3Inventory Stock or quantity of items kept to meet demand Takes on different formsFinal goodsRaw materialsPurchased/component partsLaborIn-process materialsWorking capital
4Inventory Static – only one opportunity to buy and sell units Dynamic – ongoing need for units; reordering must take place
5Demand Dependent Demand Independent Demand Items are used internally to produce a final productIndependent DemandItems are final products demanded by external customers
6Reasons To Hold Inventory To meet anticipated demandTo smooth production requirementsTo decouple components of the production-distribution systemTo protect against stock-outsTo take advantage of order cyclesTo hedge against price increases or to take advantage of quantity discountsTo permit operations
7Inventory Costs Carrying Costs Ordering Costs Costs of holding an item in inventoryOrdering CostsCosts of replenishing inventoryShortage (stockout) CostsTemporary or permanent loss of sales when demand cannot be met
8Inventory Management How much and when to order inventory? Objective: To keep enough inventory to meet customer demand and also be cost-effectivePurpose: To determine the amount of inventory to keep in stock - how much to order and when to order
9Inventory Management Requirements A system to keep track of the inventory on hand and on orderA reliable forecast of demandKnowledge of lead timesReasonable estimates of inventory costsA classification system for inventory items (ABC)
10Inventory Control Systems Control the level of inventory by determining how much to order and whenContinuous (Perpetual) Inventory System - a continual record of the inventory level for every item is maintainedPeriodic Inventory System - inventory on hand is counted at specific time intervals
11Other Control Systems/Tools Two-Bin System - two containers of inventory; reorder when the first is emptyUniversal Product Code (UPC) - Bar code printed on a label that has information about the item to which it is attachedRFID Tags
12Considerations Lead Time Cycle Counting Usage Rate Time interval between ordering and receiving the orderCycle CountingPhysical count of items in inventoryUsage RateRate at which amount of inventory is depleted
13Profile of Inventory Level Over Time Inventory CycleProfile of Inventory Level Over TimeQUsagerateQuantityon handReorderpointTimeReceiveorderPlaceorderReceiveorderPlaceorderReceiveorderLead time
14Economic Order Quantity The EOQ Model determines the optimal order size that minimizes total inventory costs
15Inventory CostsCarrying Costs – cost associated with keeping an item in stockIncludes: storage, warehousing, insurance, security, taxes, opportunity cost, depreciation, etc.Ordering Costs – cost associated with ordering and receiving inventoryDetermining quantities needed, preparing documentation, shipping, inspection of goods, etc.
16Optimal Order Quantity 2DSH2 (Annual Demand) (Order Cost)Q==oAnnual Holding Cost per unitQoDLength of order cycle =DQo# Orders / Year =
17Basic EOQ Model Annual carrying cost ordering Total cost = + Qo 2 H D TC =Where: Qo = Economic order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost
18Cost Minimization Goal The Total-Cost Curve is U-ShapedAnnual CostCarrying CostsOrdering CostsQO(optimal order quantity)Order Quantity (Q)
19EOQ Example 1 A) What is the EOQ? A local office supply store expects to sell 2400 printers next year. Annual carrying cost is $50 per printer, and ordering cost is $30. The company operates 300 days a year.A) What is the EOQ?B) How many times per year does the store reorder?C) What is the length of an order cycle?D) What is the total annual cost if the EOQ quantity is ordered?
20Given:. Demand = D = 2400. Holding Cost = H = $50 per unit per year Given: Demand = D = Holding Cost = H = $50 per unit per year Ordering Cost = S = $30What is the EOQ?B. How many times per year does the store reorder?C. What is the length of an order cycle?
21Given:. Demand = D = 2400. Holding Cost = H = $50 per unit per year Given: Demand = D = Holding Cost = H = $50 per unit per year Ordering Cost = S = $30D. What is the total annual cost if the EOQ quantity is ordered?TC = Carrying cost + Ordering cost
22EOQ Example 2 A) What is the EOQ? A local electronics store expects to sell 500 flat-screen TVs each month during next year. Annual carrying cost is $60 per TV, and ordering cost is $50. The company operates 364 days a year.A) What is the EOQ?B) How many times per year does the store reorder?C) What is the length of an order cycle?D) What is the total annual cost if the EOQ quantity is ordered?
23Given:. Demand = D = 6,000. Holding Cost = H = $60 per unit per year Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50What is the EOQ?B. How many times per year does the store reorder?C. What is the length of an order cycle?
24Given:. Demand = D = 6,000. Holding Cost = H = $60 per unit per year Given: Demand = D = 6,000 Holding Cost = H = $60 per unit per year Ordering Cost = S = $50D. What is the total annual cost if the EOQ quantity is ordered?TC = Carrying cost + Ordering cost
26Carrying cost + Ordering cost + Purchasing cost = Quantity DiscountsA price discount on an item if predetermined numbers of units are orderedTC =Carrying cost + Ordering cost + Purchasing cost =(Q / 2) H + (D / Q) S + PDwhere P = Unit Price
27Quantity Discount Example Campus Computers 2Go Inc. wants to reduce a large stock of laptops it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule as shown below. Given the discount schedule and its known costs, the bookstore wants to determine if it should take advantage of this discount or order the basic EOQ order size.QuantityPrice1 – 49$1,50050 – 89$1,00090 +$800Carrying Cost:$200Ordering Cost$1,000Annual Demand400 units
28First, determine the optimal size and cost with the basic EOQ model. QO =This order size is eligible for the discount price of $1,000… now we compute the total costTC =Compare this cost to an ordering size of $800:TC = (Q / 2) H + (D / Q) S + PD =
29What if a new discount was offered where they would receive a price of $790 if they were to order 150 or more?
30HW #13A mail-order house uses 18,000 boxes a year. Carrying costs are $.60 per box per year and ordering costs are $96. The following price schedule is offered. Determine the EOQ and the # of orders per year.# BoxesUnit Price$1.25$1.20$1.1510000+$1.10
31EOQ with Incremental Replenishment (EPQ) Used when company makes its own productConsiders a variety of costs/terms:Carrying CostSetup Cost (analogous to ordering costs)Maximum and Average Inventory LevelsEconomic Run QuantityCycle TimeRun Time
32EOQ with Incremental Replenishment (EPQ) DefinitionsS = Setup CostH = Holding CostImax = Maximum InventoryIavg = Average InventoryD = Demand/Yearp = Production or Delivery Rateu = Usage Rate
33EOQ with Incremental Replenishment Total Cost = Carrying Cost + Setup Cost(Imax/2) H + (D/Qo) SEconomic run quantityQo = 2DS/H * p/(p-u)Cycle time (time between runs)Qo /uRun time (production phase)Qo /pMaximum Inventory LevelImax = (Qo /p)(p-u)Average Inventory LevelIaverage = Imax /2
34Assumptions Only one item is involved Annual demand is known Usage rate is constantUsage occurs continually, production periodicallyProduction rate is constantLead time doesn’t varyNo quantity discounts
35EOQ Replenishment Example A toy manufacturer uses 48,000 rubber wheels per year for its product. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the:Optimal run sizeMinimum total annual cost for carrying and setupCycle time for the optimal run sizeRun time
36S = $45 H = $1 per wheel per year p = 800 wheels per day D = 48,000 wheels per yearS = $ H = $1 per wheel per yearp = 800 wheels per dayu = 48,000 wheels per 240 days, or 200 wheels per dayQo = 2DS/H * p/(p-u) =Imax = (Qo /p)(p-u) =TCmin = (Imax/2) H + (D/Qo) S =Cycle time = Qo /u =Run time = Qo /p =