1 / 45

Operations Management Inventory Management Chapter 12 - Part I

Operations Management Inventory Management Chapter 12 - Part I. Outline. Functions of Inventory. ABC Analysis. Inventory Costs . Inventory Models for Independent Demand. Economic Order Quantity (EOQ) Model. Production Order Quantity (POQ) Model. Quantity Discount Model.

Download Presentation

Operations Management Inventory Management Chapter 12 - Part I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Operations ManagementInventory ManagementChapter 12 - Part I

  2. Outline • Functions of Inventory. • ABC Analysis. • Inventory Costs . • Inventory Models for Independent Demand. • Economic Order Quantity (EOQ) Model. • Production Order Quantity (POQ) Model. • Quantity Discount Model. • Probabilistic Models with Varying Demand. • Fixed Period Systems.

  3. Types of Inventory • Raw materials. • Work-in-progress. • Maintenance/repair/operating (MRO) supply. • Finished goods.

  4. The Functions of Inventory • To smooth production: • Decouple different parts of the production process. • Link varying supply and demand. • To provide goods for customers (quick response). • To take advantage of quantity discounts. • Buy more to get a reduced price. • To hedge against inflation and upward price changes (speculation). • Buy more now if you think price will rise.

  5. The Material Flow Cycle

  6. Disadvantages of Inventory • High cost - $$$$$ • Money tied up in inventory could be better used elsewhere in the organization. • Difficult to control. • Inventories occur in many places. • Hides production problems. • Large inventories may overcome poor quality production or poor quality materials.

  7. ABC Analysis • Divide inventory into 3 classes based on annual $ volume. • Annual $ volume = Annual demand x Unit cost. A class - Most important. Usually: 15-20% of products. 60-80% of value. B class -Less important. Usually: 20-40% of products. 15-30% of value. C class - Least important. Usually: 50-60% of products. 5-10% of value.

  8. ABC Analysis • Sort products from largest to smallest annual $ volume. • Divide into A, B and C classes. • Focus on A products. • Develop class A suppliers more. • Give tighter physical control of A items. • Forecast A items more carefully. • Consider B products only after A products.

  9. Classifying Items as ABC 25 products sorted by Annual $ Volume (Sales) Product Sales % 1 100 14 2 92 13 3 88 12 4 60 8 5 58 8 6 53 7 7 49 7 8 41 6 9 32 4 10 26 4 11 21 3 12 18 2 13 16 2 14-25 66 9 Total 720 100 80 Annual $ Usage (x1000) 60 40 20 0 20 10 15 1 25 5 Product

  10. Classifying Items as ABC Class % $ Vol % Items A 39% 12% (3/25) 100 B 52% 40% (10/25) 80 C 9% 48% (12/25) Annual $ Usage (x1000) 60 A 40 20 B C 0 80 40 60 0 100 20 % of Products

  11. Inventory Accuracy • Inventory accuracy importance: • To determine when and how much to order. • To achieve high level of service. • Information system tracks inventory, but… • Not all items sold are entered (scanned) properly. • Some items disappear without being sold (theft, defective, damaged, etc.)

  12. Inventory Counting • Count products periodically to verify inventory records. • Shut down facility and count everything at one time (once per year). • Cycle counting: count items continuously (count some each week). • Count A items most frequently (once a month). • Count B items less frequently (twice a year). • Count C items least frequently (once a year).

  13. Inventory for Services • Can be large $. • “Shrinkage” (theft) is a problem. • Often over 3%! • Good personnel selection, training, and discipline is key. • Establish tight control of shipments entering and leaving the facility. • Enforce procedures for documenting product movement. • Information systems can monitor inventory levels and help ensure accuracy.

  14. Inventory Costs • Holding costs - Associated with holding or “carrying” inventory over time. • Ordering costs - Associated with costs of placing order and receiving goods. • Setup costs - Cost to prepare a machine or process for manufacturing an order. • Stockout costs- Cost of not making a sale and lost future sales.

  15. Holding Costs • Investment costs (borrowing, interest). • Insurance. • Taxes. • Storage and handling. • Extra staffing. • Pilferage, damage, spoilage, scrap. • Obsolescence.

  16. Category Investment costs Housing costs Material handling costs Labor cost from extra handling Pilferage, scrap, and obsolescence Cost as a % of Inventory Value 6 - 24% 3 - 10% 1 - 3.5% 3 -5% 2 - 5% Inventory Holding Costs – Usually 20-30% of Total

  17. Ordering Costs To order and receive product: • Supplies. • Forms. • Order processing. • Clerical support. • etc.

  18. Setup Costs To change equipment and setup for new product: • Clean-up costs. • Re-tooling costs. • Adjustment costs. • etc.

  19. Stockout Costs For not making a sale and for lost future sales: - Customer may wait for a backorder, or - Cancel order (and acquire product elsewhere). • Backorder costs: expediting, special orders, rush shipments, etc. • Lost current sale cost. • Lost future sales (hard to estimate).

  20. Inventory Questions • How much to order (each time)? • 100 units, 50 units, 23.624 units, etc. • When to order? • Every 3 days, every week, every month, etc. • When only 5 items are left, when only 10 items are left, when only 20 items are left, etc. • Many different models can be used, depending on nature of products and demand.

  21. Independent vs. Dependent Demand • Independent demand - Demand for item is independent of demand for any other item. • Dependent demand - Demand for item depends upon the demand for some other item. • Example: Demand for car engines depends on demand for new cars. • We will consider only independent demand.

  22. Inventory Models How much and when to order? • Fixed order-quantity models. • 1. Economic order quantity (EOQ). • 2. Production order quantity (POQ). • 3. Quantity discount. • Probabilistic models. • Fixed order-period models.

  23. How Much and When to Order? • Given a fixed annual demand for a product. • With many small orders: • Amount on hand is always small, so inventory is small. • Frequent orders means cost of ordering is large. • With few large orders: • Amount on hand may be large (when order arrives), so inventory may be large. • Infrequent orders mean cost of ordering is small.

  24. EOQ – Economic Order Quanitity Models • How much to order (each time)? • Order size is a constant = Q • Q is selected to minimize total cost. • When to order? • Order when amount remaining = ROP • ROP is selected so chance of running out is small.

  25. EOQ Assumptions • Known and constant demand. • Known and constant lead time. • Instantaneous receipt of material. • No quantity discounts. • Only order cost and holding cost. • No stockouts.

  26. EOQ Model - How Much to Order? Annual Cost Holding Cost Curve Order Cost Curve Order Quantity

  27. EOQ Model - How Much to Order? Annual Cost Total Cost Curve Holding Cost Curve Order Cost Curve Order Quantity Optimal Order Quantity (EOQ=Q*)

  28. Why Holding Costs Increase • For fixed annual demand, larger order quantities means: • Larger inventory (larger amount ordered each time). • Larger inventory holding cost. • Example: Annual demand = 1200 units • Order 600 each time. • Maximum inventory = 600 • Order 50 each time. • Maximum inventory = 50

  29. Why Order Costs Decrease • For fixed annual demand, larger order quantities means: • Fewer orders per year. • Smaller order cost per year. • Example: Annual demand = 1200 units • Order 600 each time. • 1200/600 = 2 orders per year. • Order 50 each time. • 1200/50 = 24 orders per year.

  30. Deriving an EOQ • Develop an expression for total costs. • Total cost = order cost + holding cost • Find order quantity that gives minimum total cost (use calculus). • Minimum is when slope is flat. • Slope = Derivative. • Set derivative of total cost equal to 0 and solve for best order quantity.

  31. D = = Expected Number of Orders per year N Q D S Order Cost per year = Q (average inventory level)  H = Holding Cost per year EOQ Model Equations D = Annual demand (relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand rate (units per day, units per week, etc.) L = Lead time (constant) (in days, weeks, hours, etc.) Determine: Q = Order size (number of items per order) Given

  32. Inventory Level Order Quantity(Q) AverageInventory (Q/2) 0 Time EOQ Model - Average Inventory Level Maximum inventory = Q Minimum inventory = 0

  33. D = = Expected Number of Orders per year N Q D S Order Cost per year = Q (average inventory level)  H = = Holding Cost per year EOQ Model Equations D = Annual demand (relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand rate (units per day, units per week, etc.) L = Lead time (constant) (in days, weeks, hours, etc.) Determine: Q = Order size (number of items per order) Given Q H 2

  34. EOQ Model - How Much to Order? Annual Cost Total Cost Curve = (D/Q)S+(Q/2)H Holding Cost =(Q/2)H Order Cost Curve = (D/Q)S Order Quantity Optimal Order Quantity (EOQ=Q*)

  35. D 1 S + H = 0 Q2 2 D Q = Total Cost S + H Q 2 EOQ Total Cost Optimization Take derivative of total cost with respect to Q and set equal to zero: Solve for Q to get optimal order size: × × 2 D S EOQ = Q* = H

  36. D = = Expected Number of Orders N Q* Working Days / Year Expected Time Between Orders = = T N EOQ Model Equations D = Annual demand S = Order cost per order H = Holding (carrying) cost × × 2 D S Optimal Order Quantity = = Q* H

  37. EOQ Model - When to order? D = Annual demand (relatively constant) d = Demand per day L = Lead time in days Determine: ROP = reorder point (number of pieces or items remaining when order is to be placed) Given D Suppose demand is 10 per day and lead time is (always) 4 days. When should you order? When 40 are left! = d Working Days / Year = × ROP d L

  38. Lead Time = time between placing and receiving an order Reorder Point (ROP) 4th order 2nd order 3rd order 1st order received 1st order placed EOQ Model - When To Order Inventory Level Q* Time

  39. EOQ Example Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Suppose the firm currently orders every month. Order size = Q = 1200/12 = 100 1200 100 Total Cost = 50 + 5 = 600 + 250 = $850/year 100 2 Can they do better?

  40. EOQ Example Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year 2 ×1200 ×50 = = 154.92 units/order; so order 155 each time Q* 5 1200/year Expected Number of Orders = N = = 7.74/year 155 1200 155 Total Cost = 50 + 5 = 387.10 + 387.50 = $774.60/year 155 2 Cost to order once a month ($850) is 9.7% higher!!

  41. 1200 Q Total Cost = 50 + 5 Q 2 EOQ is Robust Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Q = 155 units/order TC = $774.60/year Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30 Suppose we must order in multiples of 20: Q = 140 units/order TC = $778.57/year (+0.5%) Q = 160 units/order TC = $775.00/year (+0.05%) Cost with Q=140 or Q=160 is nearly optimal!

  42. 1200 Q Total Cost = 50 + 5 Q 2 EOQ is Robust Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Q = 155 units/order TC = $774.60/year Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30 Suppose we wish to order 6 times per year (every 2 months): Q = 1200/6 = 200 units/order(200/order is 29% above Q*) TC = $800.00/year = 300.00 + 500.00 (Cost is only 3.3% above optimal: $800 vs. $774.60)

  43. EOQ Model is Robust Annual Cost Total Cost Curve Small variation in cost Order Quantity 154.92 Large variation in order size

  44. Robustness • EOQ amount can be adjusted to facilitate business practices. • If order size is reasonably near optimal (+ or - 20%), then cost will be very near optimal (within a few percent). • If parameters (order cost, holding cost, demand) are not known with certainty, then EOQ is still very useful.

  45. EOQ Model - When to order? Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Lead time = 5 days 1200/year = = 4.615/day d 260 days/year ROP = 4.615 units/day 5 days = 23.07 units -> Place an order whenever inventory falls to (or below) 23 units

More Related