Inventory Management_Jan 2011_Give

Inventory Management_Jan 2011_Give - Inventory Management...

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Unformatted text preview: Inventory Management Inventory Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models Quantity Discounts Reorder Point Order Quantity for a Periodic Inventory System What Is Inventory? Stock of items kept to meet future demand Purpose of inventory management how many units to order when to order The Material Flow Cycle The The Material Flow Cycle Input Other Wait Time Move Time Queue Time Setup Time Run Time Output Cycle Time 1 Run time: Job is at machine and being worked on Job 2 Setup time: Job is at the work station, and the work station is being "setup." 3 Queue time: Job is where it should be, but is not being processed because other work precedes it. 4 Move time: The time a job spends in transit 5 Wait time: When one process is finished, but the job is waiting to be moved to the next work area. 6 Other: "Just-in-case" inventory. "Just- in- Disadvantages of Inventory Higher costs Higher Item cost (if purchased) Item Ordering (or setup) cost Ordering Costs of forms, clerks’ wages etc. Costs clerks’ Holding (or carrying) cost Holding Building lease, insurance, taxes etc. Building Difficult to control Difficult Hides production problems Hides Increasing Variability of Orders Up the Supply Chain Lee, H, P. Padmanabhan and S. Wang (1997), Sloan Management Review Lee, Review Inventory and Supply Chain Management Bullwhip effect Bullwhip demand information is distorted as it moves away demand from the end-use customer endhigher safety - stock i.e. inventories are stored to higher compensate Seasonal or cyclical demand Seasonal Inventory provides independence from vendors Inventory Take advantage of price discounts Take Inventory provides independence between Inventory stages and avoids work stoppages Inventory Classifications Two Forms of Demand Two Dependent Dependent Demand for items used to produce Demand final products Tires stored at a Goodyear plant are an example of a dependent demand item Independent Independent Demand for items used by external Demand customers Cars, appliances, computers, and houses are examples of independent demand inventory Inventory Control Systems Continuous system (fixedContinuous (fixedorder-quantity) orderconstant amount ordered constant when inventory declines to predetermined level Periodic system (fixed-timePeriodic (fixed- timeperiod) order placed for variable order amount after fixed passage of time ABC Classification ABC Class A Class 5 – 15 % of units 70 – 80 % of value 70 Class B Class 30 % of units 30 15 % of value 15 Class C Class 50 – 60 % of units 50 5 – 10 % of value Maruti maintains DOL – for monitoring of inventory of class A Maruti and certain class B items ABC Classification: Example PART 1 2 3 4 5 6 7 8 9 10 UNIT COST $ 60 350 30 80 30 20 10 320 510 20 ANNUAL USAGE 90 40 130 60 100 180 170 50 60 120 ABC Classification: ABC Example (cont.) PART TOTAL PART VALUE % OF TOTAL % OF TOTAL UNIT COSTQUANTITY % CUMMULATIVE ANNUAL USAGE VALUE 9 8 2 1 4 3 6 5 10 7 $30,600 1 16,000 2 14,000 3 5,400 4 4,800 5 3,900 3,600 6 CLASS 3,000 7 2,400 A 8 1,700 B 9 C $85,400 10 35.9 6.0 $ 60 18.7 5.0 350 16.4 4.0 30 6.3 9.0 80 5.6 6.0 30 4.6 10.0 4.2 % OF TOTAL 18.0 20 VALUE ITEMS 3.5 13.0 10 12.0 9, 8,2.8 2 71.0 320 17.0 1, 4,2.0 3 16.5 510 6, 5, 10, 7 12.5 20 6.0 90 11.0 40 A 15.0 130 24.0 60 30.0 B 100 40.0 % 58.0 180 OF TOTAL QUANTITY 71.0 170 C 83.0 15.0 50 100.0 25.0 60 60.0 120 Example 10.1 Inventory Costs Carrying cost Carrying cost of holding an item in inventory cost Ordering cost Ordering cost of replenishing inventory cost Shortage cost Shortage temporary or permanent loss of sales temporary when demand cannot be met Economic Order Quantity (EOQ) Models EOQ optimal order quantity that will minimize total inventory costs Basic EOQ model Production quantity model Assumptions of Basic EOQ Model Demand is known with certainty and Demand is constant over time No shortages are allowed No Lead time for the receipt of orders is Lead constant Order quantity is received all at once Order Inventory Order Cycle Order quantity, Q Inventory Level Demand Demand rate Average inventory Q 2 Reorder point, R 0 Lead time Order Order placed receipt Lead time Order Order placed receipt Time EOQ Cost Model Co - cost of placing order Cc - annual per-unit carrying cost perAnnual ordering cost = Annual carrying cost = Total cost = D - annual demand Q - order quantity C oD Q C cQ 2 C cQ C oD + Q 2 EOQ Cost Model EOQ Deriving Qopt TC = CoD C cQ + Q 2 Proving equality of costs at optimal point CoD C cQ = Q 2 Q2 = 2CoD Cc 2CoD Cc CoD Cc ∂TC =– 2 + Q 2 ∂Q C0D Cc 0=– 2 + Q 2 Qopt = 2CoD Cc Qopt = EOQ Cost Model (cont.) Annual cost ($) Slope = 0 Minimum total cost Carrying Cost = CcQ 2 Total Cost Ordering Cost = CoD Q Optimal order Qopt Order Quantity, Q EOQ Example EOQ Cc = $0.75 per gallon Qopt = Qopt = 2CoD Cc 2(150)(10,000) (0.75) Co = $150 TCmin = TCmin = D = 10,000 gallons CcQ CoD + Q 2 (150)(10,000) (0.75)(2,000) + 2,000 2 Qopt = 2,000 gallons Orders per year = = = D/Qopt 10,000/2,000 5 orders/year TCmin = $750 + $750 = $1,500 Order cycle time = = = 311 days/(D/Qopt) 311/5 62.2 store days Production Quantity Model An inventory system in which an order is received gradually, as inventory is simultaneously being depleted AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed p - daily rate at which an order is received over time, a.k.a. production rate d - daily rate at which inventory is demanded Production Quantity Model Production (cont.) Inventory level Maximum inventory level Average inventory level Q(1-d/p) (1- Q (1-d/p) (12 0 Order receipt period Begin End order order receipt receipt Time Production Quantity Model (cont.) p = production rate Maximum inventory level = Q Q d p d p d = demand rate =Q1Average inventory level = C oD C c Q Q + 2 1- 2CoD Qopt = Cc 1 d p Q d 1p 2 d p TC = Production Quantity Model: Production Example Cc = $0.75 per gallon Co = $150 d = 10,000/311 = 32.2 gallons per day 2 C oD Qopt = Cc 1 - d p = 0.75 1 D = 10,000 gallons p = 150 gallons per day 2(150)(10,000) 32.2 150 = 2,256.8 gallons TC = C oD C c Q d Q + 2 1- p = $1,329 Production run = 2,256.8 Q = = 15.05 days per order p 150 Production Quantity Model: Example (cont.) Number of production runs = 10,000 D = = 4.43 runs/year 2,256.8 Q d p 32.2 150 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 gallons Quantity Discounts Quantity Price per unit decreases as order quantity increases TC = where P = per unit price of the item D = annual demand CoD CcQ + + PD PD Q 2 Quantity Discount Model (cont.) ORDER SIZE 0 - 99 100 – 199 200+ PRICE $10 8 (d1) 6 (d2) TC = ($10 ) ($10 TC (d1 = $8 ) $8 TC TC (d2 = $6 ) $6 Inventory Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt 100 Q(d2 ) = 200 200 Quantity Discount: Example Quantity QUANTITY 1 - 49 50 - 89 90+ Qopt = For Q = 72.5 TC = For Q = 90 TC = PRICE $1,400 1,100 900 2 C oD = Cc Co = $2,500 Cc = $190 per TV D = 200 TVs per year 2(2500)(200) = 72.5 TVs 190 CcQopt C oD + + PD = $233,784 PD $233,784 2 Qopt C cQ C oD + + PD = $194,105 PD $194,105 2 Q Reorder Point Level of inventory at which a new order is placed R = dL dL where d = demand rate per period L = lead time Reorder Point: Example Reorder Demand = 10,000 gallons/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 gallons Safety Stocks Safety stock Safety buffer added to on hand inventory during lead buffer time Stockout Stockout an inventory shortage an Service level Service probability that the inventory available during probability lead time will meet demand Variable Demand with Variable a Reorder Point Q Inventory level Reorder point, R 0 LT Time LT Reorder Point with a Safety Stock Inventory level Q Reorder point, R Safety Stock 0 LT Time LT Reorder Point with variable demand Reorder Finding the reorder point requires an understanding of Finding the demand-during-lead-time distribution demand- during- lead- P Day 1 Day + sd=10 d =100 sd=10 d =100 Day 2 Day + sd=10 d =100 Day 3 Day = S’=17.3 DDLT DDL z ROP ROP X = 300 300 Daily demand is normally distributed with Daily a mean of d = 100 and a standard deviation of sd = 10 10 Lead time is 3 days Lead X = d × LT = 100(3) = 300 s' = sd LT = 10 3 = 17.3 Reorder Point With Variable Demand R = dL + zσd L dL where d = average daily demand L = lead time σd = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zσd L = safety stock Reorder Point for Reorder a Service Level Probability of meeting demand during lead time = service level Probability of a stockout Safety stock zσd L dL Demand R Reorder Point for Variable Demand The paint store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 gallons per day L = 10 days σd = 5 gallons per day For a 95% service level, z = 1.65 R = dL + z σd L dL = 30(10) + (1.65)(5)( 10) = 326.1 gallons Safety stock = z σd L = (1.65)(5)( 10) = 26.1 gallons Periodic Inventory System Periodic Order Quantity for a Periodic Inventory System Q = d(tb + L) + zσd where d tb L σd zσd = average demand rate = the fixed time between orders = lead time = standard deviation of demand tb + L - I tb + L = safety stock I = inventory level Fixed-Period Model with Fixed Variable Demand d = 6 packages per day σd = 1.2 packages tb = 60 days L = 5 days I = 8 packages z = 1.65 (for a 95% service level) Q= d(tb + L) + zσd tb + L - I = (6)(60 + 5) + (1.65)(1.2) = 397.96 packages 60 + 5 - 8 Thank you ...
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This note was uploaded on 03/03/2011 for the course MARKETING 101 taught by Professor Singh during the Spring '11 term at Management Development Institute.

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