Inventory Management

1. Inventory Management

2. 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 (with independent demand) • Example: product components, raw material

3. 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?

4. 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 (lead) 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

5. Adaptation o the fluctuation of demand with building up stocks DEMAND Inventory reduction Inventory accumulation CAPACITY

6. 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. • Work-in-progress: facilitating production process by providing semi-finished stocks between different processes • To provide immediate service for customers • To minimize production delays caused by lack of spare parts (for maintenance, breakdowns)

7. 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

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 • Stockout cost: economic consequences of running out of stock (lost profit and/or goodwill)

10. Inventory models

11. 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 • The item is a single product (no interaction with other products)

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

13. Total cost of inventory (trade-off between ordering frequency and inventory level) cost Total cost Holding cost (H ∙Q/2) Minimumcost Ordering cost (S ∙ D/Q) EOQ lot size

14. 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

15. 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

16. 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

17. Reordering (or replenishment) point • When to start the ordering process? • It depends on the… • Stock position: stock on-hand (+ stock on-order) • in a simple saw-tooth model it is Q, • in some cases, there can be an initial stock(Q0), that is different from Q. In this case the first order depends on Q0 • lead time (L): the time interval from setting up order to the start of using up the ordered stock • Average demand per day (d) • Rdays = Q/d – L

18. Q0 = 600 tons Q = 200 tons d = 10 tons per day L = 8 days R1= 600ts /10ts/ds – 8ds= 52. day Examples R2= 200ts /10ts/ds – 8ds= 12 days after the arrival of the first order = 52+8+12=72. day R1= 400ts /16ts/ds – 20ds= 5. day • Q0 = Q = 400 tons • d = 16 tons per day • L =20 days

19. D = 2,000 tons S = 100 euros per order H = 25 euros per order Q0 = 1,000 tons L = 12 days N = 250 days EOQ = √ (2 ∙ 2,000ts ∙ 100euro)/25euro/ts= 126,49ts d = 2,000ts/250ds = 8 ts/ds R1 = 1,000ts/8ts/ds – 12ds = 113. day R2 = 126,49ts /8ts/ds – 12ds = 3,81 = 3 days after the arrival of the first order = 113+12+3 = 128. Example on both EOQ and R Calculate the following: EOQ d R1 R2

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

21. 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

22. 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

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

24. When to order, when there is a buffer stock? ROP = d * L + b ROPdays = (Q – b)/d – L or ROP1 = (Q0 – b)/d – L Where (Q – b)is the available stock. If Q0 = 100tons, Q = 60tons, L = 2 days, b = 10tons, D = 300tons, N = 100 days, then R1,R2=? ROP = 2 * 3 + 10 = 16 tons ROP1 = (100 – 10)/(300/100) – 2 = 28. day ROP2 = 60/3– 2 = 18 days after the arrival of the first order = 28 + 2 + 18 = 48. day

25. 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

26. 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

27. ABC analysis

28. Data Capture • Techniques and error rates (Rushton et al. 2006) • Written entry – 25,000 in 3,000,000 • Keyboard entry – 10,000 in 3,000,000 • Optical character recognition (OCR) – 100 in 3,000,000 • labels that are both machine- and human-readable • for example: license plates • Bar code (code 39) – 1 in 3,000,000 • fast, accurate and fairly robust • reliable and cheap technique • Transponders (radio frequency tags) – 1 in 30,000,000 • a tag (microchip + antenna) affixed to the goods or container • receiver antenna • reader • host station that relays the data to the server • can be passive or active

29. Some more examples Calculate ROP, ROP1 and EOQ, if… • L = 2 days, b = 12tons, D = 300tons, N = 100 days, S = 50 euro, H = 20 euro/tons, Q0 = 60tons • L = 12 days, b = 20tons, D = 1300tons, N = 80 days, S = 10 euro, H = 25 euro/tons, Q0 = 300tons • D = 1000 units, N = 500 days, S = 110 euro, H = 100 euro/units, L = 20 days, b = 50tons, Q0 =100tons