4 Types of Inventory 1. Materials A. Raw material B. WIP C. Finished Goods
5 Types of Inventory 1. Components A. Subassemblies B. Purchased parts that go into 2. Distribution inventories A. Sometimes called pipeline inventories B. In a warehouse or in transit 3. MRO A. Maintenance items B. Repair parts C. Operating supplies
6 A Material-Flow Process Production Process Work in process Vendors Raw Materials Work in process Work in process Finished goods Custome
7 What is inventory and Inventory management? Inventory: a stock of materials used to facilitate production or to satisfy customer demand Managing the flow of goods into, through, and out of an organization
8 Inventory One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service
9 Purpose of Inventories To protect against uncertainties in demand supply lead times schedule changes Reduction: shorten throughput times
10 Types of Inventory External Internal
11 Types of Inventory (external) Pipeline inventory inbound or outbound stock in transit
12 Types of Inventory (internal) Raw Material product which has not yet undergone any transformation Work-in-process (WIP) inventory which has already undergone some transformation but not yet completed Finished Goods inventory which has undergone all transformations and is ready to be passed on to the customer
13 Negative Aspects of Inventory Financial cost of carrying too much inventory Risk of obsolescence or damage Large inventories hide operational problems
14 Holding (or Carrying) Cost 1. Cost to carry one unit of stock for one unit of time, e.g., $2 / unit / year A. Varies with the inventory level 2. Notation: H 3. Components: A. Capital costs or Opportunity costs B. Storage cost C. Insurance & Taxes D. Risk costs a. Pilferage & Obsolescence 4. Sometimes derived from: A. holding cost rate, e.g., 25% per year B. Multiplied by the unit value
15 Inventory Cost Structures How the 35 percent carrying cost is distributed Cost of Capital 9-20 percent Obsolescence 2-5 percent Storage 2-5 percent Material Handling 1-3 percent Shrinkage 1-3 percent Taxes & Insurance 1-3 percent Source: Mark Williams, APICS Instructor Listserv, 22 January 2001
16 Inventory Cost Structures Shrinkage shrinkage cost U.S. retailers about $41.6 billion last year. This is more than the combined total from other crimes such as robberies, auto theft and larceny. Source: Wall Street Journal, 11 July 2007, p. B4.
17 Inventory Cost Structures Stock out cost (back order or lost sales) record maintenance lost income customer dissatisfaction Typically expressed as a fixed cost per backorder or as a function of aging of backorders.
18 Hidden Costs of Inventory Longer lead times Reduced responsiveness Underlying problems are hidden rather than being exposed and solved Quality problems are not identified immediately No incentive for improvement of the process
19 Two Forms of Demand Independent demand (this chapter) finished goods, spare parts, based on market demand requires forecasting managed using replenishment philosophy, i.e. reorder when reach a pre-specified level.
20 Two Forms of Demand Dependent demand (next chapter) parts that go into the finished products dependent demand is a known function of independent demand calculate instead of forecast Managed using a requirements philosophy, i.e. only ordered as needed for higher level components or products.
21 Independent vs. Dependent Demand Independent Demand (Demand for the final endproduct or demand not related to other items) Finished product Component parts E (1 ) Dependent Demand (Derived demand items for component parts, subassemblies, raw materials, etc)
22 Basic Inventory Management Issues And Decisions 1. For which items should inventory be carried? 2. Where should inventory be stored? 3. What is the right inventory level for each product? 4. How can we control inventories? 5. How can we evaluate inventory performance? Inventory Decisions Involve Trade-Offs!
23 Inventory Systems 1. An inventory system provides the structure and operating policies for maintaining and controlling goods to be stocked in inventory. 2. The system is responsible for ordering, tracking, and receiving goods. 3. There are two essential questions to answer that define a policy: 1. How much or what quantity of an item to order 2. When should an order for that item be placed?
24 Two Types of Systems 1. Continuous review system: an inventory system that always orders the same quantity of items but has differing periods of time between orders Q Q Q T 1 T 2 2. Periodic review system: an inventory system that has a fixed time between orders but has different order quantities from order to order Q 1 Q 2 Q 3 T T
25 Order or Setup Cost 1. Cost to place an order or to initiate a production run, e.g., $10 / order A. A fixed cost 2. Notation: S 3. Components: Order Cost -> Time of personnel, receiving, inspection, etc. Setup Cost -> Opportunity cost, waste, etc.
26 Shortage Cost 1. Also known as stockout cost A. Occurs when inventory not sufficient to meet demand 2. Could result in: A. Back order B. Lost sale 3. Direct, and indirect, dollar consequences: A. Downtime of operations B. Premiums for expediting C. Extra transportation and handling D. Lost of customer goodwill
27 EOQ 1. You want to review your inventory continually 2. You want to replenish your inventory when the level falls below a minimum amount, and order the same Q each time 3. Typical of a retail item, or a raw material item in a manufacturer
28 How to Determine Q Use the EOQ formula Q D = Demand S = Order or Setup Cost H = Holding Cost 2DS H
29 EOQ Assumptions 1. For the Square Root Formula to Work Well: A. Continuous review of the inventory position B. Demand is known & constant no safety stock is required C. Lead time is known & constant D. No quantity discounts are available E. Ordering (or setup) costs are constant F. All demand is satisfied (no shortages) G. The order quantity arrives in a single shipment
30 EOQ Inventory Behavior Inventory Level Starts at Q Q Inventory Depletes at Constant Rate Process Repeats R 0 Reorder Point Hit Inventory Runs Out & Order of Size Q Arrives
31 Where the EOQ formula comes from: Find the Q that minimizes the total annual inventory related costs: Annual number of orders: N = D / Q 1. Annual Ordering Cost: S x (D / Q) Average Inventory: Q / 2 2. Annual Carrying Cost: H x Q / 2
32 How the costs behave: Annual cost ($) Order Quantity, Q
33 How the costs behave: Annual cost ($) Ordering Cost = SD Q Order Quantity, Q
34 How the costs behave: Annual cost ($) Carrying Cost = HQ 2 Ordering Cost = SD Q Order Quantity, Q
35 How the costs behave: Annual cost ($) Slope = 0 Total Cost Minimum total cost Carrying Cost Ordering Cost Optimal order Q opt Order Quantity, Q
36 How the Costs Behave Total Cost (TC) Q D TC H S 2 Q 1. Total Cost Function Has Slope of Zero at (Optimal) Value of Q Best 2. Taking First Derivative of TC and Setting Equal to Zero Gives the Square Root Equation
37 Example: Papa Joe s Pizza (Atlanta store) Uses 18,000 pizza cartons / year Ordering lead time is 1 month Decisions: 1. How many cartons should Papa Joe order? i.e., Q 2. When should Papa Joe order? R
38 Data: Inventory carrying cost is $.022 carton / year Ordering cost is $10 / order
39 EOQ for Papa Joe s EOQ , ,045.2 Q 4,045 TC(4,045) 180,000/ 4,045 $88.99/ year ,045 TC(4,000) 180,000/ 4, ,000 $89.00/ year
40 Reorder Point Q R 0 Lead Time
41 Reorder Point Calculation 1. D x L = demand during lead time 2. Set reorder point, R, equal to demand during lead time 3. R = D x L 4. For Papa Joe s A. R = (18,000 cartons / yr) x (1 / 12 yr) = 1,500 cartons 5.State Inventory Policy As: A. Order 4,000 cartons When the Inventory Level Reaches 1,500 cartons
42 Variable Demand & Safety Stock Q R Order Placed Order Demand du Received lead time Stockout
43 The Relationship Between SS, R, & L 1. R = enough stock to cover: A. What you expect to happen during a lead time plus B. What might happen during the lead time C. R = dl + SS
44 EOQ with Discounts Many companies offer discounted pricing for items that they sell. Procedure: Arrange the prices from lowest to highest. Starting with the lowest price, calculate the EOQ for each price until a feasible EOQ is found. If the first feasible EOQ is for the lowest price, this quantity is optimal and should be used. If not, proceed until feasible EOQ found. If feasible EOQ found, check ALL breakpoints above the value of the feasible Q
45 EOQ w/ Quantity Discounts Example C $3.00 D = 16,000 boxes of gloves/year S = $5/order h = 0.25 (25% of cost) C = cost per unit $5.00 for 1 to 99 boxes $4.00 for 100 to 499 boxes $3.00 for 500+ boxes Q C Q (2)(16,000)(5) (0.25)(3) Not Feasible $4.00 (2)(16,000)(5) (0.25)(4) Feasible
46 EOQ w/ Quantity Discounts For Q = 400 TC = 16, For Q = 500 (5) (0.25)(4) + (4)(16,000) = $64,400 TC = 16, (5) (0.25)(3) + (3)(16,000) = $48,347.5 Decision: Buy with Q = 500 for Lowest Possible Cost
47 EPQ You want to review your inventory continually You want to replenish your inventory when the level falls below a minimum amount, and order the same Q each time Your replenishment does NOT occur all at once Typical of a WIP item, typical of manufacturing
48 Illustration - - Papa Joe s Pizza Joe orders in batches of Q = 4000 cartons at a time He uses a low bid vendor (cheap) It takes about 1 month to get the order in Due to limited staffing, only 1000 cartons can be made and sent to Joe each week How is the inventory build up different than the Base Case (EOQ scenario)?
49 EPQ Inventory Behavior I max Inventory Level Starts at I max Inventory Depletes at Constant Rate Production Stops at I max Process Repeats R 0 Reorder Point Hit (Prepare Production Run) Inventory Runs Out & Production Begins Inventory Produced at Constant Rate Major Difference: Maximum Inventory Level
50 EPQ Equations Total cost: I MAX D TC S H Q 2 Maximum inventory: d =avg. daily demand rate p =daily production rate I MAX Q 1 d p Calculating EPQ: Q 2DS d H 1 p
51 EPQ Example
52 And when should Papa Joe reorder his cartons? R = Demand during the resupply lead time = d x L
53 Other Types of Inventory Systems Variations on the basic types of continuous and periodic reviews: ABC Systems Bin Systems Can Order Systems Base Stock Systems The Newsvendor Problem
54 ABC Systems 1. ABC systems: inventory systems that utilize some measure of importance to classify inventory items and allocate control efforts accordingly 2. They take advantage of what is commonly called the 80/20 rule, which holds that 20 percent of the items usually account for 80 percent of the value. A. Category A contains the most important items. B. Category B contains moderately important items. C. Category C contains the least important items.
55 ABC Systems 1. A items make up only 10 to 20 percent of the total number of items, yet account for 60 to 80 percent of annual dollar value. 2. C items account for 50 to 70 percent of the total number of items, yet account for only 10 to 20 percent of annual dollar value. 3. C items may well be of high importance, but because they account for relatively little annual inventory cost, it may be preferable to order them in large quantities and carry excess safety stock.
56 Bin Systems 1. Bin system: a type of inventory system that uses either one or two bins to hold a quantity of the item being inventoried; an order is placed when one of two bins is empty or a line on a single bin is reached Demand
57 Can Order & Base Stock Systems 1. Can order system: a type of inventory system that reviews the inventory position at fixed time intervals and places orders to bring the inventory up to an expected target level, but only if the inventory position is below a minimum quantity, similar to the reorder point in a continuous review system 2. Base stock system: a type of inventory system that issues an order whenever a withdrawal is made from inventory
58 Newsvendor Problem 1. Order inventory for only a one-time stocking of an item the Single-Period Inventory model 2. Examples: A. Xmas tree lots B. Newspaper stands 3. Objective: maximize profit 4. Why not just stock as many units as possible?
59 Example: Tee shirts are purchased in multiples of 10 for a charity event for $8 each. When sold during the event the selling price is $20. After the event their salvage value is just $2. From past events the organizers know the probability of selling different quantities of tee shirts within a range from 80 to 120: Customer Demand Prob. Of Occurrence How many tee shirts should they buy and have on hand for the event?
60 Payoff Table: Setup Purchase Qty 80 Demand
61 Payoff Table: Cell Calculations Profit = Revenues Costs + Salvage Revenues = Selling Price (p) Amount Sold Costs = Purchase Price (c) Purchase Qty Salvage = Salvage Value (s) Amount Leftover Amount Sold = min (Demand, Purchase Qty) Amount Leftover = max (Purchase Qty Demand, 0)
62 Payoff Table: Cell Calculations Let Q = Purchase Qty and D = Demand Case 1. Q D Profit = [p Q] [c Q] + [s 0] = (p c) Q Case 2. Q > D Profit = [p D] [c Q] + [s (Q D)]
63 Payoff Table: Cell Calculations Have p = $20, c = $8, and s = $2. Compute Profit when Q = 90 and D = 110. Profit = [p Q] [c Q] + [s 0] = (p c) Q = 12(90) = 1080 Compute Profit when Q = 100 and D = 100. Profit = [p Q] [c Q] + [s 0] = (p c) Q = 12(100) = 1200 Compute Profit when Q = 110 and D = 80. Profit = [p D] [c Q] + [s (Q D)] = 20(80) 8(110) + 2(30) = = 780
64 Payoff Table Values Purchase Qty Demand
65 Getting the Final Answer 1. For Each Purchase Quantity: A. Calculated the Expected Profit 2. Choose Purchase Quantity With Highest Expected Profit. 3. Expected Profit for a Purchase Quantity: A. Multiply Each Payoff by Its Probability, Then Sum 4. Example: A. For Purchase Quantity = 100 B. Expected Profit = (840)(0.2) + (1020)(0.25) + (1200)(0.3) + (1200)(0.15) + (1200)(0.1) =$1083
69 Newsvendor and Overbooking 1. Approximately 50% of Reservations Get Cancelled at Some Point in Time. 2. In Many Cases (car rentals, hotels, full fare airline passengers) There is No Penalty for Cancellations. 3. Problem: A. The company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. 4. Solution: A. Sell More Seats (rooms, cars) Than Capacity (Overbook) 5. Danger: A. Some Customers May Have to be Denied a Seat Even Though They Have a Confirmed Reservation. B. Passengers Who Get Bumped Off Overbooked Domestic Flights Receive : a. Up-to $400 if arrive <= 2 hours after their original arrival time b. Up-to $800 if arrive >= 2 hours after their original arrival time
70 Overbooking at Hyatt 1. The Cost of Denying a Room to the Customer with a Confirmed Reservation is $350 in Ill-Will (Loss of Goodwill) and Penalties. 2. Average Revenue From a Filled Room is $ Average Number of No Shows Per Night is How Many Rooms Should be Overbooked (Sold in Excess of Capacity)?
71 Overbooking at Hyatt No Shows Probability No Shows Probability How to Approach Problem? Payoff Table Would Be Huge (21 by 21 = 441 Cells)
72 Overbooking at Hyatt New Trick Use Critical Ratio Optimal Overbooking Ratio: C u = Cost of Underage C o = Cost of Overage C For Hyatt: C u = $159 and C o = $350 Critcal Ratio is then: u C u C Cu 159 C C u o o
73 Overbooking at Hyatt Look at Cumulative Probabilities of No Shows Find First Number of No Shows That Exceeds Critical Ratio For Critical Ratio of First Number of No Shows With Cumulative Probability That Exceeds is 7 Overbooking by 7 Rooms Is Optimal Decision Cumulative No Shows Probability
74 Summary What are the types of inventory What are the basic inventory decisions What are the basic inventory questions to solve What are holding costs Understand the shortage costs EOQ EPQ Other types of inventory control
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