inventory
