MBA 280 Fall 2017 Inventory Management Time Frame: Class 5 - Class 6 References: Operations Management Reading: Managing Inventory Simulation: Root Beer Game Played in Class 6, Oct 5th, Check Saclink email on Oct 4th for room information Task: 1 homework Agenda for Class 5 Reasons for Holding Inventory Types of Inventory Inventory-related Costs Trade-offs in Inventory Management Key Decisions in Inventory Management Classic Inventory Models Yang Li Lecture 5 1 Why Hold Inventory We do not need to hold inventory if we can continuously monitor demand and instantly adjust our supply Types of Inventory (categorized based on function) Economies of Scale: Cycle Stock Supply and Demand Uncertainties: Safety (Buffer) Stock Planned Imbalances: Anticipation/Speculation Stock Time and Distance: Pipeline/Decoupling Stock Yang Li Lecture 5 2 Types of Inventory Cycle (Lot size) Stock (Held to take advantage of Economies of Scale) Machine setup costs in production Truck/train capacity \"Waves\" of inventory Inventory Time Safety (Buffer) Stock (held to hedge demand/supply uncertainties) Demand may be higher than expectation (unfulfilled demand means lost sales/backorders) Supply may be unreliable (defects, delivery disruption, stock out at supplier) Yang Li Lecture 5 3 Types of Inventory Anticipation/Speculation Stock (held for planned Imbalances) Capacity planning Anticipation of peak demand that exceeds the capacity of the supply process. Utilize slow season's capacity. Ex. Toys for Christmas, candy for Halloween, production smoothing Forward Buy Take advantage of price discount Pipeline/Decoupling Stock (held due to time and distance differences) Supply/Production Lead time Geographic distance between the supply and demand locations Inventory in-transit from the supplier to the downstream stage Whose inventory is this? (Contract, bargaining power) Work-in-Process Stock Inventory held between interdependent operations Yang Li Lecture 5 4 Inventory-related Costs Not holding enough inventory is costly Procuring/Ordering inventory is costly Unmet demand incurs penalty cost Administrative order processing costs Loss of good will Transportation costs Lost sales Expediting Backorder penalty Holding inventory is costly Tangible Costs: Storage costs Spoilage/Breakage/Pilferage Insurance Intangible Costs (Financial holding cost): Opportunity cost Devaluation and Obsolescence Holding cost (rate) pressure for lower inventory Typically expressed as a percentage of the value of product or material per unit time (e.g., 25%-40% per year) Yang Li Shortage (stock-out) cost (rate) pressure for higher inventory Lecture 5 Manufacturing set-up costs Ordering (setup) cost pressure for higher inventory Related to replenishment frequency 5 Key Decisions of Inventory Management Review frequency How often to review the inventory status? Periodic review (daily, monthly, quarterly, yearly) Continuous review When to order? Determine event that triggers a replenishment? How much to order? Order quantity decision Which item to order/hold? Assortment planning Where to stock? Inventory allocation in a supply chain setting. Should the products be stored at the plant, or in a warehouse, or at a retail store? Which supplier to order from? Sourcing strategy. Consideration of lead time, quality, cost... Yang Li Lecture 5 6 Inventory Decision Trade-offs Trade-off of inventory decisions (when and how much): Hold/order too little Hold/order too much Benefits: Benefits: Save holding cost Stock out happens less likely Order less frequently Challenges: Experience stock out more often Challenges: Pay high stock-out cost Order large batches Have to order more frequently Pay high holding cost Pay high setup cost Yang Li Lecture 5 7 Inventory Models and Policy Three Inventory Models Newsvendor Model EOQ (Economic Order Quantity) Model Reorder Point Model Each model specifies the demand pattern, the assumptions on costs, the features of the products... Inventory Policy An inventory policy determines how to replenish inventory: When to order How much to order Objective - Determine the optimal inventory policy for each model Find the inventory policy that achieves the balance of trade-offs and minimize the total inventory-related cost. Yang Li Lecture 5 8 Newsvendor Problem Key features: Single period problem Stock quantity decision is made before the sales begins Assume: No additional order placed in the middle of the period Demand is uncertain while the stock quantity decision is made Demand in each period is assumed to follow a Normal Distribution. Uncertain demand would result in mismatch of supply and demand Costs considered in the model Mismatch costs overage cost (cost of overstocking) underage cost (cost of understocking) Any fixed ordering cost is considered as a sunk cost Any leftovers are salvaged with a relatively small value (The leftovers maybe discarded, in which case the salvage value is zero) Yang Li Lecture 5 9 Newsvendor Model Inputs: c - wholesale price (unit purchasing/ordering cost of the product) p - selling price of the product p - c - unit profit gained from selling one product c < p, otherwise no profit can be gained s - salvage value The salvage value is usually smaller than the wholesale price, i.e., s < c. For example, if the wholesale price c is $10, the salvage value s is usually less than $10. Therefore, the salvaged products only compensate the loss of the company, but not generate any profit. D - demand for each period, it is a random variable which follows Normal Distribution - mean demand (average demand) - standard deviation of the demand (measure the variability of the demand) Decision: Q* - optimal stocking level Yang Li Lecture 5 10 Key Trade-off of Newsvendor Problem Hold/order too little Hold/order too much Lost-sale happens Leftover happens For each unit of lost sale, the business loses the chance to gain profit for this unit For each unit of leftover, the business loses the money paid for purchasing it, but compensates from salvaging it. The cost of one unit of lost sale = lost gross margin per unit of shortage The cost of one unit of leftover = cost to buy salvage value per excess unit Define = p - c -- underage cost Define = c - s - overage cost In a Newsvendor problem, an optimal stocking level Q* is determined to balance the underage cost and the overage cost Q* minimizes the penalty of mismatching demand and supply caused by demand uncertainties. Yang Li Lecture 5 11 Newsvendor Optimal Decisions Ex. 50 100 250 200 300 1) Demand is most likely to be around 200 If 200 units are stocked, only 50% of the demand will be satisfied. 2) There is a VERY SMALL chance demand is 300 If 300 units are stocked, almost all demand will be satisfied. Yet, there will be almost for sure large amount of leftovers. 3) There is a VERY SMALL chance demand is only 50 If 50 units are stocked, only 50 units of demand will be satisfied. There will be almost for sure large amount of lost-sales. Determine a reasonable fill rate/service level (the percentage of orders to be fulfilled) that balances the overage and underage costs. Yang Li Lecture 5 12 Critical Fractile Given all the cost factors, the business should target a reasonable fill rate given the mismatch costs: + Critical Fractile = Critical fractile represents the expected in-stock rate measures the excepted percentage of consumers whose purchases can be fulfilled. 1- + measures the expected percentage of consumers who would experience lost sales. Ex. If = $90, = $10, then critical fractile= 90/(90+10) = 90% - It is costly for lost sales. Therefore, a high fill rate needs to be targeted. - It is not free to have leftovers. Therefore, a 100% fill rate would be too high. - A fill rate of 90% balances the underage cost and overage cost. - 90% of the consumer orders are expected to be fulfilled. -10% of the consumers are expected to experience lost-sales. Note: The critical fractile is also called \"target fill rate\MBA 280 Fall 2017 Agenda for Class Inventory Management Practice Problem Inventory Management in a Supply Chain Root Beer Game Yang Li Lecture 6 1 Practice Problems Problem 1. Sarah's Wedding Sarah is planning her wedding. She and her fianc have signed a contract with a caterer that calls for them to tell the caterer the number of guests that will attend the reception a week before the actual event. This \"final number\" will determine how much they have to pay the caterer; they must pay $60 per guest that they commit to. If for example, they tell the caterer that they expect 90 guests, they much pay $5400 (=90*$60) even if only, say, 84 guests show up. The contract calls for a higher rate of $75 per extra guest for the number of guests beyond what the couple commits to. Thus, if Sarah and her finance commit to 90 guests but 92 show up, they must pay $5550 (=$5400+2*$75). The number of wedding guests follows a normal distribution with a mean that equals to 75% of the number of invitation sent out and a standard deviation that equals to 20% of the number of invitations. Sarah and her fianc sent out 200 invitations in total. The number of guests Sarah should commit to with the caterer is 116 guests. This is a Newsvendor problem. Overage cost = a guest the couple committed to the cater, yet does not show up = the couple wastes the catering cost on this guest = $60 Underage cost = a guest the couple did not commit to the cater, yet shows up = the couple has to pay extra for this guest = $75- $60 = $15 Critical Fractile = /( + ) = 15/(15+60) = 0.2 z = norminv(0.2, 0, 1) = -0.84 Yang Li Q* = + z = 75%*200 + (- 0.84)*(20%*200) = 116.35 116 Lecture 6 2 Practice Problems Problem 2. Money in your pocket Suppose that on average, you spend $40 of cash per month at a constant rate. You estimate the inconvenience of going to the ATM at $2 per trip. By taking money from your bank account you forgo annual interest rate 4%. This is an EOQ problem: K = $2, h = $0.04/dollar/year, D = $40/month = $480/year (a) To save the overall inconvenience cost associated with the trip and the loss of interest, how much money should you get from the ATM each time? EOQ = 2 = 22480 0.04 = $219 $220 (if only $20 cash is available at the ATM ) (a) On average, how much interest you lose each year? On average, you hold $220/2 = $110 cash on hand. With an annual interest rate of 4%, you lose $110*0.04 = $4.4 on interest every year. (b) On average, how much you spend on the trips to bank each year? Given EOQ = $220, and annual demand D = $480, on average each year you need to go to the ATM $480/$220 = 2.18 times. Each trip costs $2. Then you spend $2*2.18 = $4.36 on the trips to bank each year. Yang Li Lecture 6 3 Practice Problems Problem 3. Frozen tuna steaks A supermarket orders frozen tuna steaks for its inventory on a continuous review basis: During winter, the steaks are delivered approximately once a week, in a precalculated optimal quantity (EOQ) of 5,200. In the summer, the cost of storing steaks in the inventory goes up by 25% due to increased energy consumption for refrigeration. What is the optimal economic order quantity for replenishing the inventory of tuna steaks in the summer if the ordering cost and demand for tuna steaks remain the same? Round your answer to the nearest integer. The cost of storing steaks in the inventory goes up by 25% implies the unit holding cost increases by 25%. EOQ = 2 When h increases, EOQ would decrease in the square-root fashion. So the new EOQ = 5200/ 1.25 = 4651. Yang Li Lecture 6 4 Practice Problems Problem 4. A quantity discount A beer distributor finds that it sells on average 100 cases a week of regular 12 oz. Budweiser. For this problem, assume that demand occurs at a constant rate over a 52-week year. The distributor currently purchases beer every two weeks at a cost of $8 per case. The inventory related holding cost (capital, insurance, etc.) for the distributor equals 25% of the dollar value of inventory per year. Each order placed with the supplier costs the distributor $10. This cost includes labor, forms, postages, etc. (So far, this is an EOQ problem.) Assume the brewer is willing to give a 5% quantity discount if the distributor orders 600 cases or more at a time, i.e., if the order quantity is larger than 600 cases, the purchasing cost would be reduced to $8*95% = $7.6 per case. If the distributor is interested in minimizing its total cost (i.e., purchase and inventory related costs), should the distributor begin ordering 600 or more cases at a time? Inputs: Demand rate D = 100 cases/week = 5200 cases/year Unit holding cost h = 0.25*$8 = $2 per case per year The EOQ = 2 = 2105200 2 = 228 cases Fixed ordering cost K = $10 = 2 = 2 10 5200 2 = $456 per year The total annual cost associated with EOQ = purchasing cost + C* = $8*5200 +$456 = $42,056. Since the EOQ is well below 600 cases. If we must deviate from the optimal level, we should do so by as little as possible. Hence we consider ordering exactly 600 cases. If 600 cases are ordered, holding costs are now 0.25*0.95*$8 = $1.90 per case per year. Total annual inventory costs would be 5200 600 + = 10 + 1.9 = $656.7 2 600 2 Then the total annual cost associated with order quantity Q = 600 cases = 0.95*$8*5200 + 656.7 = $40,176.7. The per-case savings more than compensate for the increased inventory costs. Yang Li Lecture 6 5 Typical Supply Chain (3-Tier) Sequential system Manufacturer (Supplier) Wholesaler (Distributor) Retailer Consumers There is one manufacturer, one wholesaler and one retailer in the system Manufacturer supplies goods to wholesaler (distributor) Wholesaler(distributor) supplies goods to retailer Retailer supplies good to consumers The demands of retailer are purchases from consumers The demands of wholesaler are orders from retailer The demands of manufacturer are orders from wholesaler(distributor) Yang Li Lecture 6 6 A Typical Supply Chain (3-Tier) Distribution system Manufacturer (Supplier) 1 ... Consumers Wholesaler 1 Retailer Consumers Wholesaler 2 Retailer Consumers Retailer Consumers Retailer Consumers ... Manufacturer (Supplier) 2 Retailer Wholesaler n Manufacturer (Supplier) m Each manufacturer supplies (different) goods to several wholesalers Each wholesaler supplies goods to several retailers Each retailer supplies good to his consumers The demands of each retailer are purchases from consumers The demands of each wholesaler are aggregated orders from all his retailers The demands of each manufacturer are aggregated orders from al the wholesaler Yang Li Lecture 6 7 Decentralization vs. Centralization Supply Chain Centralized Supply Chain - Information shared across all parties in the system - Decisions are made jointly across all stages in the supply chain - Objective: Maximum the supply chain's total benefit Extreme case: One single decision maker makes decisions for all parties in a chain, and aims to maximizes the overall supply chain benefit. Decentralized Supply Chain - Each stage owns private information and not necessarily share it with other parties in the supply chain - Each stages makes decisions independently - Stages collaborate through contracts - Objective: Each stage maximizes its own benefit (Root) Beer Game Yang Li Lecture 6 8 Issue in a Decentralized Supply Chain Bullwhip Effect: A trend of larger and larger swings in inventory from downstream to upstream in response to changes in demand. A small fluctuation of consumer demand (down stream of the supply chain) A larger fluctuation at upstream of the supply chain Bullwhip effect implies a higher level of supply disruption The large swings in inventory at upstream lead to large inventory-related cost (either large holding cost or large stock-out cost) This high level inventory-related cost may eventually be passed onto consumers through high selling price. Yang Li Lecture 6 9 Causes of Bullwhip Effect Major cause: Over-reactive ordering from misinterpreted demand information Lack of communication Demand information distorted from downstream to upstream Solution: 1. Shorten the length of the supply chain 2. Demand/sales information transparency, join inventory decision making Effective industry practice: Vendor Managed Inventory (VMI) Other common causes: lead time, batch size, price fluctuation,... Any factor that induces the supply variation to be larger than the demand variation Bullwhip Effect Reference: Core curriculum Reading: \"OPERATIONS MANAGEMENT READING: SUPPLY CHAIN MANAGEMENT\Minding the Store: Kimberly-Clark Keeps Costco in Diapers, Absorbing Costs Itself --- Under New System, Supplier Stocks Retailer's Shelves And Boosts Bottom Lines --- Averting a Huggies Squeeze By Emily Nelson and Ann Zimmerman. Wall Street Journal. (Eastern edition). New York, N.Y.: Sep 7, 2000. pg. A.1 Copyright Dow Jones & Company Inc Sep 7, 2000 One morning, a Costco store in Los Angeles began running a little low on sizeone and size-two Huggies. Crisis loomed. So what did Costco managers do? Nothing. They didn't have to, thanks to a special arrangement with Kimberly-Clark Corp., the company that makes the diapers. Under this deal, responsibility for replenishing stock falls on the manufacturer, not Costco. In return, the big retailer shares detailed information about individual stores' sales. So, long before babies in Los Angeles would ever notice it, diaper dearth was averted by a Kimberly-Clark data analyst working at a computer hundreds of miles away in Neenah, Wis. "When they were doing their own ordering, they didn't have as good a grasp" of inventory, says the Kimberly-Clark data analyst, Michael Fafnis. Now, a special computer link with Costco allows Mr. Fafnis to make snap decisions about where to ship more Huggies and other Kimberly-Clark products. Just a few years ago, the sharing of such data between a major retailer and a key supplier would have been unthinkable. But the arrangement between Costco Wholesale Corp. and Kimberly-Clark underscores a sweeping change in American retailing. Across the country, powerful retailers from Wal-Mart Stores Inc. to Target Corp. to J.C. Penney Co. are pressuring their suppliers to take a more active role in shepherding products from the factory to store shelves. In some cases, that means requiring suppliers to shoulder the costs of warehousing excess merchandise. In others, it means pushing suppliers to change product or package sizes. In the case of Costco and Kimberly-Clark, whose coordinated plan is officially called "vendor-managed inventory," KimberlyClark oversees and pays for everything involved with managing Costco's inventory except the actual shelf-stockers in store aisles. Whatever the arrangement and the terminology, the major focus for these big retailers is the same: Cutting costs along the so-called supply chain, which comprises every step from lumber mill to store shelf. The assumption is that suppliers themselves are in the best position to spot inefficiencies and fix them. For consumers, it all translates to lower prices at the cash register. Indeed, big companies' increasing focus on the supply chain is one reason U.S. prices for general merchandise -- goods from laundry detergent to wool sweaters -- fell 1.5% in 1998 and again last year and are falling at the same rate this year, according to Richard Berner, chief U.S. economist at Morgan Stanley Dean Witter. "Supply-chain management has had a major impact," says Mr. Berner, who compiled his analysis from government data. There is also a potential downside for consumers: Fewer choices in brands and types of packages. For example, two years ago, Kimberly-Clark stopped making separate diapers for boys and girls and reverted to unisex-only. Less variety makes for easier inventory-tracking in its factories and trucks, the Dallas-based company says. To a great extent, better cooperation between retailers and suppliers has been made possible by improved technology -- such as the computer link KimberlyClark uses. It's also a consequence of the greater strength of major retailers as they consolidate and expand globally. Many economists say that closer retailersupplier coordination on the supply chain is the model of the future and will ultimately determine which companies succeed in the new millennium. "A shopper buys a roll of Bounty paper towel, and that would trigger someone cutting a tree in Georgia," says Steve David, who heads supply-chain work for Procter & Gamble Co., the Cincinnati consumer-products giant. "That's the holy grail." These days, P&G stations about 250 people in Fayetteville, Ark., minutes from Wal-Mart's headquarters in Bentonville, solely to promote its products to the discount chain and ensure they move as quickly as possible to store shelves. The two giants share some inventory data. The price of inefficiencies on the supply chain is high. Revlon Inc. this year slowed its product shipments because store shelves were backed up with older inventory. Kmart Corp.'s new chief executive, Charles Conaway, has publicly blamed the retailer's sagging profits in part on a weak supply-chain infrastructure. Last month, he said he expects to spend $1.4 billion over the next two years to update Kmart's technology, including systems for coordinating with suppliers. And earlier this year, Estee Lauder Cos. hired away Compaq Computer Corp.'s executive in charge of supply chain to bolster that operation at the cosmetics concern. By several accounts, the close collaboration between Costco and Kimberly-Clark serves as a model for other merchandisers, and also helps explain strong recent sales gains by the two companies. In the past two years, Kimberly-Clark gradually expanded the program and now manages inventory for 44 retailers of its products. The consumer-products company says it wrung $200 million in costs from its supply chain during that period, and it vows to squeeze out another $75 million this year. "This is what the information age has brought to this industry," says Wayne Sanders, chairman and chief executive officer of Kimberly-Clark. "It gives us a competitive advantage." In fact, Kimberly-Clark says the cost savings it achieves on its supply chain are one reason its Huggies -- and not rival P&G's Pampers -are sold at Costco stores in most areas of the country. "If a company finds a way to lower its costs, it gets those deals," says Richard Dicerchio, Costco's chief operating officer. A spokeswoman for P&G says its supply chain is very efficient, and Costco carries many of its other products. To oversee ordering for the retailers whose inventory it manages, Kimberly-Clark employs a staff of 24 people, including Mr. Fafnis. A Kimberly-Clark spokeswoman says the benefits of the program "more than offset" additional labor costs. Last year, Kimberly-Clark posted a 51% rise in net income to $1.67 billion on $13 billion in sales, capping three years of improving results. For Costco, the benefits of such close cooperation with a major supplier are equally clear: Costco saves money not only on staffing in its inventory department, but also on storage. Before Kimberly-Clark began managing Costco's inventory, in late 1997, the retailer would keep an average of a month's supply of Kimberly-Clark products in its warehouses. Now, because KimberlyClark has proven it can replenish supplies more efficiently, Costco needs to keep only a two-week supply. What's more, Costco says its shelves are less likely to go empty under the new system. That's important for both retailer and supplier, because consumer studies indicate that a majority of customers will walk out of a store emptyhanded if they can't find a particular item they need. P&G, for example, estimates that an average retailer's loss from out-of-stocks runs about 11% of annual sales. For Costco, which keeps its costs down by typically offering just one brand-name product and its own private-label Kirkland Signature product in each category, maintaining supplies on shelves is crucial. "If we're out of stock, it means we're out of a category, so the chance of a loss of a sale is greater," Mr. Dicerchio says. Susanne Shallon of Redondo Beach, Calif., says she always buys size-four Huggies for her 22-month-old daughter, Beth, and Pull-Ups for her five-year old son, Emil, at a nearby Costco because the store is well-stocked. "It's good to have the confidence that when I go into the store, the product will be on hand," she says. For now, Kimberly-Clark manages inventory in Costco stores everywhere but the Northeast. Kimberly-Clark recently sent analysts to Costco headquarters in Issaquah, Wash., to push for a possible next stage: expanding to the Northeast and collaborating on forecasts, not just recorded sales