PowerPoint PresentationSlide 2Slide 3Slide 4Why do we care?How do you manage your inventory? How much do you buy? When?What Do you Consider?Costs of InventorySlide 9Slide 10Home DepotSlide 12Multiperiod modelSlide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20If delivery is not instantaneous, but there is a lead time L: When to order? How much to order?If demand is known exactly, place an order when inventory equals demand during lead time.Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32How to find ROP & QSlide 34Inventory ManagementInventory ManagementWhat is inventory?Inventory is the raw materials, component parts, work-in-process, or finished products that are held at a location in the supply chain.Why do we care? At the macro level:Investment in inventory is currently over $1.25 Trillion (U.S. Department of Commerce). This figure accounts for almost 25% of GNP.Enormous potential for efficiency increase by controlling inventoriesInventory is one of the biggest corporate assets ($).–Sales growth: right inventory at the right place at the right time –Cost reduction: less money tied up in inventory, inventory management, obsolescenceHigher profitWhy do we care?At the firm level:Why do we care?Each of Solectron’s big customers, which include Cisco, Ericsson, and Lucent was expecting explosive growth for wireless phones and networking gear….when the bottom finally fell out, it was too late for Solectron to halt orders from all of its 4,000 suppliers. Now, Solectron has $4.7 billion in inventory. (BW, March 19, 2001)“When Palm formally reported its quarterly numbers in June, the damage was gruesome. Its loss totaled $392 million, a big chunk of which was attributable to writing down excess inventory - piles of unsold devices.” (The Industry Standard, June 16, 2001)“Liz Claiborne said its unexpected earnings decline is the consequence of higher than anticipated excess inventories”. (WSJ, August 1993)How do you manage your inventory?How much do you buy? When?•Soda•Milk •Toilet paper•Gas•Cereal•CashWhat Do you Consider?•Cost of not having it. •Cost of going to the grocery or gas station (time, money), cost of drawing money.•Cost of holding and storing, lost interest.•Price discounts.•How much you consume.•Some safety against uncertainty.Costs of Inventory•Physical holding costs:–out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling)–All costs that may be entailed before you sell it (obsolescence, spoilage, rework...)•Opportunity cost of inventory: foregone return on the funds invested.•Operational costs:–Delay in detection of quality problems.–Delay the introduction of new products.–Increase throughput times.•Hedge against uncertain demand•Hedge against uncertain supply•Economize on ordering costs•SmoothingBenefits of InventoryTo summarize, we build and keep inventory in order to match supply and demand in the most cost effective way.Modeling Inventory in a Supply Chain…WarehouseRetailSupplierHome Depot•“Our inventory consists of up to 35,000 different kinds of building materials, home improvement supplies, and lawn and garden products.”•“We currently offer thousands of products in our online store.”•“We offer approximately 250,000 more products through our special order services.”Different types of inventory models1. Multi-period model•Repeat business, multiple orders2. Single period models•Single selling season, single orderMultiperiod model•Key questions:–How often to review?–When to place an order?–How much to order?–How much stock to keep?ordersSupplyOn-handinventory•Ordering costs•Holding costsMultiperiod model – The Economic Order Quantity•Demand is known and deterministic: D units/year•We have a known ordering cost, S, and immediate replenishment•Annual holding cost of average inventory is H per unit•Purchasing cost C per unitSupplierDemandRetailerWhat is the optimal quantity to order? Total Cost = Purchasing Cost + Ordering Cost + Inventory CostPurchasing Cost = (total units) x (cost per unit) Ordering Cost = (number of orders) x (cost per order) Inventory Cost = (average inventory) x (holding cost)Finding the optimal quantity to order…Let’s say we decide to order in batches of Q…Number of periods will be DQTimeTotal TimePeriod over which demand for Q has occurredQInventory positionThe average inventory for each period is…Q2Finding the optimal quantity to order…Purchasing cost = D x CInventory cost = Ordering cost = DQx SQ2x HSo what is the total cost?TC = D C + +In order now to find the optimal quantity we need to optimize the total cost with respect to the decision variable (the variable we control)Which one is the decision variable?DQSQ2 HWhat is the main insight from EOQ?There is a tradeoff between holding costs and ordering costsOrder Quantity (Q*)CostTotal costHolding costsOrdering costsEconomic Order Quantity - EOQQ* = 2SD H Example: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. How many times should the dealer order, and what should be the order size?548500)000,5)(000,15(2*QReceive Receive orderorderTimeTimeInventory Inventory OrderOrderQuantityQuantityQQPlacePlaceorderorderLead TimeLead TimeIf delivery is not instantaneous, but there is a lead time L:When to order? How much to order?ROP = LxDReceive Receive orderorderTimeTimeInventory Inventory OrderOrderQuantityQuantityQQPlacePlaceorderorderLead TimeLead TimeReorderReorderPointPoint(ROP)(ROP)If demand is known exactly, place an order when inventory equals demand during lead time.D: demand per periodL: Lead time in periodsQ: When shall we order? A: When inventory = ROPQ: How much shall we order? A: Q = EOQExample (continued)…What if the lead time to receive cars is 10 days? (when should you place your order?)10365D = R =103655000= 137So, when the number of cars on the lot reaches 137, order 548 more cars.Since D is given in years, first convert: 10 days = 10/365yrsReceive Receive orderorderPlacePlaceorderorderLead TimeLead TimeROP = ???StockoutPointUnfilled demandReceive Receive orderorderTimeInventory OrderOrderQuantityQuantityPlacePlaceorderorderLead TimeLead TimeIf Actual Demand > Expected, we Stock OutTo reduce stockouts we add safety