Presentation on theme: "Operations Management Dr. Ron Tibben-Lembke"— Presentation transcript:
1 Operations Management Dr. Ron Tibben-Lembke Inventory ManagementOperations ManagementDr. Ron Tibben-Lembke
2 Purposes of Inventory Meet anticipated demand Demand variabilitySupply variabilityDecouple production & distributionpermits constant production quantitiesTake advantage of quantity discountsHedge against price increasesProtect against shortages
6 Two Questions Two main Inventory Questions: How much to buy? When is it time to buy?Also:Which products to buy?From whom?
7 Types of Inventory Raw Materials Subcomponents Work in progress (WIP) Finished productsDefectivesReturns
8 Inventory CostsWhat costs do we experience because we carry inventory?
9 Inventory Costs Costs associated with inventory: Cost of the products Cost of orderingCost of hanging onto itCost of having too much / disposalCost of not having enough (shortage)
10 Shrinkage Costs How much is stolen? Where does the missing stuff go? 2% for discount, dept. stores, hardware, convenience, sporting goods3% for toys & hobbies1.5% for all elseWhere does the missing stuff go?Employees: 44.5%Shoplifters: 32.7%Administrative / paperwork error: 17.5%Vendor fraud: 5.1%
11 Inventory Holding Costs Category % of Value Housing (building) cost 4% Material handling 3% Labor cost 3% Opportunity/investment 9% Pilferage/scrap/obsolescence 2% Total Holding Cost 21%
12 Inventory Models Fixed order quantity models Fixed order period models How much always same, when changesEconomic order quantityProduction order quantityQuantity discountFixed order period modelsHow much changes, when always same
13 Economic Order Quantity AssumptionsDemand rate is known and constantNo order lead timeShortages are not allowedCosts:S - setup cost per orderH - holding cost per unit time
14 EOQ Inventory Level Q* Decrease Due to Optimal Constant Demand Order QuantityDecrease Due toConstant DemandTime
15 EOQ Inventory Level Instantaneous Q* Receipt of Optimal Optimal OrderQuantityInstantaneousReceipt of OptimalOrder QuantityTime
26 Optimal QuantityTotal Costs =Take derivative with respect to Q =
27 Optimal Quantity Total Costs = Take derivative with respect to Q = Set equalto zero
28 Optimal Quantity Total Costs = Take derivative with respect to Q = Set equalto zeroSolve for Q:
29 Optimal Quantity Total Costs = Take derivative with respect to Q = Set equalto zeroSolve for Q:
30 Optimal Quantity Total Costs = Take derivative with respect to Q = Set equalto zeroSolve for Q:
31 Adding Lead Time Use same order size Order before inventory depleted R = * L where:= average demand rate (per day)L = lead time (in days)both in same time period (wks, months, etc.)dd
32 A Question:If the EOQ is based on so many horrible assumptions that are never really true, why is it the most commonly used ordering policy?Profit function is very shallowEven if conditions don’t hold perfectly, profits are close to optimalEstimated parameters will not throw you off very far
33 Quantity DiscountsHow does this all change if price changes depending on order size?Holding cost as function of cost:H = I * CExplicitly consider price:
34 Discount ExampleD = 10,000 S = $20 I = 20% Price Quantity EOQ c = 5.00 Q < Q >=
35 Discount Pricing X 633 X 666 X 716 Total Cost Price 1 Price 2 Price 3 ,000Order Size
36 Discount Pricing X 633 X 666 X 716 Total Cost Price 1 Price 2 Price 3 ,000Order Size
37 Discount ExampleOrder 666 at a time: Hold 666/2 * 4.50 * 0.2= $ Order 10,000/666 * 20 = $ Mat’l 10,000*4.50 = $45, , Order 1,000 at a time: Hold 1,000/2 * 3.90 * 0.2= $ Order 10,000/1,000 * 20 = $ Mat’l 10,000*3.90 = $39, ,590.00
38 Discount Model 1. Compute EOQ for next cheapest price 2. Is EOQ feasible? (is EOQ in range?)If EOQ is too small, use lowest possible Q to get price.3. Compute total cost for this quantityRepeat until EOQ is feasible or too big.Select quantity/price with lowest total cost.
40 Random Demand Don’t know how many we will sell Sales will differ by periodAverage always remains the sameStandard deviation remains constant
41 Impact of Random Demand How would our policies change?How would our order quantity change?How would our reorder point change?
42 Mac’s Decision How many papers to buy? Average = 90, st dev = 10 Cost = 0.20, Sales Price = 0.50Salvage = 0.00Cost of overestimating Demand, COCO = = 0.20Cost of Underestimating Demand, CUCU = = 0.30
43 Optimal PolicyG(x) = Probability demand <= x Optimal quantity: Mac: G(x) = 0.3 / ( ) = 0.6 From standard normal table, z = =Normsinv(0.6) = Q* = avg + zs = *10 = = 93
44 Optimal Policy If units are discrete, when in doubt, round up If u units are on hand, order Q - u unitsModel is called “newsboy problem,” newspaper purchasing decisionBy time realize sales are good, no time to order moreBy time realize sales are bad, too late, you’re stuckSimilar to the problem of # of Earth Day shirts to make, lbs. of Valentine’s candy to buy, green beer, Christmas trees, toys for Christmas, etc., etc.
45 Random Demand – Fixed Order Quantity If we want to satisfy all of the demand 95% of the time, how many standard deviations above the mean should the inventory level be?
46 Probabilistic Models Safety stock = x m From statistics, Safety stock Therefore, z =Safety stock& Safety stock = zsLsLFrom normal table z.95 = 1.65Safety stock = zsL= 1.65*10 = 16.5R = m + Safety Stock= = ≈ 367
47 Random Example What should our reorder point be? demand over the lead time is 50 units,with standard deviation of 20want to satisfy all demand 90% of the time(i.e., 90% chance we do not run out)To satisfy 90% of the demand, z = 1.28Safety stock = zσL= 1.28 * 20 = 25.6R = = 75.6
48 St Dev Over Lead TimeWhat if we only know the average daily demand, and the standard deviation of daily demand?Lead time = 4 days,daily demand = 10,standard deviation = 5,What should our reorder point be, if z = 3?
49 St Dev Over LTIf the average each day is 10, and the lead time is 4 days, then the average demand over the lead time must be 40.What is the standard deviation of demand over the lead time?Std. Dev. ≠ 5 * 4
50 St Dev Over Lead Time Standard deviation of demand =
51 Service Level Criteria Type I: specify probability that you do not run out during the lead timeProbability that 100% of customers go home happyType II: proportion of demands met from stockPercentage that go home happy, on averageFill Rate: easier to observe, is commonly usedG(z)= expected value of shortage, given z. Not frequently listed in tables
52 Two Types of ServiceCycle Demand Stock-Outs Sum 1,450 55Type I:8 of 10 periods80% serviceType II:1,395 / 1,450 =96%
54 Fixed-Time Period Model Every T periods, we look at inventory on hand and place an orderLead time still is L.Order quantity will be different, depending on demand
55 Fixed-Time Period Model: When to Order? Inventory LevelTarget maximumTimePeriod
56 Fixed-Time Period Model: : When to Order? Inventory LevelTarget maximumTimePeriodPeriod
57 Fixed-Time Period Model: When to Order? Inventory LevelTarget maximumTimePeriodPeriod
58 Fixed-Time Period Model: When to Order? Inventory LevelTarget maximumPeriodTime
59 Fixed-Time Period Model: When to Order? Inventory LevelTarget maximumPeriodTime
60 Fixed-Time Period Model: When to Order? Inventory LevelTarget maximumPeriodTime
61 Fixed Order Period Standard deviation of demand over T+L = T = Review period length (in days)σ = std dev per dayOrder quantity (12.11) =
62 Inventory Recordkeeping Two ways to order inventory:Keep track of how many delivered, soldGo out and count it every so oftenIf keeping records, still need to double-checkAnnual physical inventory, orCycle Counting
63 Cycle CountingPhysically counting a sample of total inventory on a regular basisUsed often with ABC classificationA items counted most often (e.g., daily)AdvantagesEliminates annual shut-down for physical inventory countImproves inventory accuracyAllows causes of errors to be identified
64 Fixed-Period Model Answers how much to order Orders placed at fixed intervalsInventory brought up to target amountAmount ordered variesNo continuous inventory countPossibility of stockout between intervalsUseful when vendors visit routinelyExample: P&G rep. calls every 2 weeks
65 ABC Analysis Divides on-hand inventory into 3 classes A class, B class, C classBasis is usually annual $ volume$ volume = Annual demand x Unit costPolicies based on ABC analysisDevelop class A suppliers moreGive tighter physical control of A itemsForecast A items more carefully
66 Classifying Items as ABC % Annual $ VolumeItems %$Vol %ItemsA 80 15B 15 30C 5 55ABC% of Inventory Items