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Effective Inventory Management: Strategies for Optimizing Supply Chain Operations

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Inventory management is crucial for meeting customer demand, controlling costs, and minimizing risks. Understanding the purposes of inventory, including managing supply and demand variability, is essential for efficient operations. Key questions like how much to buy and when to buy guide decision-making. Companies must consider various inventory types, associated costs, and strategies like Economic Order Quantity (EOQ) to optimize processes. This guide explores foundational concepts in inventory management, from demand forecasting to cost analysis, ensuring you are equipped to improve your inventory operations.

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Effective Inventory Management: Strategies for Optimizing Supply Chain Operations

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  1. Inventory Management Operations Management Dr. Ron Tibben-Lembke

  2. Purposes of Inventory • Meet anticipated demand • Demand variability • Supply variability • Decouple production & distribution • permits constant production quantities • Take advantage of quantity discounts • Hedge against price increases • Protect against shortages

  3. 2006 13.81 1857 24.0% 446 801 58 1305 9.9 2007

  4. Source: CSCMP, Bureau of Economic Analysis

  5. Two Questions Two main Inventory Questions: • How much to buy? • When is it time to buy? Also: Which products to buy? From whom?

  6. Types of Inventory • Raw Materials • Subcomponents • Work in progress (WIP) • Finished products • Defectives • Returns

  7. Inventory Costs What costs do we experience because we carry inventory?

  8. Inventory Costs Costs associated with inventory: • Cost of the products • Cost of ordering • Cost of hanging onto it • Cost of having too much / disposal • Cost of not having enough (shortage)

  9. Shrinkage Costs • How much is stolen? • 2% for discount, dept. stores, hardware, convenience, sporting goods • 3% for toys & hobbies • 1.5% for all else • Where does the missing stuff go? • Employees: 44.5% • Shoplifters: 32.7% • Administrative / paperwork error: 17.5% • Vendor fraud: 5.1%

  10. 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%

  11. Inventory Models • Fixed order quantity models • How much always same, when changes • Economic order quantity • Production order quantity • Quantity discount • Fixed order period models • How much changes, when always same

  12. Economic Order Quantity Assumptions • Demand rate is known and constant • No order lead time • Shortages are not allowed • Costs: • S - setup cost per order • H - holding cost per unit time

  13. EOQ Inventory Level Q* Optimal Order Quantity Decrease Due to Constant Demand Time

  14. EOQ Inventory Level Instantaneous Receipt of Optimal Order Quantity Q* Optimal Order Quantity Time

  15. EOQ Inventory Level Q* Reorder Point (ROP) Time Lead Time

  16. EOQ Inventory Level Q* Average Inventory Q/2 Reorder Point (ROP) Time Lead Time

  17. Total Costs • Average Inventory = Q/2 • Annual Holding costs = H * Q/2 • # Orders per year = D / Q • Annual Ordering Costs = S * D/Q • Cost of Goods = D * C • Annual Total Costs = Holding + Ordering + CoG

  18. How Much to Order? Annual Cost Holding Cost = H * Q/2 Order Quantity

  19. How Much to Order? Annual Cost Ordering Cost = S * D/Q Holding Cost = H * Q/2 Order Quantity

  20. How Much to Order? Total Cost = Holding + Ordering Annual Cost Order Quantity

  21. How Much to Order? Total Cost = Holding + Ordering Annual Cost Optimal Q Order Quantity

  22. Optimal Quantity Total Costs = Take derivative with respect to Q = Set equal to zero Solve for Q:

  23. d d 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.)

  24. 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 shallow • Even if conditions don’t hold perfectly, profits are close to optimal • Estimated parameters will not throw you off very far

  25. Quantity Discounts • How does this all change if price changes depending on order size? • Holding cost as function of cost: • H = I * C • Explicitly consider price:

  26. Discount Example D = 10,000 S = $20 I = 20% Price Quantity EOQ c = 5.00 Q < 500 633 4.50 501-999 666 3.90 Q >= 1000 716

  27. Discount Pricing Total Cost Price 1 Price 2 Price 3 X 633 X 666 X 716 Order Size 500 1,000

  28. Discount Pricing Total Cost Price 1 Price 2 Price 3 X 633 X 666 X 716 Order Size 500 1,000

  29. Discount Example Order 666 at a time: Hold 666/2 * 4.50 * 0.2= $299.70 Order 10,000/666 * 20 = $300.00 Mat’l 10,000*4.50 = $45,000.00 45,599.70 Order 1,000 at a time: Hold 1,000/2 * 3.90 * 0.2= $390.00 Order 10,000/1,000 * 20 = $200.00 Mat’l 10,000*3.90 = $39,000.00 39,590.00

  30. 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 quantity • Repeat until EOQ is feasible or too big. • Select quantity/price with lowest total cost.

  31. Inventory Management-- Random Demand

  32. Random Demand • Don’t know how many we will sell • Sales will differ by period • Average always remains the same • Standard deviation remains constant

  33. Impact of Random Demand How would our policies change? • How would our order quantity change? • How would our reorder point change?

  34. Mac’s Decision • How many papers to buy? • Average = 90, st dev = 10 • Cost = 0.20, Sales Price = 0.50 • Salvage = 0.00 • Cost of overestimating Demand, CO • CO= 0.20 - 0.00 = 0.20 • Cost of Underestimating Demand, CU • CU = 0.50 - 0.20 = 0.30

  35. Optimal Policy G(x) = Probability demand <= x Optimal quantity: Mac: G(x) = 0.3 / (0.2 + 0.3) = 0.6 From standard normal table, z = 0.253 =Normsinv(0.6) = 0.253 Q* = avg + zs = 90+ 2.53*10 = 90 +2.53 = 93

  36. Optimal Policy • If units are discrete, when in doubt, round up • If u units are on hand, order Q - u units • Model is called “newsboy problem,” newspaper purchasing decision • By time realize sales are good, no time to order more • By time realize sales are bad, too late, you’re stuck • Similar 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.

  37. 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?

  38. Safety stock & Safety stock = zsL Therefore, z = sL Probabilistic Models Safety stock = x m From statistics, From normal table z.95 = 1.65 Safety stock = zsL= 1.65*10 = 16.5 R = m + Safety Stock =350+16.5 = 366.5 ≈ 367

  39. Random Example • What should our reorder point be? • demand over the lead time is 50 units, • with standard deviation of 20 • want to satisfy all demand 90% of the time • (i.e., 90% chance we do not run out) • To satisfy 90% of the demand, z = 1.28 • Safety stock = zσL= 1.28 * 20 = 25.6 • R = 50 + 25.6 = 75.6

  40. St Dev Over Lead Time • What 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?

  41. St Dev Over LT • If 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

  42. St Dev Over Lead Time • Standard deviation of demand = • R = 40 + 3 * 10 = 70

  43. Service Level Criteria • Type I: specify probability that you do not run out during the lead time • Probability that 100% of customers go home happy • Type II: proportion of demands met from stock • Percentage that go home happy, on average • Fill Rate: easier to observe, is commonly used • G(z)= expected value of shortage, given z. Not frequently listed in tables

  44. Two Types of Service CycleDemand Stock-Outs 1 180 0 2 75 0 3 235 45 4 140 0 5 180 0 6 200 10 7 150 0 8 90 0 9 160 0 10 40 0 Sum 1,450 55 Type I: 8 of 10 periods 80% service Type II: 1,395 / 1,450 = 96%

  45. Fixed-Time period models

  46. Fixed-Time Period Model • Every T periods, we look at inventory on hand and place an order • Lead time still is L. • Order quantity will be different, depending on demand

  47. Fixed-Time Period Model: When to Order? Inventory Level Target maximum Time Period

  48. Fixed-Time Period Model: : When to Order? Inventory Level Target maximum Time Period Period

  49. Fixed-Time Period Model:When to Order? Inventory Level Target maximum Time Period Period

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