Ch. 12 Inventory Management
If ROP = Expected Demand during Expected Lead Time
"Service level is 50%" 50% chance of Stockout 50% Chance of Excess Inventory
Back to the Car Dealership Example: When to Order? and How Much to Order? and Intro to ROP
"Since cars are being ordered from far away there is a lead time. if we wait until inventory is 0 then we will run out of material until the cars show up after the lead time so how much is ordered should be determined by EOQ, consider how much demand per day there is ( for a certain period of time) and what the lead time is (how many days it take for him to get it) to determine point of reordering so you don't lose profit" d x L
EOQ Problem Example Determine the Total Annual Inventory Cost D= 1,000 S=$10 H= $.50 Q*= 200 units
$50 + $50 = $100 "there is also a shortcut, if optimum order Quantity is 200 units and Setup cost = holding cost, then you could just divide 200 by 2"
A Pareto Analysis
(20/80 rule) is used to segment items into value categories depending on annual dollar volume.
Annual Setup Cost Formula
(D/Q) x S
The Actual Cost of Material (Product Cost) is represented by what symbol?
(P) **find out difference between Total cost formula with DP included and without DP
Annual Holding Cost
(Q/2) x H
ABC Cycle Counting (or Ranked Method): Often policy for planned count schedule is:
-"A" items about 6 times/yr. "every other month" -"B" items about 4 times/ yr. "every quarter" -"C" items about 2 times/yr *This is also on final*.
Example, Economic Order Quantity- EOQ Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. What should be the order size? "in other words what is the optimal order quantity they should order" How many times should the dealer order?
-548 = 9.12 or 10 orders /yr. or? -Order ~556 cars 9 times/yr.
ABC Cycle Counting (or Ranked Method)
-Based on ABC item classifications, the higher $ value items are counted more frequently than lower $ value items
Operational Costs
-Delay in detection of quality problems -Delay the introduction of new products -Increase throughput times-"the more gummed up out operation" "This is a Work in Progress WIP"
Inventory Management Systems & Policies
-Items Classifications -Record Keeping "the more expensive, the more you pay attention and classify, keep a record of it"
Maintenance/ Repair/ Operating (MRO)
-Necessary to keep processes efficiently productive "you're looking at exam questions" "For Operations, you need an inventory of utensils, tools, etc. For maintenance, inventory of cleaning items For Repair inventory of tools in case things go wrong"
4.- Single Period Ordering Model
-Only one order is placed for a product -Units have little or no value at the end of the sales period - Examples: Newspaper, Christmas Tree, Fresh Bread. etc.
Physical holding costs
-Out-of-pocket expenses for storing inventory (Warehouse Rental, Security, Insurance, Cooling/Heating, etc. ) -All costs involved before the final sale (Spoilage, Obsolescence, Theft, Repair, etc.) "This is the biggest cost of inventory, cost of renting the space, cleaning it, cooling it, not too humid, no theft." "one of the biggest costs of inventory is obsolescence"
3.- Quantity Discount Models
-Reduced prices are often available when larger quantities are purchased -Trade-off is between Reduced Product Cost and Increased Holding Cost -So, the Total Cost is the determining factor "the higher percentage you buy the larger the discount, so consider the total cost, H is changed to IP"
The Supply Chain Overview: Material/ Product Flow Issues:
-The uncertainty of demand "We do not know how much demand there is" -The uncertainty of Supply "There might be delays" -Economies of Scale "we know demand comes in but not at the rate of production it makes sense to use economies of scale to produce things more and hold them, that's why we have inventory" -Smoothing out production "We have scrap and a small percentage extra so we build a little more to smooth production"
Inventory Models for Independent Demand
1. Basic economic order quantity (EOQ) model 2. Production order quantity (POQ) model 3. Quantity discount (QD) model 4. Probabilistic Model (PM) 5. Single-Period Ordering (SPO) Model **Cycle Counting can ensure ongoing inventory accuracy and assist in avoiding increased costs.
Cycle Counting Advantages
1. Eliminates shutdowns and interruptions 2. Eliminates annual inventory adjustment 3. Have Trained personnel audit inventory accuracy 4. Maintains accurate inventory records 5. Allow causes of errors to be identified and corrected
Cost of Inventory (3)
1. Physical Holding Costs 2. Opportunity Cost of Inventory 3. Operational Costs
Types of Inventory (4)
1. Raw Materials 2. Work in Progress 3. Finished Goods 4. Maintenance/ Repair/ Operating (MRO)
Topics we will discuss
1. Types of Inventory 2. cost of inventory 3. Inventory Accuracy & management System: -Items Classification - Counting & Maintenance of Inventory Records 4. Inventory Ordering Models
Annual Holding Cost Formula
1/2Q (1-d/p)(H)
ABC Cycle Counting (or Ranked Method): Example At a warehouse with 10,000 items, 2,000 items are "A" Items, 3,000 items are "B" and 5,000 items are "C". Using the Cycle counting Policy of 6, 4, and 2 times per year respectively, how many items should be counted daily?
136 Items Counted/Day Most Operations have 250 Days 80/20 Rule in inventory terms, means that 20% of the items in inventory account for 80% of sales or cost of inventory.
EOQ Problem Example Determine the Optimal Number of an Item to Order Demand= 1,000 Units Setup= $10 Per Order Holding Costs= $0/50 per unit per year
200 Units
Production Order Quantity Example D= 1,000 Units S= $10 H= $.50 per Unit Daily Production: p= 8 units per day D/250 : d =4 units per day What is the Optimum Order Quantity (Q*p)?
282.8 ~ = 283 units
If ROP = Expected Demand during Expected Lead Time + Safety Stock
50% chance of Stockout "if inventory is more than what you expect than you have a stockout situation, if it is less you have exess inventory. so to deal with this you use Safety Stock"
Cost Shortage (Cs)
= Sales Price/Unit -Cost /Unit
Cost of Overage (Co)
=Cost of Overage= Cost/Unit-Salvage Value
Another EOQ Problem Example A warehouse Stock Item has an Annual Demand (D) of 19,700 Units, Ordering Cost (S) of $23 / order, and Holding Cost (H) of $3/ unit/ year. A. What would be the Economical Order Quantity (EOQ) for this item? B. At the EOQ, what would be the Annual Holding Cost for this item? C. At the EOQ, what would be the Annual Setup/ Ordering Cost for this item? D. What is the Total Cost?
A. ~Q* = 549.6 or 550 B =$825 C. =$824 D.= 1,680
Service Period Problem Example A local Club is selling Christmas trees and deciding how many to stock for the month of December. The trees have no salvage value at the end of the month, Cost $20 each, and sell for $50. A.) What is the Otimum Service Level for this Business? B.) If Demand for the trees is normally distributed with a mean of 100 and STD of 20, What is the Optimum Stocking Level of the Christmas Trees?
A= 60% B= Optimal Stocking Level = 105
Inventory Items Classification: The ABC Analysis
ABC Classification or Ranking is used to establish Level of Control and Frequency of Review of inventory items based on Dollar Value, Criticality and Importance
Cycle Counting: More Preventative Techniques
ABC Cycle Courting Methods
Record Accuracy
Accurate Records are a Critical prerequisite for Inventory management and Production Planning.
(Minimizing Cost & Formula) Optimal Order Quantity is found when...
Annual setup cost =annual holding cost
Finished Goods
Completed Product awaiting shipment/ Meeting Demand
Factors in Inventory Model: Setup Cost
Cost to prepare a machine or process for manufacturing an order
Service Level Formula
Cs/(Cs + Co)
Number of Times We Order Per Year Formula
D/Q
Production Order Quantity Model- (d)
Daily Demand/Usage Rate
Production Order Quantity Model- (p)
Daily Production Rate
a.) Probabilistic Model, Variable Demand with Constant Lead Time + Formulas
Demand During the lead time should be your base + the SS Z - Number of STDs related to the desired Service Level x Sigma (d) STD of Demand/ day STD of Demand During lead time is Sigma (d)(LT)= Sigma (d)(radial over Lead time) = SS= Z x Sigma(d)(LT) so, ROP= (Avg. of d x L) + SS
Difference between EOQ & ROP
EOQ answers the "How Many" Question The ROP tells "numerically" When to order ^"How much do we have In our inventory that tells us it is time to re-order"
Key Questions to Inventory Management Issues: How Much to Order?
Expected Demand
Fixed Period (P) Ordering Systems: Fixed Period Ordering instead of
Fixed Quantity Ordering.
Opportunity Cost of Inventory
Foregone return on the funds invested "If we are investing 50-70$ worth of Tesla in our showroom that money can not be used for other investments"
Quantity Discount Models Formula
H= %P so, H = IP "Holding cost, in reality, is the percentage of the cost of the product."
Production Order Quantity Model- (H)
Holding Cost per unit per year
Inventory Models
Independent Demand Dependent Demand
Inventory Management
Inventory Management is the art and science of building and keeping inventories to match Supply and Demand in the most effective way
Fixed Period (P) Ordering Systems: instead of a Perpetual Inventory System for each item added and removed we use...
Inventory at end of a Fixed Period
Key Questions to Inventory Management issues: When to Place Orders?
Lead Time "how long does it take to receive it and replenish it"
Which types of inventory are MRO Inventory
Maintenance Repairs Operations
Maximum Inventory Formula
Max Inventory= Q (1-d/p) "average inventory would be half of this"
Optimum Order Quality Explained
Minimizing total inventory Costs for a given Demand At Optimal order Quantity (Q*), Holding Costs=Setup Costs "the more we order the Larger the holding cost, so they equal each other" "where the Lowest total cost point is on the graph with the red line, is where the optimal order quantity is"
For the first half of the chapter, the inventory models Assumption to this point is that the Demand & Lead time were constant... In the real world, the Demand & Lead time is...
Not Constant or known (i.e. Demand for lemonade, bagels, autos, etc.)
Optimal Order Quantity Formula (Q*)
Optimal Order Quantity (Q*) is found when... Annual Setup Cost= Annual Holding Cost
Key Questions to Inventory Management issues: How Stock to Keep?
Ordering & Holding Costs "how much to keep based on cost and setup"
In Inventory Models, Setup Costs are considered the same as...
Ordering Costs, They are the same and are shown as "S"
What kind of models can we use to deal with Real-world Types of Demand & Lead time?
Probabilistic Models of Inventory Management
Average Inventory Formula
Q/2
1. Basic EOQ Model
Q/2 - Average inventory "the cornerstone of inventory management for all models" "in business the quantity ordered is constant, quantity ordered is shown by "Q"
Quantity Discount Example Demand/ Yr. = 5,000 Setup Cost = $49 Holding Cost = 20% Discount #1 Discount Quantity: 0-999 Discount Price (P): $5.00 What is Q* for Discount #1? Discount #2 Discount Quantity: 1,000 to 1,999 Discount Price (P): $4.80 What is Q* for Discount #2? Discount #3 Discount Quantity: >2,000 Discount Price (P): $4.75 What is Q* for Discount #3?
Q1* = 700 units/order Q2*= 714 units/order ~ 1,000 Adjusted "you need at least 1,000 to get a discount" Q3*= 718 units/order ~ 2,000 Adjusted "you need at least 2,000 to get a discount"
Finding the Optimal Quantity to Order Example Questions 1: Our Demand Per Year is D (1,000 Units) We decide to order in batch quantity of Q (100 Units). What is the number of times we will order per year? Question 2: let's say that our Setup/Ordering Cost is S ($250 Yr.) What is the Annual Setup Cost? Question 3: Now, let's say that our annual Holding Cost per unit is H ($2/ unit/ Yr.) What is the Annual Holding Cost?
Q1: 10 Orders/ Yr Q2: $250/yr. Q3: $100/ Yr.
Production Order Quantity Model- (Q)
Quantity, Number of Pieces per order
Reorder Point (ROP) Formula
ROP = d x L d= Demand per period (Units) L = Lead time in periods (days)
Probabilistic Example 4 Average Daily Demand (Normally Distributed= 150 Units Standard Deviation of Demand = Sigma(LT) = 16 Average Lead Time 5 Days (Normally Distributed) Standard Deviation of Lead Time = Sigma(LT) = 1 day Service Level= 95%, so Z= 1.65 (Be able to find Z on your own) what is the ROP?
ROP= (Avg. Daily Demand X Avg. Lead Time) + SS 1.004 Units
c.) Probabilistic Model, Variable Demand and Variable Lead Time + Formula
ROP= (Avg. Daily Demand X Avg. Lead Time) + SS SS is Unique to this model refer to photo for SS formula *this type of problem will most likely only be extra credit
Probabilistic Example 2 Mu= Avg. Demand During Lead time (dxL)=350 units Sigma(d)(LT)= STD of demand during lead time = 10 Units ( Service Level Policy = 95% (or 5% stockout) What should be the ROP? 95%~ Z=1.65
ROP= 366.5 or 367 units
Probabilistic Example 3 Daily Demand(Constant) =10 Units Average Lead times =6 Days Standard of Lead time= Sigma(LT) = 1 days Service Level = 98% Z = 2.055 ROP=?
ROP= 81 Units
Reorder Point (ROP) Formula explained
ROP= d x L
Probabilistic Example Average Daily Demand (Normally distributed) =15 units STD of Daily Demand = 5 units Lead time is constant= 2 days Desired Service Level = 90% Z (from Appendix I) = 1.29 What is the ROP?
ROP= d x L +SS Z= 90%=.8997=1.28 39 Units (Safety Stock is about 9 Units)
Types of Inventory (6)
Raw Materials Inventory Work-In-Progress Inventory (WIP) Finished Goods Inventory Maintenance Repairs Operations
Sample ABC Analysis
Rough estimation to identify important from not important items "Annual Volume (Units) X Unit cost =Annual Dollar Volume" "with annual dollar volume, you get a percentage of annual dollar volume and can rank items by level of importance based on the percentage A, B, C items" "They need to look at this periodically"
Safety Stock Formula
SS= Z x Sigma(d)
b.) Probabilistic Model, Constant Demand, and Variable Lead Time + Formula (simplest option)
Sigma(LT)= STD of Lead Time in Days SS= Z x (daily Demand) x Sigma(LT) ROP= (Daily Demand x Average Lead time in days) + Z x (daily Demand) x Sigma(LT)
What is the aim of Probabilistic Models
The aim is to avoid Stockout and Maintaining Service Levels with these uncertainties
Service level
The complement of Stockout (i.e., 10% probability of Stockout = Service level of 90%
Factors in Inventory Model: Holding Cost
The costs of Holding (Carrying) inventory over time (e.g., Warehouse Rental, Cooling/Heating, Security, Insurance Pilferage, Obsolescence, etc.) Shown as "H"
Factors in Inventory Model: Ordering Cost
The costs of placing an order + vendor's setup costs + cost of receiving the goods
Dependent Demand
The demand for item is dependent upon the demand for some other item in the inventory (Focus of Ch.14) "All the components inside a product and having inventory for it"
Lead Time (L)
The time between Placing and Receiving an order
Total Annual Inventory Cost Formula
Total Annual Inventory Cost = Setup Cost+ Holding Cost
Total Annual Inventory Cost Formula
Total Cost= Setup Cost + Holding Cost
B Items
Typically ~30% of items have ~15% the inventory dollar
A Items
Typically ~20% of Items have ~80% of the inventory dollar "20 percent of items are occupying 80% of the dollar value of inventory
C Items
Typically ~50% of items account for only ~5% of the inventory dollar value. "50% of items (Furniture) are only 5% of schools (SDSU's) value "
2.- Production Order Quantity Model Slide
Units are Produced or Delivered & Used Simultaneously "For example grandma making pancakes, she wants to make 15 but her grandkids eat them as she is making them so she never gets to 15" "consider the rate of production and rate of consumption"
Fixed Period (P) Ordering Systems: Orders bring inventory...
Up to target levels
Periodic Systems
Where the inventory on hand is checked once or twice per year (Issues: Lack of visibility between reviews, and extra inventory needed against possible shortages) "There can be many small mistakes and problems with this system"
Perpetual/ Cycle Counting System
a method for auditing inventory accuracy and reconciling errors on a cyclical schedule rather than once or twice a year "This method is preferred over the Periodic system, we use the ABC model in this counting method and pay most attention to A Items"
Probabilistic Models
a)When Demand is Variable and Lead Time is Constant "Demand is variable (shows up as average demand)" b)When Lead Time is Variable and Demand is Constant "in this model demand is constant" c)When both Demand and Lead Time are Variable "Demand is variable (shows up as average demand)" "three sets of formulas have identical solutions" "However SS is calculated differently depending on the model"
Car Dealer Example Continued: If the Lead Time to receive cars is 10 days, when should the dealer place its orders? If the annual demand is 5,000, and the dealer has 250 working days per year d=? L=? ROP=?
d= 20/day L= 10 days ROP= 200 So when the number of cars on the lot reaches 200 (200 is the limit), the dealer orders 548 (Q*) more cars.
Another Reorder point Example Demand = 8.000 iPads per year 250 working day year Lead time for orders is 3 working days, may take 4
d= 32 Units ROP: 3 days= 96 Units 4 Days = 128 Units *the extra 32 units can be used as safety Stock*
Demand per period (d)
d= Demand / Number of Working days in a year
Raw Materials
purchased but not processed
Optimum Production Order Quantity Formula (Q*p)
refer to photo
Quantity Discount Example Continued... Annual Product Cost? Annual Ordering/ Setup Cost? Annual Holding Cost? Total Cost? What is the Optimal Order Quantity?
refer to picture
Independent Demand
the demand for item is independent of the demand for any other item in inventory ( Focus of Ch.12) "you look at how many of something you have and manage that inventory"
Work-in-Progress (WIP)
undergone some change but not completed "at any given time you have sugar, water and lemon juice mixed, not raw but in progress"
