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Inventory Management

Inventory Management. Inventory management. A subsystem of logistics Inventory: a stock of materials or other goods t o facilitate production or to satisfy customer demand Main decisions: Which items should be carried in stock? How much should be ordered? When should an order be placed?.

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Inventory Management

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  1. Inventory Management

  2. Inventory management • A subsystem of logistics • Inventory: a stock of materials or other goods to facilitate production or to satisfy customer demand • Main decisions: • Which items should be carried in stock? • How much should be ordered? • When should an order be placed?

  3. The need to hold stocks 1 • Buffer between Supply and Demand • To keep down production costs: to achieve low unit costs, production have to run as long as possible (setting up machines is tend to be costly) • To take account of variable supply times: safety stock to cover delivery delays from suppliers • To minimize buying costs associated with raising an order • To accommodate variations (on the short run) in demand (to avoid stock-outs) • To account for seasonal fluctuations: • There are products popular only in peak times • There are goods produced only at a certain time of the year

  4. Adaptation fo the fluctuation of demand with building up stocks DEMAND Inventory reduction Inventory accumulation CAPACITY

  5. The need to hold stocks 2 • To take advantage of quantity discounts (buying in bulk) • To allow for price fluctuations/speculation: to buy large quantities when a good is cheaper • To help production and distribution operations run smoothly: to increase the independence of these activities • To provide immediate service for customers • To minimize production delays caused by lack of spare parts (for maintenance, breakdowns) • Work-in-progress: facilitating production process by providing semi-finished stocks between different processes

  6. Types of Stock-holding/Inventory • raw material, component and packaging stock • in-process stocks (work-in-progress; WIP) • finished products (finished goods inventory; FGI) • pipeline stocks: held in the distribution chain • general stores: contains a mixture of products to support • spare parts: • Consumables (nuts, bolts, etc.) • Rotables and repairables

  7. Independent vs. dependent demand • Independent demand: • Influenced only by market conditions • Independent from operations • Example: finished goods • Dependent demand: • Related to the demand for another item • Example: product components, raw material

  8. Another typology of stocks • working stock: reflects the actual demand • cycle stock: follows the production (or demand) cycles • safety stock: to cover unexpected fluctuations in demand • speculative stock: built up on expectations • seasonal stock: goods stockpiled before peaks

  9. Inventory cost • Item cost: the cost of buying or producing inventory items • Ordering cost: does not depend on the number of items ordered. Form typing the order to transportation and receiving costs. • Holding (carrying) cost: • Capital cost: the opportunity cost of tying up capital • Storage cost: space, insurance, tax • Cost of obsolescence, deterioration and loss • Sometimes designated by management rather than computed • Stockout cost: economic consequences of running out of stock (lost profit and/or goodwill)

  10. Economic Order Quantity (EOQ) • Assumptions of the model: • Demand rate is constant, recurring and known • The lead time (from order placement and order delivery) is constant and known • No stockouts are allowed • Goods are ordered and produced in lots, and the lot is placed into inventory all at one time • Unit item cost is constant, carrying cost is linear function of average inventory level • Ordering cost is independent of the number of items in a lot • Marginal holding cost is constant • The item is a single product (no interaction with other products)

  11. The „SAW-TOOTH” Inventory level Order inteval Orderquantity(Q) Average inventory level = Q/2 Time

  12. Total cost of inventory (tradeoff between ordering frequency and inventory level) Total cost Holding cost (H ∙Q/2) Minimumcost Ordering cost (S ∙ D/Q) EOQ

  13. Calculating the total cost of inventory • Let… • S be the ordering cost (setup cost) per oder • D be demanded items per planning period • H be the stock holding cost per unit • H=i∙C, where C is the unit cost of an item,and i is the carrying rate • Q be the ordered quantity per order (= lot) • TC = S ∙ (D/Q) + H ∙ (Q/2) • (D/Q) is the number of orders per period • (Q/2) is the average inventory level in this model

  14. The minimum cost (EOQ) • TC = S ∙ (D/Q) + H ∙ (Q/2) • бTC/бQ = 0 • 0 = - S ∙ (D/Q 2) + H/2 • H/2 = S ∙ (D/Q 2) • Q 2 = (2 ∙ S ∙ D)/H • EOQ = √ (2 ∙ S ∙ D)/H

  15. D = 1000 units per year S = 100 euro per order H = 20 euro per unit Find the economic order quantity! (we assume a saw-tooth model) Example EOQ = √ (2 ∙ 1,000units ∙ 100euro)/20euro/unit EOQ = √ 10,000units2 = 100units

  16. The EOQ zone

  17. Reordering (or replenishment) point • Whento start theorderingprocess? • Itdependsonthe… • Stock position: stockon-hand (+ stockon-order) • in a simplesaw-toothmodelit is Q, • insomecases, therecan be an initialstock(Q0), that is differentfrom Q. InthiscasethefirstorderdependsonQ0 • lead time (LT): thetimeintervalfromsettingupordertothe start of usinguptheorderedstock • Averagedemand per day (d) • ROP = d (LT ) + safetystock

  18. Q0 = 600 tons Q = 200 tons d = 10 tons per day LT = 8 days What is the ROP and whenwereachthatlevel? What is thetime of thenextreorder? ROP = 80 tons (600 – 80)/10= 52. day Examples 52 + 8 + (200 – 80)/10 = 72. day ROP = 16 ∙ 20 = 320 tons Firstreorder: (400– 320)/16 = 5. day • Q0 = Q = 400 tons • d = 16 tons per day • LT = 20 days • ROP = ? • Firstreardertime?

  19. D = 2,000 tons S = 100 euros per order H = 25 euros per order Initialstock = 1,000 tons LT = 12 days N = 250 days EOQ = √ (2 ∙ 2,000ts ∙ 100euro)/25euro/ts= 126.49ts d = 2,000ts/250ds = 8 ts/ds; ROP = 12 ∙ 8 = 96 tons Reroder1 = (1,000 – 96)/8 = 113 Reorder2 = 113 + 12 + (126.49 – 96)/8 = 128.81 = 128 Examples Calculatethefollowing: EOQ d ROP first and secondreordertime

  20. The SAW-TOOTHwith safety stock Inventory level Continuous demand Orderquantity b Safety stock or buffer stock Time

  21. Buffer stock depends • Demand rate and lead time • Variability of demand and lead time • Desired service level

  22. Service level • The probability that demand will not exceed supply during lead time. • Service level = 100 percent - stockout risk

  23. Buffer (safety) stock b = z ∙ σ where z = safety factor from the (normal) distribution σ = sandard deviation of demand over lead time Let z be 1,65 (95%), and the standard deviation of demand is 200 units/lead time. b = 1,65 ∙ 200units = 330units

  24. Example • Lead time = 10 days • Average demand over lead time: 300 tons • Standard deviation over lead time: 20 tons • Accepted risk level: 5% • Safety stock = ? Reorder quantity = ? • b = z * σ = 1,65 * 20 = 33 tons • ROP = 300 + 33 = 333 tons

  25. Q0 = 600 tons Q = 200 tons d = 10 tons per day LT = 8 days b = 33 tons ROP = 8 * 10 + 33 = 113 Examples ROP = 386 • Q0 = Q = 400 tons • d = 16 tons per day • LT=20 days • b = 66 tons

  26. Economic production quantity (EPQ) • Production of spare parts /materials done in batches (lots) • Only on item • Annual demand is known • Usage rate (u) is constant • Usage occurs continually but production occurs periodically • Production rate is constant (p) • Lead time (LT) does not vary • No quantity (Q) discounts • Setup cost instead of ordering cost

  27. EPQ with incremental inventory replenishment

  28. Total cost in EPQ • TCEPQ = carryingcost + setupcost = = (Imax/2)H + (D/Q)S • The economicrunquantity:QEPQ = (2DS/H)0,5 ∙ [p/(p – u)]0,5 • Cycletime = QEPQ / u • Runtime = QEPQ / p • Imax= (QEPQ / p)(p – u) • Iaverage= Imax/ 2

  29. EOQ example

  30. Quantitydiscounts • The buyerstotalcostcurvetominimze: Price reductionsforlargeorders Example:

  31. Advantages • Forthebuyer • Fewerorderset-ups (D*S/Q) • Cheaperprice (P*D) • Fortheseller: • Decreased holding costs (I*H/2) • Decreasedadministrativecosts (FC) • Loweropportunitycost

  32. A TC görbe, ha szerepeltetjük a beszerzési költséget is

  33. Allowances and TC curves

  34. Constantcarryingcosts

  35. Carryingcostsarestatedas a percentage of unit price Cost Quantity

  36. Finding EOQ withconstant holding cost • D = 816 pieces/year • S = 12 dollars/order • H = 4 dollars/piece/year • Prices: • 20 dollars 1-49 pieces, • 18 dollars 50-79 pieces, • 17 dollars 80-99 pieces, • 16 dollars over 100 pieces

  37. Calculating EOQ

  38. Solution • QEOQ = (2*816*12/4)0,5 = 69.97 = 70 pieces • TC70 = (70/2)*4 + (816/70)*12 + 18*816 == 14.968 dollars • TC80 = 14.154 • TC100 = 13.354

  39. Withnon-constant holding costs • D = 4.000 pieces, S = 30 dollars, H = 0.4*P • Prices: • 1-499 pieces 0.9 dollar; • 500-999 0.85 dollar; • over 1.000 pieces 0.8 dollar.

  40. Solution • QEOQ(0,8)=866 pieces→ notfeasible • QEOQ(0,85)=840 pieces→ feasible • TC840=30*(4000/840)+0,4*0,85*(840/2)+4000*0,85==3685,66 dollars→ is itprofitabletoorder a greaterlot? • TC1000=30*(4000/1000)+0,4*0,8*(1000/2)+4000*0,8==3480 dollars→ yes, it is profitable.

  41. L L L T T T Alternative models 1 Periodic review system: • Stock level is examined at regular intervals • Size of the order depends on the quantity on stock. it should bring the inventory to a predetermined level Stock on hand Q Q Q time

  42. Stock on hand Q Q R L L L Alternative models 2 Fixed-order-quantity system: • A predetermined stock level (reorder point) is given, at which the replenishement order will be placed • The order quantity is constant

  43. Elements of demand patterns (forecasting) • Actual demand: • Trend line • Seasonal fluctuacion • Weekly fluctuation • (Daily fluctuation) • Random fluctuation

  44. Inventory decisions and Multiple Distribution Centres / warehouses The ‘square root law’: • A rule of thumb • The total safety-stock holding in a distribution system is proportional to the square root of the number of depot locations • Example: If we reduce the number of DCs from 10 to 5, the savings in safety stock is: 1 – (√5 / √10) = 29% Pareto’s law or the ’80/20 rule’: • A rule of thumb • Approximately 20% of storage items account for 80% of the inventory value measured in money. • ABC analysis (or Pareto analysis): • ‘A’ lines: fast movers (20%) – 80% of money usage • ‘B’ lines: medium movers (30%) – 15% of money usage • ‘C’ lines: slow movers (C+D 50%) – 5% of money usage • ‘D’ lines: obsolete / dead stock

  45. Example • Initialnumber of warehouses: 6 • Initial sum of safetystocks: 6,000 • New number of warehouses: 2 • What is thenew sum of safetystocks? • 6000*(2/6)0.5=3464.10

  46. ABC analysis

  47. ABC analysis

  48. ABC analysis exercise

  49. ABC analysis exercise

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